Intelligent Agent Characterization and Uncertainty Management with

Fuzzy Set Theory

A Tool to Support Early Supplier Integration Journal of Intelligent Manufacturing (1999) 10

Author : Pamela McCauley-Bell

Intelligent Agent

Outline

IntroductionArchitectural InnovationArchitectural Innovation through Early

Supplier Integration Intelligent AgentsFuzzy Set Theory ImplementationConclusion

1. Introduction

Intelligent manufacturing systemSome important computational toolsAgent theoryUncertainty management

Intelligent Manufacturing System

The field of intelligent manufacturing system :

Simulation

Virtual reality

Robotics

Some important computational tools :

Personal computer (PC)

Knowledge-based systems (KBS)

Neural networks

Programming logic controllers (PLC)

Intelligent agents (IA)

Computational Tools

Agent theory is concerned with the question of what an agent is , and the use of mathematical formalisms for representing and reasoning about the properties of agents.

Agent Theory

Uncertainty Management

Uncertainty representation Uncertainty managementUncertainty measurementUncertainty modeling

Uncertainty Management

Uncertainty management approaches :

Probability model

Dempster-Shafer theory

Certainty factors

Fuzzy set theory

4. Intelligent Agents

Agent definitionAgent categoriesAgent classificationsAgent CharacteristicsHeterogeneous agent systems

Agent definition

Agents are referred to the assumption of autonomy.

Autonomy is a basic consideration because the entity is expected to function with a mission and without the benefit of continuous supervision or guidance.

Agent definition

An Autonomous agent can be defined as a system situation within, and existing as a part of an environment. The agent senses the predefined parameters and actors on them, over time, in pursuit of its own agenda to effect what it senses in the future.

Agent categories

Biological agents

Robotic agents

Computational agentsArtificial life agents

Software agents

Task specific agents

Entertainment agents

Viruses agents

Agents classifications

Collaborative agentsInterface agents

Mobile agents

Reactive agents

Information/internet agents

Hybrid agentsSmart agents

Agent CharacteristicsAutonomyCommunication ability (Mobility)Capacity for cooperation

Rule-based

Capacity for reasoning (Intelligence)

Knowledge-basedArtificial evolution-based

Adaptive behaviorTrustworthiness

Heterogeneous agent systems

To create the service for a wide range domains, a key requirement for interoperation among heterogeneous agents is having an agent communication language that permits agents of varying origins to communicate with each other.

Heterogeneous agent systems

Three important questions: What is an appropriate agent communication language?

How are agents capable of communicating in this language constructed?

What communication architectures are conductive to cooperation?

Fuzzy Set Theory

Fuzzy modeling approach is more consistent with human information processing, because humans have an ability to analyze imprecise concepts, which are not thoroughly understood or quantified.

The “imprecise” knowledge is essential to human-cognitive processes and is effectively modeled through the use of linguistic values and degrees of membership in fuzzy set theory(FST).

FST deals with the imprecision associated with many variables by permitting a grade of membership to be defined over the interval [0,1].

Mathematical Definition of Fuzzy Sets

Consider a finite set of objects X, define the finite set as :

X = x1 , x2,…, xn

where xi are elements in the set X.

Each element, xi, has a particular membership value, ui, which represents its grade of membership in a fuzzy set.

A fuzzy set A can be represented as a linear combination of the following form:

A = u1(x), u2(x) ,…, un(x),

The methods of dealing with uncertainty in decision support

Probability : Bayes’ theorem

Probability intervals : Dempster-Shafer theory

Fuzzy variables

Probability : Bayes’ Theorem

In non-numerical combination algorithms that merge multiple hypothesis data vectors from N sensors, the sensors that are used to make the decisions include statistical classifiers that classify measured features into a vector of parameters.

For the Bayesian inference case, these parameters are forward-conditional probabilities. Bayes’ rules is applied to compute a composite, a posteriori probability.

The maximum a posteriori (MAP) is applied to select the most likely hypothesis.

Bayes’ Theorem

The law of total probability

P(C) = P(C1)P(C | C1) + P(C2)P(C | C2) +…+ P(Ck)P(C | Ck)

=

Bayes’ theorem

P(Cj | C)=

k

i

ii CCPCP1

)|()(

k

i

ii

jjj

CCPCP

CCPCP

CP

CCP

1

)|()(

)|()(

)(

)(

P(Cj ) is called prior probability of Cj ,

P(Cj | C) is called posterior probability.

Probability Intervals : Dempster-Shafer Theory

The Dempster-Shafer theory of uncertainty attempts to distinguish between ignorance and certainty.

This model permits

P(A) + P(B) 1 ≦

where the P(A) and P(B) represents the strength of evidence or confidence.

Probability Intervals : Dempster-Shafer Theory

Based on identifying the believability of a function or proposition, the function f represents the measure of belief committed to a given proposition or piece of sensory information.

Each hypothesis is represented by two parameters: supportability and a plausibility variable.

( 0 S(X) 1 )which describe the degree to which measurement support the hypothesis;

(2) a plausibility variable

( 0 P(X) 1 )which represents the degree to which the evidence fails to refute the hypothesis.

(1) supportability

Probability Intervals : Dempster-Shafer Theory

The difference in plausibility and supportability

D(I) = P(x) - S(x)

is a measure of ignorance about the hypothesis.

Dempster’s rule of combination, analogous to Bayes’ rule, provides a means of computing composite supportability / plausibility intervals (credibility intervals) for each hypothesis, reducing the uncertainty in the measured data.

Probability Intervals : Dempster-Shafer Theory

Fuzzy Variables

Fuzzy set theory manages uncertainty in decision making by representing the level of certainty in a proposition through a membership function.

