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Mario García-valdez - One of the best experts on this subject based on the ideXlab platform.
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A comparative study of type-1 Fuzzy Logic systems, interval type-2 Fuzzy Logic systems and generalized type-2 Fuzzy Logic systems in control problems
Information Sciences, 2016Co-Authors: Oscar Castillo, Leticia Amador-angulo, Juan R. Castro, Mario García-valdezAbstract:This paper presents a comparative study of type-2 Fuzzy Logic systems with respect to interval type-2 and type-1 Fuzzy Logic systems to show the efficiency and performance of a generalized type-2 Fuzzy Logic controller (GT2FLC). We used different types of Fuzzy Logic systems for designing the Fuzzy controllers of complex non-linear plants. The theory of alpha planes is used for approximating generalized type-2 Fuzzy Logic in Fuzzy controllers. In the defuzzification process, the Karnik and Mendel Algorithm is used. Simulation results with a type-1 Fuzzy Logic controller (T1FLC), an interval type-2 Fuzzy Logic controller (IT2FLC) and with a generalized type-2 Fuzzy Logic controller (GT2FLC) for benchmark plants are presented. The advantage of using generalized type-2 Fuzzy Logic in Fuzzy controllers is verified with four benchmark problems. We considered different levels of noise, number of alpha planes and four types of membership functions in the simulations for comparison and to analyze the approach of generalized type-2 Fuzzy Logic systems when applied in Fuzzy control.
Oscar Castillo - One of the best experts on this subject based on the ideXlab platform.
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A comparative study of type-1 Fuzzy Logic systems, interval type-2 Fuzzy Logic systems and generalized type-2 Fuzzy Logic systems in control problems
Information Sciences, 2016Co-Authors: Oscar Castillo, Leticia Amador-angulo, Juan R. Castro, Mario García-valdezAbstract:This paper presents a comparative study of type-2 Fuzzy Logic systems with respect to interval type-2 and type-1 Fuzzy Logic systems to show the efficiency and performance of a generalized type-2 Fuzzy Logic controller (GT2FLC). We used different types of Fuzzy Logic systems for designing the Fuzzy controllers of complex non-linear plants. The theory of alpha planes is used for approximating generalized type-2 Fuzzy Logic in Fuzzy controllers. In the defuzzification process, the Karnik and Mendel Algorithm is used. Simulation results with a type-1 Fuzzy Logic controller (T1FLC), an interval type-2 Fuzzy Logic controller (IT2FLC) and with a generalized type-2 Fuzzy Logic controller (GT2FLC) for benchmark plants are presented. The advantage of using generalized type-2 Fuzzy Logic in Fuzzy controllers is verified with four benchmark problems. We considered different levels of noise, number of alpha planes and four types of membership functions in the simulations for comparison and to analyze the approach of generalized type-2 Fuzzy Logic systems when applied in Fuzzy control.
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Type-2 Fuzzy Logic
Type-2 Fuzzy Logic: Theory and Applications, 2007Co-Authors: Oscar Castillo, Patricia MelinAbstract:We introduce in this chapter a new area in Fuzzy Logic, which is called type-2 Fuzzy Logic [84]. Basically, a type-2 Fuzzy set is a set in which we also have uncertainty about the membership function [42]. Of course, type-2 Fuzzy systems consist of Fuzzy if-then rules, which contain type-2 Fuzzy sets [13]. We can say that type-2 Fuzzy Logic is a generalization of conventional Fuzzy Logic (type-1) in the sense that uncertainty is not only limited to the linguistic variables but also is present in the definition of the membership functions [56].
Juan R. Castro - One of the best experts on this subject based on the ideXlab platform.
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A comparative study of type-1 Fuzzy Logic systems, interval type-2 Fuzzy Logic systems and generalized type-2 Fuzzy Logic systems in control problems
Information Sciences, 2016Co-Authors: Oscar Castillo, Leticia Amador-angulo, Juan R. Castro, Mario García-valdezAbstract:This paper presents a comparative study of type-2 Fuzzy Logic systems with respect to interval type-2 and type-1 Fuzzy Logic systems to show the efficiency and performance of a generalized type-2 Fuzzy Logic controller (GT2FLC). We used different types of Fuzzy Logic systems for designing the Fuzzy controllers of complex non-linear plants. The theory of alpha planes is used for approximating generalized type-2 Fuzzy Logic in Fuzzy controllers. In the defuzzification process, the Karnik and Mendel Algorithm is used. Simulation results with a type-1 Fuzzy Logic controller (T1FLC), an interval type-2 Fuzzy Logic controller (IT2FLC) and with a generalized type-2 Fuzzy Logic controller (GT2FLC) for benchmark plants are presented. The advantage of using generalized type-2 Fuzzy Logic in Fuzzy controllers is verified with four benchmark problems. We considered different levels of noise, number of alpha planes and four types of membership functions in the simulations for comparison and to analyze the approach of generalized type-2 Fuzzy Logic systems when applied in Fuzzy control.
Leticia Amador-angulo - One of the best experts on this subject based on the ideXlab platform.
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A comparative study of type-1 Fuzzy Logic systems, interval type-2 Fuzzy Logic systems and generalized type-2 Fuzzy Logic systems in control problems
Information Sciences, 2016Co-Authors: Oscar Castillo, Leticia Amador-angulo, Juan R. Castro, Mario García-valdezAbstract:This paper presents a comparative study of type-2 Fuzzy Logic systems with respect to interval type-2 and type-1 Fuzzy Logic systems to show the efficiency and performance of a generalized type-2 Fuzzy Logic controller (GT2FLC). We used different types of Fuzzy Logic systems for designing the Fuzzy controllers of complex non-linear plants. The theory of alpha planes is used for approximating generalized type-2 Fuzzy Logic in Fuzzy controllers. In the defuzzification process, the Karnik and Mendel Algorithm is used. Simulation results with a type-1 Fuzzy Logic controller (T1FLC), an interval type-2 Fuzzy Logic controller (IT2FLC) and with a generalized type-2 Fuzzy Logic controller (GT2FLC) for benchmark plants are presented. The advantage of using generalized type-2 Fuzzy Logic in Fuzzy controllers is verified with four benchmark problems. We considered different levels of noise, number of alpha planes and four types of membership functions in the simulations for comparison and to analyze the approach of generalized type-2 Fuzzy Logic systems when applied in Fuzzy control.
Scott Dick - One of the best experts on this subject based on the ideXlab platform.
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Toward complex Fuzzy Logic
IEEE Transactions on Fuzzy Systems, 2005Co-Authors: Scott DickAbstract:Complex Fuzzy Logic is a postulated Logic system that is isomorphic to the complex Fuzzy sets recently described in a previous paper. This concept is analogous to the many-valued Logics that are isomorphic to type-1 Fuzzy sets, commonly known as Fuzzy Logic. As with Fuzzy Logics, a complex Fuzzy Logic would be defined by particular choices of the conjunction, disjunction and complement operators. In this paper, an important assertion from a previous paper, that only the modulus of a complex Fuzzy membership should be considered in set theoretic (or Logical) operations, is examined. A more general mathematical formulation (the property of rotational invariance) is proposed for this assertion, and the impact of this property on the form of complex Fuzzy Logic operations is examined. All complex Fuzzy Logics based on the modulus of a vector are shown to be rotationally invariant. The case of complex Fuzzy Logics that are not rotationally invariant is examined using the framework of vector Logic. A candidate conjunction operator was identified, and the existence of a dual disjunction was proven. Finally, a discussion on the possible applications of complex Fuzzy Logic focuses on the phenomenon of regularity as a possible fuzzification of stationarity.
