toward a creative problem-solving methodology with knowledge provision

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TOWARD A CREATIVE PROBLEM-SOLVINGMETHODOLOGY WITH KNOWLEDGEPROVISIONZhiqiang Zhu a , Sev Nagalingam a & Hung-Yao Hsu aa School of Advanced Manufacturing and Mechanical Engineering ,University of South Australia , Mawson Lakes, South Australia,AustraliaPublished online: 17 Oct 2011.

To cite this article: Zhiqiang Zhu , Sev Nagalingam & Hung-Yao Hsu (2011) TOWARD A CREATIVEPROBLEM-SOLVING METHODOLOGY WITH KNOWLEDGE PROVISION, Applied Artificial Intelligence: AnInternational Journal, 25:9, 836-881, DOI: 10.1080/08839514.2011.613570

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TOWARD A CREATIVE PROBLEM-SOLVING METHODOLOGYWITH KNOWLEDGE PROVISION

Zhiqiang Zhu, Sev Nagalingam, and Hung-Yao HsuSchool of Advanced Manufacturing and Mechanical Engineering, University of SouthAustralia, Mawson Lakes, South Australia, Australia

& In this article, a knowledgeable creative problem-solving methodology (KCPS) is proposed. Inaddition to being applied as a creative problem-solving methodology, this KCPS method also aimsto provide human users the knowledge that is important and necessary for the generation of creativesolutions. The development of KCPS is based on the research achievement in the area of humancreativity, which suggests that knowledge plays a crucial role in the evolvement of creativity inhuman mind. Consequently, knowledge provision is one of the key components of the KCPS method.Additionally, according to the models of human creativity, information processing andMeta-behaviors are identified as the other two components of the KCPS. Information processingfacilitates human users in analyzing, processing information, and obtaining knowledge in orderto approach problems creatively. Meta-behaviors indicate the mental activities of human users whenthey apply the KCPS method. Subsequently, appropriate techniques that can realize the functions ofknowledge provision and information processing are selected and integrated for the development ofthe KCPS. The operation of the KCPS method is then discussed.

A case study is illustrated with twelve new design concepts for articles of balancing equipment,which were generated by applying the KCPS method. This case study demonstrates that the KCPSmethod has the capacity to assist human users for the generation of innovative concepts.

INTRODUCTION

Creativity has been highly valued in human society throughout history.The history of civilization is regarded as a history of humankind’s creativeefforts through the centuries (Yan 1998). It plays important roles and is aterm that appears in many disciplines, such as industry, business, tradeand commerce, education, science, arts, engineering, and even

The authors acknowledge the support provided by the company for sharing its product infor-mation.

Address correspondence to Zhiqiang Zhu, School of Advanced Manufacturing and MechanicalEngineering, University of South Australia, Mawson Lakes, South Australia, Australia 5095. E-mail:[email protected]; [email protected]

Applied Artificial Intelligence, 25:836–881, 2011Copyright # 2011 Taylor & Francis Group, LLCISSN: 0883-9514 print=1087-6545 onlineDOI: 10.1080/08839514.2011.613570

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international relations. The passion for pursuit of creativity has neverdiminished, and therefore, there is a need for some practical approachesthat can enhance people’s creativity with regard to their problem-solvingactivities. To meet this need, a large number of Creative Problem Solving(CPS) methodologies and models have been proposed and developedsince the 1960s (Thompson and Lordan 1999). These methods are ident-ified in literature (Yan 1998; Geschka 1986; Higgins 1994; Dhillon 2003;Jay 2000; Piirto 2004; Clegg and Birch 2002) and are applicable to a varietyof situations for solving problems and enhancing creativity (Hicks 1991;Van Gundy 1984; Vidal 2008; Strzalecki 2000). Some of the well-knownCPS methods include the Osborn-Parnes CPS process model (McPherson1977; Proctor 2005), Brainstorming (Rawlinson 1981; Clapham and Larisa2003), Synectics (Gordon 1961; Higgins 1994; Prince 1970), Mind mapping(Buzan 1983), TRIZ (Altshuller, Shulyak, and Rodman 1997; Altshuller1984), and others.

However, most of the existing CPS methods enhance creativity by pro-viding various guidelines and steps for people to follow. Essentially, theseapproaches are merely a series of rules, laws, and execution proceduresfor human users; but they are not sufficient on their own for the evolve-ment of creativity. Brainstorming, for example, is one of the well-knownCPS approaches. As illustrated in Figure 1, brainstorming consists of a setof procedures: defining the problem; restating the problem from varied

FIGURE 1 Flow chart of a brainstorming session, revised after Rawlinson (1981).

Creative Problem-Solving Methodology with Knowledge Provision 837

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perspectives; selecting a basic restatement as the lead-in question to thebrainstorming session; warming-up with a simple question before the startof the main brainstorming session; conducting the brainstorming, whichincludes recording ideas and encouraging people; selecting the wildestideas and turning them into useful ideas. From the procedural point ofview, everyone can use the brainstorming method to generate newideas. The outcomes will be different for seasoned engineers and fornovices, however, in a comparison brainstorming session for generatingnew engineering design concepts.

What makes the difference between an outstandingly creative personand a less creative one is not any special power, but greater knowledge inthe form of practiced expertise (Gruber 1974). In the study of a brainstorm-ing task, Rietzschel et al. (2007) suggested that creative-idea generation isenhanced by deep exploration of relevant domain knowledge. Results indi-cated that primed participants generated higher productivity and orig-inality of ideas within the primed categories than participants who hadbeen unprepared or who had been prepared with an irrelevant topic.Another experiment, conducted by Bonnardel (2000), showed that pro-fessional designers appear to adopt a more general approach than novices.This general approach makes seasoned designers take into account differ-ent viewpoints, which allow them to discover alternatives, and therefore,to enhance the quality of the designed artifacts (Bonnardel 2000).

Although in some circumstances creativity might be inhibited to anextent by habitual thinking styles related to experiences, knowledge playsa crucial role in producing creative ideas. Knowledge in the form of experi-ence provides the foundation from which the creative solutions are derived(Weisberg 2006). The creative cognition approach views creativity as thegeneration of novel and appropriate products through the application ofbasic cognitive processes to existing knowledge structures (Ward 2007).Creative ideas are firmly planted on the previous knowledge that the cre-ative person has. Knowledge is applied in interpreting the problem, under-standing the situation in which the problem lies, and supplyingantecedents as the basis for the creation of new ideas. Various knowledgeis involved in creative work, from shared domain knowledge to individual,extraneous knowledge that can generate insights (Vivacqua and de Souza2004). The ability to devise new ideas is greatly enhanced by having a wide,rich knowledge base (Clegg and Birch 2002).

Even though knowledge is crucial to the generation of creative solu-tions, it has not been considered by most of the existing CPS methodolo-gies. As a consequence, to produce the highest quality solutions, theeffectiveness and efficiency of these approaches largely depend on theskills, experience, and background knowledge possessed by humanusers (Srinivasan and Kraslawski 2006). The solid knowledge of physics,

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chemistry, biology, and mathematics, as well as specific domain knowledgeassociated with seasoned engineers, is not included in contemporary,prevalent CPS techniques.

The exclusion of knowledge from the CPS methodology can become anissue that undermines its performance in improving human creativity andthus requires attention. To address this issue, in this article, research resultsrelated to human creativity is first discussed in the next section, ‘‘Inspira-tions from Human Creativity,’’ in an attempt to understand the compo-nents that possibly contribute to the generation of creativity. On the basisof the inspirations received from that topic, a Knowledgeable CreativeProblem-Solving (KCPS) methodology is developed in the section that fol-lows. The KCPS method emphasizes the knowledge provided to humanusers during a problem-solving session. The section titled ‘‘Operation ofthe KCPS Method’’ discusses stages of the operation of KCPS and is fol-lowed by a section that describes a case study. There follows a sectiondevoted to ‘‘Discussion,’’ and then the points presented in this article aresummarized in ‘‘Concluding Remarks.’’

