63

Interval Type-2 Fuzzy Logic in Hybrid Neural PatternRecognition Systems

Patricia Melin

Abstract. We describe in this paper an overview of new methods that we have beenworking on for building intelligent systems for pattern recogni-tion using type-2fuzzy logic and soft computing techniques. Soft Computing (SC) consists of severalcomputing paradigms, including type-1 fuzzy logic, neural networks, and geneticalgorithms, which can be used to create powerful hybrid intelligent systems. In thispaper, we are reviewing the use of a higher order fuzzy logic, which is called type-2fuzzy logic. Combining type-2 fuzzy logic with traditional SC techniques, we areable to build powerful hybrid intelligent systems that can use the advantages thateach technique offers in solving pattern recognition problems.

63.1 Introduction

Fuzzy logic is an area of soft computing that enables a computer system to reasonwith uncertainty [2]. A fuzzy inference system consists of a set of if-then rulesdefined over fuzzy sets. Fuzzy sets generalize the concept of a traditional set by al-lowing the membership degree to be any value between 0 and 1. This corresponds,in the real world, to many situations where it is difficult to decide in an unambigu-ous manner if something belongs or not to a specific class. The main disadvantageof fuzzy systems is that they can’t adapt to changing situations. For this reason, itis a good idea to combine fuzzy logic with neural networks or genetic algorithms,because either one of these last two methodologies could give adaptability to thefuzzy system. On the other hand, the knowledge that is used to build these fuzzyrules is uncertain. Such uncertainty leads to rules whose antecedents or consequentsare uncertain, which translates into uncertain antecedent or consequent membershipfunctions. Type-1 fuzzy systems, like the ones mentioned above, whose member-ship functions are type-1 fuzzy sets, are unable to directly handle such uncertainties.We also consider in this paper, type-2 fuzzy systems, in which the antecedent orconsequent membership functions are type-2 fuzzy sets. Such sets are fuzzy setswhose membership grades themselves are type-1 fuzzy sets; they are very useful incircumstances where it is difficult to determine an exact membership function fora fuzzy set. Type-2 fuzzy systems have been applied with relative success in manyreal-world applications, like in control, time series prediction, classification and deci-sion, diagnosis, and pattern recognition. Uncertainty is an inherent part of intelligentsystems used in real-world applications. The use of new methods for handling in-complete information is of fundamental importance [1]. Type-1 fuzzy sets used in

R. Seising et al. (Eds.): On Fuzziness: Volume 2, STUDFUZZ 299, pp. 435–439.DOI: 10.1007/978-3-642-35644-5_63 © Springer-Verlag Berlin Heidelberg 2013

436 63 Interval Type-2 Fuzzy Logic in Hybrid Neural Pattern Recognition Systems

conventional fuzzy systems cannot fully handle the uncertainties present in intelli-gent systems. Type-2 fuzzy sets that are used in type-2 fuzzy systems can handlesuch uncertainties in a better way because they provide us with more parameters.Neural networks are computational models with learning (or adaptive) characteris-tics that model the human brain [3]. Neural networks can be classified in supervisedand unsupervised. The main difference is that in the case of the supervised neuralnetworks the learning algorithm uses input-output training data to model the dynamicsystem, on the other hand, in the case of unsupervised neural networks only the inputdata is given. In the case of an unsupervised network, the input data is used to makerepresentative clusters of all the data. It has been shown, that neural networks areuniversal approximators, in the sense that they can model a continuous and boundedfunction to a specified accuracy and for this reason neural networks have been ap-plied to problems of system identification, control, diagnosis, time series prediction,and pattern recognition. We have worked on special structures called modular andensemble neural networks. Basically, a modular or ensemble neural network usesseveral monolithic neural networks to solve a specific problem. The basic idea isthat combining the results of several simple neural networks we will achieve a betteroverall result in terms of accuracy and also learning can be done faster and fuzzylogic is the best approach to combine or aggregate the outputs of the modules Ge-netic algorithms and evolutionary methods are optimization methodologies based onprinciples of nature [4]. Both methodologies can also be viewed as searching al-gorithms because they explore a space using heuristics inspired by nature. Geneticalgorithms are based on the ideas of evolution and the biological process that occurat the DNA level. Basically, a genetic algorithm uses a population of individuals,which are modified by using genetic operators in such a way as to eventually obtainthe fittest individual. Any optimization problem has to be represented by using chro-mosomes, which are a codified representation of the real values of the variables inthe problem. Both, genetic algorithms and evolutionary methods can be used to opti-mize a general objective function. In particular, evolutionary methods can be used tooptimize the structure and parameters of neural networks and fuzzy systems, whichis required in applications to achieve optimal results.

