A comparison of fuzzy methods for modeling

Abstract

Type-1 Fuzzy Logic Controllers (FLCs) have been used in control applications for more than thirty years. However, traditional type-1 FLCs are de cient in dynamical unstructured environments and in many real-time applications that include large amount of uncertainties. Further to this, fuzzy logic systems work cooperatively with many optimization techniques. Conventionally, the antecedent and consequent part of the rules are tuned to obtain minimum error response. However, this situation is not desirable where the expert knowledge about the system is signi cant. Thus, scientists have started to seek new approaches or develop existing methods. In literature, there are a number of noteworthy publications on type-1 fuzzy logic with parameterized t-norms. During the optimization process in this fuzzy model, the parameters of the operators and consequent part of the rules are tuned; therefore, the expert knowledge about the system is not lost or distorted. In line with this trend, the most important contribution of this thesis is that parameterized conjunctions are expanded and Constrained Fuzzy Sets (CFSs) with parameterized conjunctions are proposed. By using constrained fuzzy sets with parameterized conjunctions, both the uncertainty and the expert knowledge are taken into account. Thus, the expert knowledge about the system is not lost or distorted and the fuzzy model has more design parameters. This study has the goal of comparing the performance of four di erent approaches to fuzzy modeling, using parameterized conjunctions, a novel concept named Constrained Fuzzy Sets (CFSs), CFSs with parameterized conjunctions, and unnormalized interval type-2 Takagi Sugeno Kang (IT2 TSK). The theoretical and mathematical backgrounds of the four approaches are brie y described and their performances are compared in approximating a nonlinear function.