INSPIRATIONS FROM HUMAN CREATIVITY

Creativity, which is closely associated with the functions, mechanisms,and operation of the human mind, has been studied extensively over theyears (Boden 2004; Bohm 2003; Runco 2007; Sternberg 1999; Weisberg2006). Because human beings are considered to be creative, the factors thatcontribute to people’s creativity are examined, attempting to provideinspirations for the development of the KCPS method. For this purpose,two types of human creativity models are discussed in this section. Theyare (1) three components of individual creativity (TCIC), and (2) thehuman creative behavior model (HCBM).

Three Components of Individual Creativity (TCIC)

Although the occurrence of creative ideas is difficult to predict, threekey components closely associated to human creativity have been identifiedby Teresa Amabile (Amabile 1998; Harvard Business School 2003). Thesethree components include (1) expertise, (2) creative-thinking skills, and(3) motivation, as shown in Figure 2.

Expertise is technical, procedural, and intellectual knowledge (HarvardBusiness School 2003), which plays an important role in creativity. As a mat-ter of reality, creative persons, such as artists, scientists, engineers, andothers have possession of vast knowledge, especially in their specific fields.Creative-thinking skills are defined as the ways in which people approach


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problems with achievement of creative solutions. Some of the thinkingskills for creativity have been identified, such as combination (Koestler1975; Boden 2004; Ishikawa and Terano 1996; Poincare 1982), generaliza-tion (Yan 1998; Gael 1997), analogy (Gael 1997; Mayer 1989; Itkonen2005; Vosniadou and Ortony 1989; Gomes et al. 2006), divergent thinking(Guilford 1950; Csikszentmihalyi 1996; Simonton 1999), and others. Motiv-ation can be the passion, interest, or incentives that influence people dedi-cated to the mission of exploring creative solutions when they addressproblems.

Human Creative Behavior Model (HCBM)

Having examined the creative behaviors associated with the creativeengineers, Rouse (1986) proposed the HCBM that suggests the elementsinvolved in human creative activities. As shown in Figure 3, HCBM indicatesthree elements, including (1) knowledge provision, (2) informationprocessing, and (3) meta-behaviors, which lead to the products of creativity.

Knowledge provision means that creative engineers have a greater varietyof exposure to information content across disciplines (Kasperson 1978;Rouse 1986). They also continually exchange ideas with their colleaguesabout the latest developments in their fields (Smith 1985; Rouse 1986).Information processing is the way in which this information has been pro-cessed. Creative engineers mix algorithmic reasoning and heuristic search-ing, combine conceptual thinking and graphic coding, and see usefulconnections and distinctions (Rouse 1986). Mental Activities, Mental States,

FIGURE 2 The three components for creativity, revised after Harvard Business School (2003).

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and Ego Involvement in Figure 3 are classified as ‘‘meta’’ behaviors. Mentalactivity has been found to correlate with assessments of the diversity anddegree of the originality of solutions (Popescu, Facaoaru, and Tudor1977). People have reported that their mental states are different whenthey are being creative (Hlavsa and Kobylka 1974). Creative designers havereported a high level of ego involvement and effort in their work(Popescu-Neveanu 1977).

Inspirations from TCIC and HCBM

The TCIC and the HCBM describe human creativity, respectively; how-ever, the components that are identified by them, to a large extent, showconsistency in the following three aspects:

1. Knowledge provision vs. Knowledge – knowledge provision means thecreative person is exposed to information across various domains. Oncethis information has been analyzed and processed by the person, itbecomes his knowledge.

2. Information Processing vs. Creative-Thinking Skills – information pro-cessing means the way the creative person processes the information,whereby creative-thinking skills are certainly adopted to approachproblems creatively.

FIGURE 3 Human creative behavior model, revised after Rouse (1986).


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3. Meta-behaviors vs. Motivation–according to the description in the sec-tion about Human Creative Behavior, meta-behaviors suggest thehuman factor to creativity, in which the ego involvement is similar tothe ‘‘motivation’’ component described in TCIC.

Consequently, for the development of KCPS, inspirations received from theTCIC and the HCBM are two-fold:

1. Knowledge provision and information processing with creative-thinkingskills are two components necessary for the generation of creativity.Therefore, for the development of the KCPS method, techniquesthat can realize these two components need to be identified andintegrated.

2. Meta-behaviors indicate the human factor to creativity. Since the KCPSmethod is designed to be applied by human users, their involvementfor the generation of creative solutions is necessary for consideration.

On the basis of these inspirations, a general structure of KCPS isachieved and illustrated in Figure 4.

TechKPi (i¼ 1, 2, . . . , m, (m is integer, m> 0)) denotes Techniques forKnowledge Provision; whereas TechIPj (j¼ 1, 2, . . . , n, (n is integer,n> 0)) denotes Techniques for Information Processing.

FIGURE 4 The general structure of KCPS.

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As shown in Figure 4, KCPS is composed of three main components:knowledge provision, information processing, and meta-behaviors. Accord-ingly, knowledge provision is performed by techniques TechKP1, Tech-KP2, . . . , and TechKPm. Similarly, information processing can be achievedthrough techniques, TechIP1, TechIP2, . . . , and TechIPn.

In KCPS, meta-behaviors emphasize the mental activities of humanusers for solving problems, functioning through the following perspectives:

. To understand and utilize the knowledge and information provided

. To ensure the techniques between the knowledge provision and infor-mation processing can function seamlessly

. To interpret the problem so that it can be smoothly analyzed by theappropriate information processing techniques

. To select the most suitable information processing techniques forexamining the problem

. To evaluate the creativeness of the solutions achieved

. To judge and determine the optimal solutions for problems

THE KCPS METHOD WITH SPECIFIC TECHNIQUES

On the basis of the general structure of KCPS, specific techniques areidentified in this section to realize the functions of knowledge provisionand information processing, which have been indicated in Figure 4.Additionally, the selected techniques should be compatibly integratedand should function cohesively.

Techniques for Knowledge Provision

Techniques that have the potential for knowledge provision are ident-ified; these include Database, Knowledge Base, and Case-Based Reasoning(CBR).

Techniques of database have been developed since the 1960s to supportthe storage and management of large amounts of data efficiently (Ullmanand Widom 2002). A database system can store large data collections andretrieve data with the query process. Knowledge base is a special type ofdatabase. In addition to providing all the services of a database, the knowl-edge base also represents knowledge at the conceptual level (Krishna1992). The aim of a knowledge base is to represent a relevant body ofknowledge about a specific application domain in order to supportknowledge-based programs. Additionally, knowledge base can answer adhoc queries about the state of the application domain (Wagner 1998).Detailed discussions on the database and knowledge base techniques can


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be found in literature (Krishna 1992; Ullman and Widom 2002; Maier andSpringer-Verlag 2007; Wagner 1998).

Originated in the 1970s (Schank and Abelson 1977), CBR remembersand reapplies old solutions to solve new problems in similar situations. Gen-erally, a CBR system has a case library to store previously contextualizedexperiences. According to the new problem, a similar previous caseis recalled and then adapted to suit the new situation. Finally, the newsolution is retained in the case library for future reference.

As a paradigm of remembering previous experiences in problem solv-ing, CBR has an excellent memory to store a large and varied amount ofinformation. With appropriate indexing and searching schemes, the CBRmethod can seek, retrieve, and supply necessary information across variousdisciplines. Further, CBR cases record concrete previous-problem-solvingexperiences in context; these records comprise the descriptions of prob-lems, the processes involved in solving the problems, and the solutions.The contextualized contents stored in CBR cases provide not just the infor-mation but also the scenarios and the ways of manipulating and acting onthat information. From this point of view, the contents of CBR cases areconsidered to be knowledge.

To provide knowledge to human users, CBR has its advantages in thefollowing four perspectives: (1) knowledge organization, (2) knowledgestorage, (3) knowledge retrieval, and (4) knowledge updates.