Three important principles for managing uncertainty are:

minimal uncertainty maximal uncertainty minimal invariance

Implementation

The process for the development of fuzzy intelligent agents:

A. Evaluate the needs of the environment and required agents.

B. Identify the role of agents.

C. Describe the personification of agents.

D. Characterize the types of uncertainty.

E. Define agents’ interaction.

Identifying the Roles of Agents

Missionaries : work to deliver information and attempt to reach or convert as many agents as possible by giving them their information.

Brokers : represent objects and negotiate for objects, can change belief function of an object.

Dispatcher :distributes information, gives instructions; capable but not required to store information for learning.

Scout :sound alarm if something appears wrong.

Controller: brains of community mayor; capable of storing information and learning.

Identifying the Personality

Personality : used to simulate a community of individuals interacting.

Aggressiveness

Vulnerability

Attractiveness

Truth constant

Aggressiveness

It is used to define the fervor with which a given agent is expected to pursue to other agents.

The degree of aggressiveness of an agent is effected by the number of agents (x) that the given agent direct access or links to in the model.

If x is larger, then the agent is considered aggressive because it has the ability to influence a large variety of agents in the system.

The membership function for aggressiveness is a s-shape curve.

Vulnerability

A function of the basic personality and the number of incoming source (y) or agents that have the potential to influence or reach the agent.

If the agent only contacts with one of these agents, the information which the agent possesses is untrustworthy.

The membership function for vulnerability is an increasing s-shape curve.

It is also a function of the basic personality, but may be enhanced or reduced by the agent interaction or input-to-output ratio (z).

The smaller the ratio is, the more attractive the agent is considered.

The membership function for attractiveness is an decreasing s-shape curve.

Attractiveness

It is used to evaluate the nature of the environment. The truth constant is an integer value on the interval [1,5].

A low-truth constant is associated with a hostile environment indicating that the integrity of the information can not be certified due to parameters beyond the systems control or knowledge.

The overall belief function will be a function of the aggressiveness, attractiveness, vulnerability, and truth constant.

Truth Constant

The categories and quantification of uncertainty

The types of uncertainty:

Non-specificity (imprecision)

Fuzziness (vagueness)

Strife/discord

Nonspecificity

Nonspecificity : Vi = [U1, U2 ,…, Un], and this type of uncertainty is manifested when two or more alternatives are left unspecified. This may be a result of variety, generality, diversity, equivocation.

Nonspecificity

Hartley function (U) provides an effective method to quantify the uncertainty. For any non-empty fuzzy set A defined on a finite universal set X, the generalized Hartley function has the form:

||log)(

1 )(

0 2A

Ah

Ah

U(A) =

where denotes the cardinality of the -cut of A and h(A) is the height of A.Observe that U(A), which measures nonspecificity of A, is a weighted average of values of the Hartley function for all distinct -cut of the normalized counterpart of A, defined by A(x)/h(A) for all x X.

|| A

Discord/strife

Discord /strife : Di = [D1, D2 ,…, Dn], is the type of uncertainty characterized by disagreement in choosing among alternatives and may result from dissonance, incongruity, discrepancy, and conflict.

The value will be obtained by taking the general form of the union, which takes the largest membership value contained within the set to represent the union.

Fuzziness

Fuzziness : Xi = [F1, F2 ,…, Fn], is characterized by lack of definite or sharp distinction among alternatives and may result from vagueness or any variety of indecisiveness.

Fuzziness will be obtained by using the Hamming distance.

In general, a measure of fuzziness is a function

where denotes the set of all fuzzy subsets of X (fuzzy power set)

For each fuzzy set A, this function assigns a non-negative real number of f(A) that expresses the degree to which the boundary of A is not sharp.

RXf )(:)( X

Relationship between personality traits and measures of uncertainty

The personality traits and the measures of uncertainty are metrics used to describe the capabilities and truthfulness associated with an agent and its information.

The personality traits provides an indication of the behavior and the interactability of the agent with other community members.

The measures of uncertainty produces a measure of reliability for the task that the agent has performed.

Agent Interaction

The initiation of activity in the fuzzy-agent environment begins with a trigger event.

Trigger events may be defined as the presentation of information and may be produced from the activity of a related event, acquisition of information, given set of instructions, or the lapse of a pre-defined time period.

Agent Interaction

The trigger event for each agent is different and is code into the rule base.

The process is continuous, but a task within the process ends with the termination or delivery of a specific piece of information.

In the initial model, all agents are not free to interact with each other.

Example

The hypothetical example consist of a prime and three first tier suppliers.

The developing steps:

1. Identify prime and the first tier suppliers.

2.identify significant second tier suppliers.

3.Define the bank of information, or the necessary inputs.

Example

4.Identify types of agent roles.

. Provide personality,

. Provide truth constant,

5.Provide guidelines for agent interaction

6.Define trigger events

7.Design electronic blackboard to display the information.

Fig. 1. Structure for early supplier integration network.

Example

Prime

IA Team 1 IA Team 2 IA Team 3

Supplier 1 Supplier 2 Supplier 3

SS11 SS12 SS21 SS22 SS31 SS32

Table 2. Team of agents to support early supplier integration

Primary personality

Primary personality

Primary personality

Primary personality

Missionary

Scout

Runners

Time keepers

Aggressive

Aggressive

Aggressive

VulnerableAttractive

To deliver information to the prime and all relevant suppliers

Search for violation of constraints

Deliver information to the primes database

To deliver information to the prime and all relevant suppliers

Continuous: Ongoing dissemination of information to predefined sources

Violation of a system constraint

Continuous

A modification that produces a change in the active product schedule

Example

Conclusion

Produces a framework for the development of fuzzy generic agents;

Uses the fuzzy agents to manage uncertainty in product development system;

Provides continuous interaction among suppliers and the prime;

The model can be easily translated to model the needs of intelligent industries process.