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Interval Type-2 Fuzzy Logicfor Hybrid Intelligent Control

Oscar Castillo

Abstract. We provide in this paper a short review of my research work on devel-oping new methods for building intelligent control systems using type-2 fuzzy logicand soft computing techniques. Soft Computing (SC) consists of several computingparadigms, including fuzzy logic, neural networks, and genetic algorithms, whichcan be used to create powerful hybrid intelligent systems. Combining type-2 fuzzylogic with traditional SC techniques powerful hybrid intelligent systems can be builtfor solving complex control problems.

14.1 Introduction

Fuzzy logic is an area of soft computing that enables a system to reason with uncer-tainty [1]. A fuzzy inference system consists of a set of if-then rules defined overfuzzy sets. Fuzzy sets generalize the concept of a traditional set by allowing themembership degree to be any value between 0 and 1. This corresponds, in the realworld, to many situations where it is difficult to decide in an unambiguous mannerif something belongs or not to a specific class. Fuzzy expert systems, for example,have been applied with some success to problems of decision, control, diagnosis andclassification, just because they can manage the complex expert reasoning involvedin these areas of application. The main disadvantage of fuzzy systems is that theycan’t adapt to changing situations. For this reason, it is a good idea to combine fuzzylogic with neural networks or genetic algo-rithms, because either one of these lasttwo methodologies could give adaptability to the fuzzy system. On the other hand,the knowledge that is used to build these fuzzy rules is uncertain. Such uncertaintyleads to rules whose antecedents or consequents are uncertain, which translates intouncertain antecedent or consequent membership functions. Type-1 fuzzy systems,like the ones mentioned above, whose membership functions are type-1 fuzzy sets,are unable to directly handle such uncertainties. We also mention in this paper, type-2 fuzzy systems, in which the antecedent or consequent membership functions aretype-2 fuzzy sets [2]. Such sets are fuzzy sets whose membership grades themselvesare type-1 fuzzy sets; they are very useful in circumstances where it is difficult todetermine an exact membership function for a fuzzy set.

Uncertainty is an inherent part of intelligent systems used in real-worldapplications. The use of new methods for handling incomplete information is of

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92 14 Fuzzy Conceptual Data Analysis Applied to Knowledge Management

fundamental importance. Type-1 fuzzy sets used in conventional fuzzy systems can-not fully handle the uncertainties present in intelligent systems [3]. Type-2 fuzzysets that are used in type-2 fuzzy systems can handle such uncertainties in a betterway because they provide us with more parameters. This paper reviews the use ofintelligent systems based on interval type-2 fuzzy logic for minimizing the effects ofuncertainty produced by the instrumentation elements, environmental noise, etc.

14.2 Summary of Research Work on Type-2Fuzzy Logic in Control

We have performed work on the design of type-2 fuzzy logic controllers using ge-netic algorithms and bio-inspired optimization methods [3]. In this section we offera review of the work that we have done on using type-2 fuzzy logic for differentcontrol applica-tions.

As a first example, we have considered the design of type-2 fuzzy systems for thelongitudinal control of an F-14 airplane using genetic algorithms [3]. The longitudinalcontrol is carried out by controlling only the elevators of the airplane. To carry outsuch control it is necessary to use the stick, the rate of elevation and the angle of attack.These 3 variables are the input to the fuzzy inference system, and we obtain as outputthe value of the elevators. After designing the fuzzy inference system we turn to thesimulation stage. Simulation results of the longitudinal control are obtained usinga plant in Simulink and those results are compared against the PID controller. Foroptimizing the fuzzy logic control design we use a genetic algorithm (GA).

Another example is the use of an evolutionary algorithm approach for the opti-mization of type-2 fuzzy reactive and tracking controllers applied to a mobile robot.The algorithm optimizes the type-2 fuzzy inference systems for each of the con-trollers. Both the reactive and tracking controllers are needed to achieve autonomousnavigation of the mobile robot. The use of new methods for handling incomplete in-formation is of fundamental importance in engineering applications. We have alsoconsidered the simulation of the effects of uncertainty produced by the instrumenta-tion elements in type-1 and type-2 fuzzy logic controllers to perform a comparativeanalysis of the systems’ response, in the presence of uncertainty [3]. We have pre-sented an innovative idea to optimize interval type-2 membership functions using anaverage of two type-1 systems with the human evolutionary model. We have showncomparative results of the optimized proposed method. We found that the optimizedmembership functions for the inputs of a type-2 system increases the performance ofthe system for high noise levels.