Knowledge OrganizationCBR was originally inspired by the observation that people tend to rely

on remembering previous instances in many problem-solving tasks. There-fore, information in the CBR memory is primarily organized and stored ascases that record specific, prior problem-solving episodes. As this infor-mation organization of CBR conforms to the thinking habits of humansin many situations by referring back to precedent experiences, it can benaturally adopted by people to facilitate their problem-solving practices.Then, the contextualized prior experiences provided by CBR cases can giverecommendations on the course of creating new solutions.

Knowledge StorageKnowledge and information are required for the generation of creative

work (Weisberg 2006; Rietzschel, Nijstad, and Stroebe 2007). This includesshared domain knowledge as well as the individual and extraneous knowl-edge that can generate insights. CBR, as a paradigm of remembering pre-vious cases in problem solving, has an excellent memory to store a largeamount and variety of information. The case library of CBR applicationstores large amounts of previous design knowledge and other information

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across different disciplines. Related cases can be searched and retrievedduring the problem-solving process. The retrieved cases provide the back-ground information, design knowledge, and other relevant informationrequired for the production of creative work.

Although human beings are good at utilizing the experiences of pre-vious problem-solving cases in new situations in order to seek solutions,they are not very good at remembering all the cases that could possiblybe matched to the new situation (Bosch et al. 1997). The efficiency ofhuman beings in using their memories can be affected at the moment ofproblem solving by many internal or external factors such as mood, physi-cal conditions, environments, and so forth. The use of CBR for storingexperiences in many cases can address this problem of forgetfulness.

Additionally, a human mind can store only the problem-solving scen-ario and the knowledge that it has experienced and learned. In comparisonwith the amount of knowledge available to the entire human society andhistory, an individual can store only a rather small fraction in his or hermemory. To overcome this relatively limited experience and knowledgefor a single person, the CBR method provides a knowledge pool ofcases, which incorporates many minds and much knowledge into a single,structured, and accessible knowledge base.

Knowledge RetrievalThe retrieval process in CBR is conducted actively. Rather than leave

the problem of how to formulate the right query to the human user forthe most part, the CBR method can determine appropriate retrieval cuesitself (Leake 1996). Sometimes so little is known that a so-called situationassessment is necessary, from which additional features of the situation needto be derived. Therefore, the CBR system is often designed to start from aninput description using features that are quite different from thoseincluded in its cases. For example, in predicting which team will win agame, the ratio of defender strength to attacker strength between teamsis predictive, rather than the defender strength or attacker strength of a sin-gle team. Consequently, similar previous cases need to be matched on thebasis of the ‘‘ratio’’ (a derived feature) instead of the strength values of anyindividual teams.

Further, CBR supports flexible querying and inexact matching. Insteadof doing exact matching between queries and stored information, the goalof CBR is to retrieve a ‘‘most similar’’ (the nearest neighbor) case or a set ofmost similar cases (Leake 1996). In general, two commonly adopted algo-rithms for similarity assessment in CBR are nearest-neighbor retrieval andinductive retrieval (Watson 1997). Whether a case should be retrieveddepends not only on the similarity of the particular case itself, but whether


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other, more similar cases exist in memory. The most similar cases retrievedby CBR may include conflicts with some of the attributes that were specifiedin the retrieval query.

Knowledge UpdatesKnowledge updates are achieved by the learning capacity of the CBR

method, in which a new solution has been inserted into the existing caselibrary. Through the learning process, successful design cases and othernewly acquired related information are continuously accumulated inthe CBR case library. This learning process not only increases the pros-pect for human users to generate creative solutions, but also makes theincreasingly growing CBR case library a valuable intellectual property.

Considering the advantages aforementioned, CBR is therefore selectedto perform the function of knowledge provision in KCPS.

Techniques for Information Processing

Because of their capacities to improve people’s creative thinking, tech-niques of the Extenics and Attribute Dependency Template (ADT) have beenselected to conduct the function of information processing in KCPS.

ExtenicsEstablished in the 1980s (Cai, Yang, and Lin 2003; RIEE 2006), Extenics

studies the transformation and extensibility of objects, rules, methods, andproblem domains for revealing matters from various perspectives and thenuses them for solving problems. Viewing a problem from various anglesextends the conceptual spaces, which subsequently can make people thinkdifferently and address problems creatively. For this purpose, three ele-ments are provided in Extenics: (1) matter-element, (2) matter-elementtransformations, and (3) divergent tree method. These will be introducedbriefly in this section. Detailed discussion on Extenics can be found in theliterature (Cai, Yang, and Lin 2003).

Matter-Element. Extenics regards the objective world as a world ofmatter-elements. Therefore, the real-world matter is represented as thematter-element mode as in Equation (1):

R ¼ ðN ; C ; V Þ; ð1Þ

where N, represents the name of the matter; C, the characteristics; V, thevalue of the characteristics C.

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When a matter has many characteristic elements, it can be described bym-dimensional matter-elements as in Equation (2):

R ¼

N ; C1 V1

C2 V2

C3 V3

� � � � � �Cm Vm

0BBBB@

1CCCCA ð2Þ

For instance, a book and a car can be represented by its matter-elementmode as shown in Equations (3) and (4):

R1 ¼ Book; Title; theCreativeMindð Þ ð3Þ

R2 ¼

Car ; Make; FordModel ; FestivaYear ; 2006Price; $29; 999

0BB@

1CCA ð4Þ

The matter-element R provides a knowledge presentation scheme thatshows the name, selected characteristics, and characteristic values of theobject being studied. With this matter-element representation scheme,other information processing skills such as matter-element transformation,combination, analogy, and generalization can operate by examining the rel-evant name, characteristics, and characteristic values shown in thematter-element of the object.

Matter-Element Transformation. A transformation of matter-element isdefined as the operation of turning one matter-element R0 into anothermatter-element Rn, and it is described in Equation (5):

R0 ¼ ðN0; C0; V0 ÞTR0 ¼ Rn ¼ ðNn; Cn; Vn Þ;

ð5Þ

where T denotes the transformation operation.Matter-element transformation changes any of the three key elements

ðN0; C0; V0 Þ or their combination. The transformation process realizesthe extendibility of matter-element and shows a possible way to create newmatters in solving problems. There are four basic matter-element transfor-mations: (1) Replacement, (2) Decomposition, (3) Increasing=Decreasing,and (4) Expansion=Contraction.

(1) Replacement – Replacement is a transformation process of changingthe name, and=or characteristics, and=or values in a matter-element


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as required in certain situations. For instance, replacement occurswhen a logistics company replaces the regular unleaded petrol(ULP) originally used in their fleet with the ethanol-gasoline-blend(EGB) for lower fuel cost. This replacement is shown in Equations(6) and (7):

R0 ¼ULP ; effect; providingPower

price; x � dollars

� �ð6Þ

TR0 ¼EGB; effect; providingPower

price; y � dollars

� �ð7Þ

(2) Decomposition – When one matter-element can be decomposed intotwo or more matter-elements, this transformation is expressed asDecomposition, as shown in Equation (8):

*R0 ¼ R1 � R2 � � � � � Rn

*TR0 ¼ fR1;R2; . . . ;Rng;ð8Þ

where � means ‘‘the addition of matter-elements.’’The matter-element R0 is added by a set of matter- elements:R1;R2; . . . ; and Rn as R0¼R1�R2� . . .�Rn. For instance, air is com-posed of oxygen, nitrogen, carbon dioxide and others. Throughdecomposition, air can be transformed into the individual elementssuch as oxygen, nitrogen, carbon dioxide, and others.