63.2 Type-2 Fuzzy Logic Applications in Pattern Recognition

One approach that we have worked on for face recognition uses modular neural net-works with a fuzzy logic method for response integration [4]. The method for achiev-ing response integration is based on the fuzzy Sugeno integral and type-2 fuzzy logic.Response integration is required to combine the outputs of all the modules in themodular network. We have applied the new approach for face recognition with a realdatabase of faces from students and professors of our institution. The results of themodular neural network approach gives excellent performance overall and also incomparison with the monolithic approach. Also, the method for achieving responseintegration is based on the fuzzy Sugeno integral. Response integration is requiredto combine the outputs of all the modules in the modular network. Another approach

63.2 Type-2 Fuzzy Logic Applications in Pattern Recognition 437

has been the use of neural networks, fuzzy logic and genetic algorithms for voicerecognition [4]. In particular, we have considered the case of speaker recognitionby analyzing the sound signals with the help of intelligent techniques, such as theneural networks and fuzzy systems. We use the neural networks for analyzing thesound signal of an unknown speaker, and after this first step, a set of type-2 fuzzyrules is used for decision making. We need to use fuzzy logic due to the uncertaintyof the decision process. We also use genetic algorithms to optimize the architectureof the neural networks. We have also considered the use of three modular neural net-works as systems for recognizing persons based on the iris biometric measurementof humans [5]. In these systems, the human iris database is enhanced with imageprocessing methods, and the coordinates of the center and radius of the iris are ob-tained to make a cut of the area of interest by removing the noise around the iris. Theinputs to the modular neural networks are the processed iris images and the outputis the number of the person identified. We also have worked on human recognitionfrom ear images as bio-metric using modular neural networks with preprocessingear images as network inputs [5]. In this case, we have proposed a modular neuralnetwork composed of twelve modules, in order to simplify the problem making itsmaller. Comparing with other biometrics, ear recognition has one of the best per-formances, even when it has not received much attention. The Recognition resultsachieved with this approach were excellent.

Fig. 63.1. Prof. Zadeh with the Mexican hat at the IFSA 2007 Congress

438 63 Interval Type-2 Fuzzy Logic in Hybrid Neural Pattern Recognition Systems

We have also proposed a new approach for human recognition using as informa-tion the combination of three biometric measures, iris, ear, and voice of a person [5].Now we have considered the integration of these three biometric measures to im-prove the accuracy of human recognition. The new approach integrates the informa-tion from three main modules, one for each of the three biometric measures. The newapproach consists in a modular structure that contains three basic modules: iris, ear,and voice. The final decision is based on the results of the three modules and usestype-2 fuzzy logic to take into account the uncertainty of the outputs of the modules.

Fig. 63.2. Prof. Zadeh receiving an Award during the IFSA 2007 banquet

63.3 Motivation by Prof. Zadeh’s Work

The inspiring ideas and research work of Prof. Zadeh have been fundamental inmy own work [6], [7], [8]. He has always supported my research group’s work andkindly accepted our invitation to offer a keynote lecture at the World IFSA 2007Congress that was held in Cancun, Mexico in 2007 (in which I was Program Chair),which was a very important lecture, especially for Latin America and Mexico. InFigure 63.1 we show a photo of Prof. Zadeh with the classical Mexican hat duringthe banquet of IFSA 2007. Also, in Figure 63.2 Prof. Zadeh is receiving an Awardfrom Prof. Melin during the banquet of IFSA 2007.

References 439

63.4 Conclusions

In this paper an overview of new methods for building intelligent sys-tems for patternrecognition using type-2 fuzzy logic and soft computing techniques was presented.Type-2 fuzzy logic is of fun-damental importance in the area of pattern recognitionas a way to manage uncertainty in decision making and will be used with morefrequency in the future. We are grateful to Prof. Zadeh’s original work in this areaand also for his support to work along this line of research.

References

1. Castillo, O., Melin, P.: Soft Computing and Fractal Theory for Intelligent Manufacturing.Physica-Verlag, Heidelberg (2003)

2. Castillo, O., Melin, P.: Type-2 Fuzzy Logic: Theory and Applications. STUDFUZZ,vol. 223. Springer, Heidelberg (2008)

3. Melin, P., Castillo, O.: Modelling, Simulation and Control of Non-Linear Dynamical Sys-tems. Taylor and Francis, London (2002)

4. Melin, P., Castillo, O.: Hybrid Intelligent Systems for Pattern Recognition. STUDFUZZ,vol. 172. Springer, Heidelberg (2005)

5. Melin, P.: Modular Neural Networks and Type-2 Fuzzy Systems for Pattern Recognition.STUDFUZZ, vol. 389. Springer, Heidelberg (2012)

6. Zadeh, L.A.: Fuzzy Logic = Computing with Words. IEEE Transactions on Fuzzy Sys-tems 4(2), 103 (1996)

7. Zadeh, L.A.: Knowledge Representation in Fuzzy Logic. IEEE Transactions on Knowl-edge Data Engineering 1, 89 (1989)

8. Zadeh, L.A.: Fuzzy Logic. Computer 1(4), 83–93 (1998)