We have also considered the use of Ant Colony Optimization (ACO) for the balland beam control problem, in particular for the problem of tuning a fuzzy controllerof Sugeno type [3]. In our study case the controller has four inputs, each of themwith two membership functions, and we consider the interpolation point for everypair of membership function as the main parameter and their individual shape assecondary ones in order to achieve the tuning of the fuzzy controller by using anACO algorithm. Simulation results show that using ACO and coding the problem

14.4 Conclusions 93

with just three parameters instead of six, allows us to find an optimal set of member-ship function parameters for the fuzzy control system with less computational effortneeded.

We have also considered the application of a simple ACO as a method of opti-mization for membership functions’ parameters of a type-2 fuzzy logic controller inorder to find the optimal intelligent controller for an autonomous wheeled mobilerobot [3]. Simulation results show that ACO outperforms a GA in the optimizationof fuzzy logic controllers for an autonomous mobile robot.

We have also used the Particle Swarm Optimization (PSO) method to find theparameters of the membership functions of a type-2 fuzzy logic controller (Type-2 FLC) in order to minimize the state error for linear systems [3]. PSO is usedto find the optimal Type-2 FLC to achieve regulation of the output and stability ofthe closed-loop system. For this purpose, we change the values of the cognitive,social and inertia variables in the PSO. Simulation results, with the optimal FLCimplemented in Simulink, show the feasibility of the proposed approach.

In general, the above mentioned applications of type-2 fuzzy logic in intelligentcontrol are representative of the state of art in the area. However, we also have tomention that there exist applications of type-2 fuzzy logic in pattern recognition, timeseries prediction, and classification, which have been successful in the real world,but are not the main concern in this paper, [5], [6]. There have also been importanttheoretical advances on type-2 fuzzy logic that have enable more efficient processingand type reduction, which have helped obtaining solutions to real world problems.

14.3 Motivation by Prof. Zadeh’s Work

The inspiring ideas and research work of Prof. Zadeh have been fundamental inmy own work [7], [8], [9]. 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, which was a very importantlecture, especially for Latin America and Mexico. In Figure 1 the arrival of Prof.Zadeh to the Opening reception of IFSA 2007 is shown.

Type-2 fuzzy logic has been always supported by Prof. Zadeh as he was the firstone to initially suggest the idea. In this sense he has always supported the work ofthe main researchers in this area, like J. M. Mendel, R. John, H. Hagras, P. Melinand others like me. We consider that type-2 fuzzy control will be one of the mostimportant areas in the near future to consider working on as many open problems,both theoretically and application wise still remain unsolved.

14.4 Conclusions

We have described in this paper a review of the new methods for building intelligentsystems using type-2 fuzzy logic and soft computing techniques. In this paper, wehave considered the use of fuzzy logic to a higher order, which is called type-2 fuzzy

94 References

logic. Combining type-2 fuzzy logic with traditional SC techniques, we can buildpowerful hybrid intelligent systems that can use the advantages that each techniqueoffers in solving complex control problems. Finally, the application of bio-inspiredoptimization techniques, like GAs, PSO and ACO, has been proposed to automati-cally design optimal type-2 fuzzy logic controllers in different applications.

Fig. 14.1. Arrival of Prof. Zadeh to the IFSA 2007 World congress

References

1. Castillo, O., Melin, P.: Soft Computing for Control of Non-Linear Dynamical Systems.Springer, Heidelberg (2001)

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

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

4. Melin, P., Castillo, O.: Modelling, Simulation and Control of Non-Linear Dynamical Sys-tems. Springer, Heidelberg (2002)

5. Castillo, O.: Type-2 Fuzzy Logic in Intelligent Control Applications. Springer, Heidelberg(2012)

6. Melin, P., Castillo, O.: Hybrid Intelligent Systems for Pattern Recognition. Springer, Hei-delberg (2005)

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

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

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