(3) Increasing or Decreasing – In marketing, to meet customers’ demands,some additional components or items are attached to their leadingproducts to increase the products’ functions. From an Extenics per-spective, they are employing an Increasing Transformation, and, viceversa, it is called Decreasing Transformation (Cai, Yang, andLin 2003). An application of increasing transformation is shown inEquations (9) through (11):

R0 ¼ ðmilk� bottle A; function; holding milkÞ ð9Þ

R1 ¼ ðthermometer A; function; measuring temperatureÞ ð10Þ

TR0 ¼ R0 � R1 ¼ ðmilk� bottle� thermometer A;

function; holding milk�measuring temperatureÞ:ð11Þ

Then T is called the increasing transformation of R0.(4) Expansion or Contraction – Based on normal experience, when we fail

to pull out a cork, the bottle is usually heated to solve the problem. Theidea of expansion transformation is embodied in this solution and is

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expressed in Equations (12) through (14):

R0 ¼ ðbottle A; volume; 1 cm3Þ ð12Þ

TR0 ¼ aR0 ¼ ðbottle A0; volume; a� 1 cm3Þ; ð13Þ

where

Expansion Transformation; a > 1Contraction Transformation; 0 < a < 1.

�ð14Þ

Transformations of matter-elements perform any changes made to thekey features and their values for the objects. In the fact that everymatter-element is directly linked to the object it represents, any transforma-tions on the matter-element result in the change of the original object.Therefore, it is reasonable to assume that appropriate transformation madeon matter-elements can generate the alternation on the current objects andthus the emergence of the concepts of new objects, among which creativityhas a good chance to exist.

Divergent Tree Method. Divergence of a matter-element is expressed asone matter that has many characteristics; a characteristic is shared by manymatters; a value can be used to describe the characteristics of many matters(Cai, Yang, and Lin 2003). The method of employing divergence to solveproblems is called the divergent tree method. The divergent tree methodextends the views and perspectives of studying the objects by divergingthe names, characteristics, and values of the matters. The original solutiondomain can be expanded after divergence. New connections may be estab-lished across varied domains, and thus creative solutions can be achievedwith reference to the information in previously remote domains. A set ofsix types of divergent trees are provided in the literature (Cai, Yang, andLin 2003). These are shown in Equations (15) through (20), where ‘‘a’’means ‘‘can be extended to’’:

1. A matter can have many characteristics after divergence as denoted by

ðN ; c; vÞ a fðN ; c1; v1Þ; ðN ; c2; v2Þ; . . . ; ðN ; cn; vnÞg ð15Þ2. One characteristic can be shared by a number of matters, as denoted

by

ðN ; c; vÞ a fðN1; c; v1Þ; ðN2; c; v2Þ; . . . ; ðNn; c; vnÞg ð16Þ3. A value can be shared by the characteristics of many matters, as

denoted by

ðN ; c; vÞ a fðN1; c1; vÞ; ðN2; c2; vÞ; . . . ; ðNn; cn; vÞg ð17Þ


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4. A characteristic and its value can be shared by a set of matters, asdenoted by

ðN ; c; vÞ a fðN1; c; vÞ; ðN2; c; vÞ; . . . ; ðNn; c; vÞg ð18Þ

5. Different characteristic of a matter can have the same value, as denotedby

ðN ; c; vÞ a fðN ; c1; vÞ; ðN ; c2; vÞ; . . . ; ðN ; cn; vÞg ð19Þ

6. A matter can have different values as to a certain characteristic, asdenoted by

ðN ; c; vÞ a fðN ; c; vðt1ÞÞ; ðN ; c; vðt2ÞÞ; . . . ; ðN ; c; vðtnÞÞg ð20Þ

Extenics for Generalization and Analogy

Generalization. Generalization represents objects in a general form,which consists of the common features applicable to every member of agroup (Merriam-Webster Inc. 2008). For instance, the function of the doorand window curtain can be generalized as a common feature of ‘‘covering acertain amount of area.’’ Generalization is a fundamental element of logicand human reasoning for the creation of new design concepts. With a gen-eralization method, products have been represented in simplified formswith key features, from which rational methods and creative techniquescan be adopted for the new concept derivation (Yan 1998).

In Extenics, objects are represented in matter-elements wherein rel-evant characteristics and values are listed. On the basis of thematter-element, generalization on a specific characteristic can be embo-died by changing its value. Matter-elements in Equation (21)show the aforementioned generalization made on the example of the doorfunction:

R0 ¼ ðDoor; Function; open and closeÞRgeneration ¼ ðDoor; Function; covering a certain amount of areaÞ

ð21Þ

Analogy. Analogy in design was generally characterized by Gael (1997)as reminding and transferring knowledge about one design situation toanother, where the transfer can occur in the service of any design task inthe new situation. In the creative process, knowledge needed to address aproblem typically is not available in a form directly applicable to the prob-lem; instead, at least some of the needed knowledge must be acquiredfrom other knowledge sources (Gael 1997). The central role that

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analogy plays in human creative thinking has been revealed in literature(Gael 1997; Mayer 1989; Itkonen 2005; Vosniadou and Ortony 1989; Gomeset al. 2006).

In Extenics, the characteristics and values in matter-elements createlinks among previously unrelated objects, from which a new analogy mightbe inspired and then established. Analogy achieved by studying the charac-teristics values in matter-elements is illustrated in the ‘‘Case Study forKCPS’’ section.

Attribute Dependency TemplateAttribute Dependency Template (ADT) is a method that finds two inde-

pendent attributes of the product and establishes dependency betweenthem. The ADTapproach had been proposed by Goldenberg and Mazursky(2002) in an aim to generate creative design concepts on the basis ofstudying the attributes of the current products.

Moreover, ADTcan be integrated compatibly with Extenics. In Extenics,characteristics in the matter-element of an object essentially represent itsattributes. Therefore, characteristics in a matter-element are usable forthe application of ADT to examine dependency among them, throughwhich creative design concepts may evolve. Further, the knowledgeretained in CBR can be utilized to establish new dependencies that willgenerate new design concepts.

FIGURE 5 The KCPS with specific techniques.


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The Structure of KCPS with Specific Techniques

After having been selected (see the ‘‘Techniques for KnowledgeProvision’’ and ‘‘Techniques for Information Processing’’ subsections of thisarticle), these techniques are integrated, and thus the KCPS with specifictechniques has been achieved and is illustrated in Figure 5.

As shown in Figure 5, KCPS comprises the techniques of CBR, Extenics,and ADT, as well as the meta-behaviors. Additionally, Extenics consists ofmatter-element, divergent tree method, and matter-element transforma-tions, and supports the generalization and analogy as well. Among thesetechniques, CBR is responsible for the knowledge provision, whereasExtenics and ADT conduct the information processing. These techniquesare expected to function cohesively so that KCPS can enhance people’screativity when they solve problems. The operation of KCPS is discussedin the following section.

OPERATION OF THE KCPS METHOD

The detailed problem solving procedure of the KCPS method has beenshown in Figure 6 and includes the following four stages: (1) knowledgerepresentation, (2) new matter-elements (M=Es) exploration, (3) evalu-ation, and (4) new concepts realization and retainment. Having beendeployed by human users, KCPS, as a method, assists them to thinkcreatively, which subsequently improves the prospect of the generation ofcreative design concepts.

As depicted in Figure 6, the processes of knowledge provision and infor-mation processing in the KCPS method have been marked, respectively:

. The cylinder shape signifies CBR and its case library, in which relatedinformation and problem-solving experiences are stored. Indicated bythe white arrow, during the operation of KCPS, CBR conducts the pro-cess of knowledge provision that supports the information processingfor the generation of creative ideas. Through the process of knowledgeprovision, relevant background knowledge, previous solutions, and a var-iety of information in related domains can be searched and employed byhuman users for information processing.

. The shaded area denotes the process of information processing, fromwhich creative solutions can be derived.

A problem-solving scenario with the application of the KCPS methodcommences with the problem description. Creative solutions are expectedto evolve through the completion of the four stages of the KCPS method.

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Stage I: Knowledge Representation

The KCPS method is initialized with the problem description as theinputs. Two tasks are conducted in this stage:

. Formation of a primitive solution

. Representation of the primitive solution in matter-element

On the basis of the problem description, a primitive solution is initiallyformed by the human users. The primitive solution can be achievedthrough the knowledge provided by CBR, which searches its case library

FIGURE 6 The operation of the KCPS method.


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where previously successful solutions are retained. The prior case that tosome extent either has similar features or situations as those in the newproblem will be sought and fetched. Solution in the retrieved precedentcase is adopted as the primitive solution. At this stage, the primitive sol-ution is not aimed to solve the design problem completely, but to be estab-lished as a background or starting point from which creative solutions areexplored.

When the KCPS method is applied to solve a design problem, the prob-lem descriptions can be the requirements set by the design-problem speci-fications. Additionally, to increase the chances of having more creativedesign concepts generated, the design requirements should refrain fromintroducing too many constraints (Hoffmann et al. 2005). Excessive con-straints at the early stage of the design process will inhibit the subsequentcreativity. In addition, good design requirements should avoid specifyingsolutions prematurely. For instance, a design requirement should specifywhat a product must do rather than how it should do it. It is not the scopeof this thesis to give detailed discussion on the relationship between designrequirements and creativity. Further information on this topic can befound in the article by Hoffmann et al. (2005).

With reference to the problem description, human users select the rel-evant information from the primitive solution. This relevant information issubsequently translated into the characteristics and characteristics valuesthat constitute the corresponding matter-element. Representation bymatter-element has the flexibility of accommodating a wide range of infor-mation pertaining to the primitive solution. Relevant characteristics andvalues can be selected, shown, generalized, analyzed, and evaluated indi-vidually in the matter-element. Knowledge representation with thematter-element mode provides an effective platform for the subsequentstage of new matter-elements exploration, as discussed following.

Stage II: New Matter-Elements Exploration

The new matter-element exploration is the key stage for producing anumber of new matter-elements, among which the creative ones may exist.In this stage, five methods for information processing are applied, includ-ing divergent tree method, matter-element transformation, generalization,analogy, and ADT. These information processing methods can be selectedby human users to manipulate the matter-element of the primitive solutionachieved in Stage I. As discussed in the subsection, ‘‘Techniques and Infor-mation Processing,’’ these information processing methods are able to aidhuman users to generate new matter-elements on the basis of thematter-element of the primitive solution.

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. Divergent tree method deploys the divergent thinking on thematter-element. With the divergent tree method, the name, characteris-tics, or characteristics value of a matter-element are diverged from theexisting settings. The production of many diverse variants leads to thegeneration of the new matter-elements from which novel design conceptscan be realized.

. Matter-element transformations change the characteristics and theirvalues of a matter-element. These transformations on the matter-elementcause the change of the original object and the conceptual space. There-fore, through appropriate transformations made on matter-elements,alternation on the primitive solution can be made and thus can causethe emergence of creative solutions.

. Generalization represents objects with the common features applicableto every member of a group. Generalization can be made on the charac-teristics or characteristics values of a matter-element. The abstractedcharacteristics or values through generalization can identify and formthe new links among objects in various domains. Consequently, thesenew links, based on the generalized common features, assist theprocesses of cross-domain combination or analogy, from which creativesolutions can evolve.

. Analogy is to transfer knowledge within or across domains in novelways. Analogy is undertaken on the basis of the examination andanalysis of the name, characteristics, or values of a matter-element.This examination and analysis lead to the reminiscence and transferof the related information within or across domains. The informationtransfer process incurred by analogy fosters the creation of innovativeconcepts.

. The ADT examines the dependency relationship among the characteris-tics of a matter-element. As explained in a previous subsection, ‘‘TheStructure of KCPS with Specific Technologies,’’ the establishment ofnew dependency among previously independent characteristics is anapproach to generate creative ideas and solutions.

The applications of these information processing methods operatingfor the new matter-elements exploration are demonstrated by a case studyin the next section.

Stage III: Evaluation

In this stage, the newly generated matter-elements are evaluated byhuman users. Normally, a number of new matter-elements could beacquired after the previous stages. The objectives of evaluation are


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1. to delete the redundant characteristics and=or characteristics values inthe new matter-elements; and

2. to remove the matter-elements that have less potential to be creative.

The motivation to conduct the evaluation is to avoid the situation inwhich too many new matter-elements have been generated in previousstages. Therefore, in order to effectively conduct a KCPS session, the pur-pose of the evaluation is to delete the matter-elements that have redun-dancy. Additionally, based on their experiences, human users can alsoremove the matter-elements that plainly have less potential to be creative.However, this removal should be conducted with caution because creativesolutions may originate from the matter-elements that appear to be lesscreative initially.

Subsequently, matter-elements that passed the evaluation are referredto as creative matter-elements, from which creative design solutions areexpected to be derived. If, in some situations, no creative matter-elementis obtained, the process would return to either Stage II or Stage I, as judgedby human users.

When the process returns to Stage II, alternative information proces-sing methods or their combinations are applied to the originalmatter-element of the primitive solution. Accordingly, new matter-elementscan be generated and then evaluated.

When the process goes back to Stage I, there are two options:

1. On the basis of the original primitive solution, new characteristics andcharacteristic values are selected and represented in a newmatter-element.

2. On the basis of the problem description, a new primitive solution isdevised.

The process can reiterate between Stage I and Stage III so that creativematter-elements are achieved.

Stage IV: New Solutions Realization and Retainment

This stage is to realize the creative matter-elements into solutions forthe problem. The creative matter-elements achieved in Stage III can giveinspirations to human users. On the basis of the creative matter-elements,human users develop creative solutions. The process of realizing the cre-ative matter-elements into creative solutions is facilitated by the processof knowledge provision. The characteristics and=or characteristics valuesincluded in the creative matter-elements are used as the key words for

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searching relevant information stored in the CBR case base. When appro-priate cases are retrieved, related information, background knowledge,and precedent experiences are supplied for human users in order that theymight form new solutions.

Finally, successful new solutions are saved as new cases into the CBRcase library. Relevant information from the new solutions will be translatedinto cases and retained in the CBR memory for future reference.

CASE STUDY FOR KCPS

This case study demonstrates the operation of the KCPS method that isapplied by human users to generate creative solutions. Further, this casestudy also shows that people’s creativity can be improved by being providedrelated knowledge. For this purpose, the task of designing new balancingequipment by a playground manufacturing company (referred to as ‘‘thecompany’’ in this article), is used as an example. The company is a designerand manufacturer of various pieces of playground equipment, such asslides, swings, rockers, and others. When customers submit an order tothe company that specifies the functions and other requirements, the com-pany proposes a preliminary design concept and then responds to the cus-tomer with a quote. In order to accelerate the process of the preliminarydesign, the company first refers to a case-based system that has collectedthe designs done in the past.

The design requirement of the balancing equipment is set as: a design ofa balance device that can be challenging and fun. The target group using thisdevice is kindergarten children. According to the American Heritage Dic-tionary (Morris 1981), challenging is defined as ‘‘calling for full use of

FIGURE 7 The balance log.


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one’s abilities or resources in a difficult but stimulating effort.’’ Similarly,fun is explained as ‘‘a source of enjoyment, amusement, or pleasure.’’

According to the design specifications, the design of a balance log(shown in Figure 7), has been retrieved from among the company’s pre-vious designs stored in the case-based system; this design of the balancelog is used as the primitive solution.

TABLE 1 New Design Concepts Achieved with KCPS Method

Design concepts achieved with application of KCPS method

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With the application of the KCPS method, twelve design concepts ofnew balancing equipment are generated by human users. These new con-cepts are illustrated in Table 1. Due to the page limits, the detailed reason-ing process of the KCPS method for the generation of these new designconcepts has been attached in Appendix A. As has been described in thereasoning process, the previous design information and knowledge pro-vided by CBR play a key role in assisting human users to generate newdesign concepts.

DISCUSSION

Through this case study, the KCPS method demonstrates its capacity toassist human users to generate new concepts. With the adoption of KCPS,human users are provided with related knowledge and methods in order tosolve problems creatively. The advantage of the KCPS method can be foundin the following three perspectives:

1. As a creative problem-solving methodology, KCPS is developed andfounded on the study of human creativity that suggests how the creativeproducts might be generated. Accordingly, information seeking, infor-mation processing, and meta-behavior are the three key contributorsto creative work. Consequently, in addition to the meta-behaviors, theconstitution of the KCPS with CBR for knowledge provision, Extenics,and ADT for information processing ensures and increases the chancesof delivering creative solutions.

2. The KCPS method emphasizes that the knowledge provision is crucial tothe evolvement of creative solutions for a CPS methodology. Accordingly,previous experience, background knowledge, and other related infor-mation in varied domains are provided during the operation of KCPS.In this case study, knowledge provided to human users by the KCPSmethod plays a key role for the generation of those new designs shownin Table 1. Particularly, the previous designs of playground equipmentthat are stored in CBR have been retrieved and inspire human users forthe formation of new design concepts. For example, a prior design of abalance log has been first provided as the primitive solution, from whichthe new design concepts have been developed. Table 2 also summarizesthe previous playground designs that are retrieved by CBR and providedto human users together with the concepts of new balancing equipment.As discussed in the case study (Appendix A), human users adopt this pro-vided knowledge to realize the achieved matter-elements into new designconcepts. These new concepts may not be generated unless human usersare provided with the knowledge about those previous designs.


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Moreover, KCPS can learn by continuously adding the latest successfulsolutions into its memory. In the long run, this learning process will builda considerable knowledge pool in the KCPS method, which improves theeffectiveness and efficiency in creating novel solutions in the future.

3. In addition to providing knowledge, the KCPS method also focuses oninvolving the appropriated information processing methods, including

TABLE 2 Summary of New Concepts Corresponding with the Knowledge About Previous Designs

Previous playground designs Concepts of new balancing equipments

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Extenics and ADT, for human users to utilize. These methods assisthuman users to manipulate data and information available and thusenhance their capacity to generate creative solutions in problem-solvingpractices.

Further, the KCPS method is an open system. As discussed in ‘‘Inspira-tions from Human Creativity,’’ the KCPS method has been fundamentallydeveloped with reference to the human creativity. The essential compo-nents that contribute to the evolvement of creativity within the KCPSmethod are knowledge provision, information processing, andmeta-behaviors. As KCPS is a method applied by human users, themeta-behaviors indicate the human mental activities involved for creativity.Consequently, the other two components have been realized with selectedtechniques. However, the techniques in the current KCPS method are notfixed. Other techniques that demonstrate better performance for knowl-edge provision and information processing will be considered for the possi-bility of being integrated into the KCPS. This structural openness givesKCPS the potential to update itself with the later addition of new techni-ques, and thus leads to a desirable advantage of continuous improvementsin the future.

As a newly emerged approach, KCPS is regarded as the first step towarda creative problem-solving methodology with knowledge provision. Theperformance of KCPS can be improved with further research undertakenin following directions:

. To identify knowledge required for problem-solving in specific domainsand to develop an appropriate scheme to have it represented andorganized in KCPS so that it can be retrieved efficiently

. To configure a process that updates the knowledge in KCPS so that newknowledge can be added

. To develop approaches or tools that can facilitate human users in termsof the meta-behaviors

. To apply the KCPS method to solve more complex problems

CONCLUSION

In this article, a method, KCPS, has been proposed to enhance people’screativity by emphasizing the provision of necessary knowledge during thecreative problem-solving process. The development of the KCPS methodhas been inspired by studying the models of human creativity, which sug-gest that creativity can be derived from the components of knowledge pro-vision, information processing, and meta-behaviors. Consequently, in theKCPS method, knowledge provision has been conducted by CBR because


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of its competence in remembering and retrieving previous problem-solvingexperiences and other related information and knowledge. For the infor-mation processing, the techniques of Extenics and ADT are selected.Extenics is composed of matter-element, matter-element transformations,and the divergent tree method. Meanwhile, Extenics can also supportthe generalization and analogy for the generation of creativity. Thesetechniques in KCPS assist human users for the derivation of creativesolutions.

The meta-behaviors of human users unite the components of knowl-edge provision and information processing to ensure that they functionseamlessly. The meta-behaviors also manipulate knowledge provided byCBR; adopt the appropriated information processing methods to examinethe matter-elements; conduct evaluation when necessary; and determinethe solutions to the problem.

The operation of the KCPS method includes four stages: (1) knowledgerepresentation; (2) new matter-elements exploration; (3) evaluation; and(4) new solutions realization and retainment. This operation is initializedwith the problem descriptions as the inputs, upon which a primitive sol-ution is formed by human users with reference to the previous experiencestored in the CBR. Next, the primitive solution is represented in amatter-element that serves as a starting point, from which creative solutionsare explored. Then, the matter-element of primitive solution is processedby human users with the aid of the information processing methods,including the divergent tree methods, matter-element transformations,generalization, analogy, and ADT, for the generation of new matter-elements. Subsequently, the newly generated matter-elements are evalu-ated. Matter-elements that passed the evaluation are referred to as creativematter-elements, from which creative solutions are expected to evolve.Finally, the creative matter-elements are realized into new solutions byhuman users supported by the knowledge in CBR. The achieved creativesolutions are stored in the CBR case base for reference in the future.

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APPENDIX A: GENERATION OF INNOVATIVE DESIGNCONCEPTS WITH THE KCPS METHOD

Matter-Element Representation of the Balance Log

To commence the exploration of new design concepts, this balancelog design (shown in Figure 7) is translated into a matter-element,where relevant characteristics and values of the balance log have beenidentified and represented in its matter-element mode. As shown inEquation (22), the matter-element of the balance log has four character-istics, including Installation, Shape, Dimension, and Functions, and theircorresponding values. For some characteristics, their values are com-prised of sub characteristics. For instance, the value set of characteristicInstallation has three sub characteristics, namely Style, Positions, andAmounts, with respective values as fixed, at End and two as denoted inEquation (23).

R ¼ RBalance Log ¼

Balance

LogInstallation

Style fixedPositions atEndAmount two

24

35

Shape

Along Axis straightCross Section roundBar Style solidAmount 6

2664

3775

DimensionsOverall Length 1:8mHeight 0:3m

� �

Functions Challenging&Fun

2666666666666664

3777777777777775

ð22Þ

RðInstallationÞ ¼Style fixedPositions atEndAmount two

24

35 ð23Þ

These characteristics and characteristic values in the balance log’smatter-element mode reflect main design properties, and in a large scaledetermine the design of the balance log. Any modification adopted oncharacteristics, subcharacteristics or their values would result in the alter-ation of the original design of the balance log. For this reason, manipula-tions on these characteristics and their values are investigated in order toproduce creative design solutions. To conduct the manipulations, the infor-mation processing methods that have been discussed in ‘‘Techniques forInformation Processing’’ are deployed.


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Divergent Tree Method and Replacement Transformation forNew Design Concepts

Divergent tree method is deployed on the matter-elements of the bal-ance log (defined in the first Appendix section) in an attempt to findthe alternatives for the name, characteristics, and values of the matter–elements. In this case study, the characteristics and subcharacteristics ofthe balance log shown in Equation (22) are kept, whereas the values ofcharacteristics and subcharacteristics will be diverged for alternatives. Thenew generated matter–elements will be renamed accordingly. This typeof divergent tree was shown in Equation (16). As the characteristic Functionsin Equation (22) determines the objectives of this playground equipmentdesign and should be consistently fulfilled in any new design concepts,no transformation of it will be considered. However, it does set the goal;that is, any new design concepts should be challenging and fun.

RBalanceLoga

NewBalancingTools

Installation

Style fmove limitedly; move vertically;move freely; horizontally; . . .g

Positions fonCenter; null; . . .gAmount fone; three; four; . . .g

2664

3775

Shape

Along Axis fnot straight; curve; zigzag; . . .gCross Section fsquare; rectangular; oval; . . .gBar Style fnot solid; movable; rotary . . .gAmount f2; 3; 4; 5;6; . . .g

2664

3775

DimensionsOverall Length f2m; 3m; 4m; . . .gHeight f0:4m; 0:5m; 0:6m; . . .g

� �


266666666666666664

377777777777777775

ð24Þ

Equation (24) shows the new alternative values for characteristics andsubcharacteristics of the balance log. The matter–element is named NewBalancing Tools, which will be renamed accordingly after new matter–elements with the new characteristic values emerge. For representation pur-poses, alternative characteristic values options are listed together andshown in bold italic fonts in a brace. The sources of these alternative valuesare on the basis of knowledge from natural language, design informationcases, and past successful alternative characteristic values in the CBR caselibrary.

A large number of new characteristic values can be obtained throughthe divergent tree method. To verify the values that are either redundantor deemed as having less potential for generating new concepts, an evalu-ation process is applied before the new matter-elements are created by thereplacement transformation with the new characteristic values. In this casestudy, new characteristic values selected after evaluation for the new

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concept generation are shown in Equation (25). Blank braces denote thatno new characteristic value exists and the original values in Equation (22)remain.

RBalance Loga

NewBalancingTools

Installation

Style fmove limitedly;move vertically;move freely andhorizontallyg

Positions fgAmount fg

26666664

37777775

Shape

Along Axis fgCross Section fgBar Style fnot solid; rotarygAmount fg

2664

3775

DimensionsOverall Length fgHeight fg

� �


2666666666666666666664

3777777777777777777775

ð25Þ

To gain a clear view of the new concepts generated from each specificalternative characteristic value, each new value for these characteristics,including Installation, Shape, and Dimension, is to be studied individuallyunder the assumption that all the other characteristics and characteristicvalues remain original if possible. However, in some contexts, after newconcepts are generated, some original characteristic values could need tobe changed to be compatible with the new concepts. This situation hap-pens to the new concepts of balance chain as shown in Figure 16 and Equa-tion (31). Furthermore, the combination of some new characteristic valuescan contribute to the generation of new concepts as well. This can beachieved after each of new characteristic values has individually evolvedinto new ideas.

R1 ¼ TInstallation!StyleR ¼

Chained

Balance

Log

InstallationStyle move limitedlyPositions atEndAmount two

24

35

Shape


2664

3775


� �


2666666666666664

3777777777777775

ð26Þ


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Spring

Based

Balance

Log

InstallationStyle move verticallyPositions atEndAmount two

24

35

Shape


2664

3775


� �


266666666666666664

377777777777777775

ð27Þ


Roller

Balance

Log

Installation

Style move freely andhorizontally

Positions atEndAmount two

2664

3775

Shape


2664

3775


� �


266666666666666664

377777777777777775

ð28Þ

R4 ¼ TShape!BarStyleR ¼

Balance

ChainInstallation


24

35

Shape

Along Axis straightCross Section roundBar Style not solidAmount 6

2664

3775


� �


2666666666666664

3777777777777775

ð29Þ

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R5 ¼ TShape!BarStyleR ¼

Rotary

BalanceLog

InstallationStyle fixedPositions atEndAmount two

24

35

Shape

Along Axis straightCross Section roundBar Style rotaryAmount 6

2664

3775


� �


2666666666666664

3777777777777775

ð30Þ

After the replacement transformations have been made on the newcharacteristic values shown in Equation (25), new matter-elements areobtained and shown in Equations (26) through (30).

On the basis of the new characteristic values in the newmatter-elements,related cases from the CBR case library are searched and retrieved whenavailable. Analogy between related cases gives new insights on the formationof new design concepts. The achieved new design concepts are discussed inthe first five subsections of the ‘‘Chained Balance Log’’ section of thisAppendix. All the design concepts of the new balancing tools will suppos-edly increase the challenge and fun when children play on them.

Chained Balance LogMatter-element shown in Equation (26) suggests that the installation

can move limitedly. Using the phrase ‘‘move limitedly’’ as the feature tosearch previous designs in the CBR case base, designs of monkey rings havebeen retrieved and provided to users. As shown in Figure 8, the rings havea chain connection to the mainframe, which allows the rings to movelimitedly when children move and swing, using their hands as a monkeydoes, swaying among the tree branches.

FIGURE 8 Monkey rings.


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With reference to the chained connection of the monkey rings, the con-cept of the chained balance log is formulated by users. As illustrated in Figure 9,the balance log has been chain-linked to the four posts. Rather than beingfixed on the ground, this chain-linked installation gives the balance barthe freedom of further movement within certain limits. The moving capacityof this chained balance log demands more attention and balancing skillsthan the normal balance log when children walk and play on it.

Spring-Based Balance LogThe Installation characteristic of the matter-element shown in Equation

(27) indicates that this new balance device should be able to move vertically.When search for the prior design case with the key feature ‘‘move verti-cally,’’ a rocker design has been found in the CBR case base. As shown inFigure 10, this rocker has a spring base, which generates the moving up

FIGURE 9 Chained balance log.

FIGURE 10 Rocker.

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and down when children ride on it. Having made an analogy from therocker design by transferring the spring-based structure onto the balancelog, the concept of spring-based balance log has been generated and illu-strated in Figure 11. In the new design concept, the originally fixed instal-lation has been replaced by two sets of springs. This spring-basedinstallation makes the balance log move up and down vertically when chil-dren walk on it. In comparison with the original balance log, these extra upand down movements require more attention and challenge the children’sbalancing skills. Additionally, children will be excited by the up and downmovement. Walking on an up and down log with occasional little leaps toarouse bravery will produce great fun for children.

Roller Balance LogThe matter-element shown in Equation (28) suggests that the new bal-

ance device should be able to move freely and horizontally. According to thisrequired feature, relevant products are retrieved from the CBR library.They are roller blade and skating board, as illustrated in Figure 12.

FIGURE 11 Spring-based balance log.

FIGURE 12 Roller blade and skating board.


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On the basis of the analogy which transfers relevant features from theroller blade and skating board to the balance log, a new concept of rollerbalance log is generated by users. As pictured in Figure 13, the roller balancelog integrates two sets of wheels onto the original balance log design. Theadditional rollers allow the balance log to move freely on the ground in acourt. In this scenario, walking on a free-moving balance log is expected tobe a big challenge and consequently fun for children. (Helmet or otherprotective equipment may be needed for safety.)

Further, as visualized in Figure 14, two identical roller balance logs areinstalled as a set. With appropriate accessories for foot grips, children canstand on these dual roller balance logs, one for each foot. The length of thelog makes it possible to accommodate several children to play on ittogether, which can promote the sense of team work. Unlike playing alone,children need to cooperate to deal with the challenge as a team. In order to

FIGURE 13 Roller balance log.

FIGURE 14 Dual roller balance log.

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successfully walk on this dual roller balance log, acting in perfect harmonyis the key. Children are expected to learn and enjoy playing as a team.

Balance ChainThe matter-element in Equation (29) suggests a new balance device with

not solid shape feature. When using this ‘‘not solid’’ feature to search in theCBR case base, the designs of climber have been retrieved. As shown inFigure 15, these designs of climber include several chains that are ‘‘not solid.’’

By using this chain structure to realize the not solid feature in Equation(29), a design concept of balance chain has been generated and illustratedin Figure 16. In this new concept, the solid bar in the original balance loghas been removed and replaced with a chain. In comparison with the solidbars in the previous balance log design, the balance chain is flexible (notsolid). After having had the new concept, some characteristic values listedin Equation (29) need to be adjusted to make them compatible with theconcept of balance chain. The updated matter-element of the concept ofbalance chain is shown in Equation (31).

R 04 ¼ R4 update ¼

Balance

ChainInstallation


24

35

Shape

Along Axis curvedCross Section ringChainBar Style not solidAmount numerous

2664

3775


� �


2666666666666664

3777777777777775

ð31Þ

FIGURE 15 Climbers.


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Rotary Balance LogOn the basis of the matter-element shown in Equation (30), some bar

segments of the new balance device are rotatable. When using the ‘‘rotat-able’’ feature to search the previous design in the CBR case base, the designof barrel roll has been retrieved. As shown in Figure 17, the barrel in lightgrey on the bottom can spin around its axis when children stand on itand walk with their hands holding onto the handle.

Having referred to the rotatable structure on the barrel roll, the con-cept of the rotary balance log has been created and is illustrated inFigure 18. The rotary balance log characterizes a new style of bar design.Instead of the fixed balance bar in the original design, some bars on therotary balance log are able to spin around their axes. As visualized inFigure 18, the bars in dark grey can rotate freely around their axes, while

FIGURE 16 Balance chain.

FIGURE 17 Barrel roll.

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the light grey bars are fixed. The rotation movement of the parts of the bal-ance bars makes it more challenging for children to maintain a balancewhen they walk on it than the fixed counterparts do. As the fixed and rotarybars are arranged alternately, extra attention is called for in order to dealwith the transition between the movable and unmovable surfaces of thebalance bar.

Transformations of Matter-Element for New Design Concepts

Among the four transformations of matter-elements in Extenics,replacement transformation works together with the divergent treemethod and has been illustrated in the previous section of this Appen-dix. The roles of other transformations of matter-element, includingdecomposition, increasing=decreasing, and expansion=contraction, inthe creation of new design concepts are demonstrated in the followingcases.

Decomposition TransformationThe balance log (shown in Figure 7) is composed of six segments of

log-bar. According to the decomposition transformation, the original bal-ance log can be decomposed into six balance log-bars and each of themcan be transformed into a mini balance log, expressed as Rmini Log. Thisdecomposition transformation process made on the original balance logdesign has been presented in Equation (32). The length of each minilog is determined by Llog-bar, the length of the bar segment of the originalbalance log. In Equation (33), Llog-bar is calculated on the basis of the para-meters shown in Equation (22). The matter-element for the mini balance

FIGURE 18 Rotary balance log.


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log is expressed in Equation (34).

*RBalance Log ¼ RLog�bar1 � RLog�bar2 � � � � � RLog�bar6

*TRBalance Log ¼ fRmini Log1; Rmini Log2; � � � ;Rmini Log6gwhere; Rmini Log1 ¼ Rmini Log2 ¼ � � � ¼ Rmini Log6 ¼ Rmini Log

ð32Þ

Llog�bar ¼overallLength

Amount¼ 1:8m

6¼ 0:3m ð33Þ

Rmini Log ¼

Mini

Balance

Log


24

35

Shape


2664

3775


� �

Functions Challenging & Fun

2666666666666664

3777777777777775

ð34Þ

On the basis of the matter-element Rmini Log and relevant design infor-mation in the CBR data base, a set of mini balance logs is arranged asdepicted in Figure 19. In addition to the slow and careful walking abilitydemanded on the original balance log, children are challenged with theskill of skipping certain distances and the tactics of safely landing on anaimed-for log. Leaping over these mini balance logs can bring children lotsof fun.

FIGURE 19 Mini balance log set.

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Increasing=Decreasing TransformationIn this case study, only the increasing transformation for new concepts

is demonstrated, and the reverse operation is just the decreasing transform-ation.

The spring-based balance log is illustrated in Figure 11. As explained inthe Spring-Based Balance Log section of this Appendix, the concept ofspring-based balance log is linked with the rocker design as shown inFigure 10. Both of them have the characteristic of moving up and down. Anew design concept of balance rocker can therefore be derived throughthe increasing transformation made on the rocker with the spring-basedbalance log. This increasing transformation process is shown in Equation(35). The new achieved concept of the balance rocker is shown inFigure 20. To fit with the structure of the rocker, the number of supportsfor the balance log has been reduced from ‘‘two’’ to ‘‘one,’’ and installationpoints are modified from ‘‘at ends’’ to ‘‘on the center.’’

RRocker ¼ ðRocker; Movement; rocking ÞRBalance Log ¼ ðBalance Log;Movement;walking with balanceÞTRRocker ¼ RRocker � RBalance Log ¼ RBalance Rocker

¼ ðRocker�Balance Log;Movement; rocking �walking withbalanceÞð35Þ

This balance rocker requires greater balancing skills than the simplebalance log (shown in Figure 7). Walking on the balance rocker, childrenare confronted with the additional rocking actions made from their teammates. From this perspective, the balance rocker can provide a stage fora teams contest. In a contest, children are divided into two teams: balancing

FIGURE 20 Balance rocker.


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team, who are walking on the balance log; and rocking team, who are sittingon the rocker’s seats. Rules of the game can be simply set. For example, theaim of the children on the balancing team is to walk across the balance logwithout falling off. On the contrary, the job of the rocker team is to rock thebalance log in order to make their rivals drop off the balance log. Duringthe game, the two teams may switch their positions, and a scoring schemecan also be set. Children are expected to have a great deal of fun whenplaying with this balance rocker.

Expansion=Contraction TransformationExpansion=contraction transformation are among the dimension

characteristic values shown in Equation (22). The value of the characteristicDimension!Heightis transformed by multiplying with a factora; a 2 ð0;þ1Þ. This transformation process is expressed in Equation (36).

TRBalance Log

¼ aRBalance Log ¼

NewBalanceLog


24

35

Shape


2664

3775

DimensionsOverall Length 1:8mHeight a� 0:3m

� �

Functions Challenging & Fun

2666666666666664

3777777777777775

ð36Þ

When the value of the factorais set as a¼ 6, (a> 1), it is an expansiontransformation. The height of the new balance log is six times the original,and accordingly named high balance log. The matter-element of the highbalance log is shown in Equation (37).

RHigh Balance Log ¼

High

Balance

Log


24

35

Shape

AlongAxis straightCrossSection roundBarStyle solidAmount 6

2664

3775


� �


2666666666666664

3777777777777775ð37Þ

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FIGURE 21 High balance log.

FIGURE 22 ADT creates dependency between length and height.

FIGURE 23 Step balance log.


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The concept of the high balance log is illustrated in Figure 21. Based onthe normal experience, human beings, particularly children, tend to feelmore nervous when walking in higher places and looking down to theground. The increased height of the balance log can make it more chal-lenging for children to walk on it (safety net and other features may berequired for security and accessibility considerations). In addition to thebalancing skill called for by a normal balance log, this high balance logcan foster and show bravery, a valuable character trait, among children.Further, with appropriate security accessories, falling from the log can bescary but thrilling. It can be reasonably foreseen that some children woulddeliberately slip off the high balance log and enjoy the safe landing ontothe ground.

ADT for New Design Concepts

As shown in Equation (22), the values of the characteristics ‘‘OverallLength’’ and ‘‘Height’’ are constant and independent. The ADT method

FIGURE 24 Other types of dependency between length and height.

FIGURE 25 Slope balance log.

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is to form a relationship between the dimensions of the overall length andheight of the original balance log. The new created dependency betweenthese two values is illustrated in Figure 22. The design concept of step bal-ance log is shown in Figure 23. When children walk along the step balancelog, extra movements of walking up and down the step are required andchallenge their balancing skills.

Additionally, other sorts of dependencies can be formed and are shownin Figure 24. Similarly, on the basis of these two new dependencies, designconcepts, slope balance log and down-step balance log, can be generated and areillustrated in Figures 25 and 26, respectively. These two types of balance logcan also be fun for children when they walk on the slope or up and downthe step, balancing their movements.

FIGURE 26 Down-step balance log.


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toward a creative problem-solving methodology with knowledge provision

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