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Toward a Fuzzy Logic System Based on General Forms of Interval Type-2 Fuzzy Sets

机译:基于区间第二类模糊集一般形式的模糊逻辑系统

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Recent years have witnessed a widespread in the use of interval type-2 fuzzy logic systems (IT2 FLSs) in real-world applications. It has been shown recently that interval type-2 fuzzy sets (IT2 FSs) are more general than interval-valued fuzzy sets (IV FSs) [1]. Hence, there is a need to explore the capabilities of the more general forms of IT2 FSs (beyond IV FSs) and the applications areas they will be more suitable for. In addition, there is a need to develop the theory of the general forms of IT2 FLSs (gfIT2 FLSs), which employ IT2 FSs that are not equivalent to IV FSs and can have nonconvex secondary membership functions (MFs). Although these systems could be considered within the scope of general type-2 FLSs (GT2 FLSs), the practical implementation of GT2 FLSs has traditionally required the secondary MFs to be convex and normal type-1 fuzzy sets (T1 FSs). In addition, the type-reduction operation still presents a challenge for GT2 FLSs because of its computational complexity. In this paper, we present a complete framework for a type-2 FLS that uses the most recent perception of IT2 FSs (the so called general forms of interval type-2 fuzzy sets, gfIT2 FSs), whose secondary grades can be nonconvex T1 FSs. This framework includes new equations for the meet and join operations of gfIT2 FSs, as well as a new type reduction procedure for the type-2 FLS involving gfIT2 FSs. In addition, we present the type-2 FLS operation for singleton and nonsingleton fuzzification. We will introduce the various operations employed within a gfIT2 FLSs, from fuzzification (including singleton and nonsingleton) to inference, type-reduction, and defuzzification. We will also present two examples in which these gfIT2 FSs arise naturally when modeling sonar sensors input noise and the antecedents/consequents from a survey including different users.
机译:近年来,在现实应用中广泛使用间隔2型模糊逻辑系统(IT2 FLS)。最近显示,区间2型模糊集(IT2 FS)比区间值模糊集(IV FS)更通用[1]。因此,有必要探索更通用形式的IT2 FS(超越IV FS)的功能以及它们将更适合的应用领域。另外,需要发展IT2 FLS(gfIT2 FLS)的一般形式的理论,这些理论采用的IT2 FS不等同于IV FS,并且可以具有非凸次要隶属函数(MF)。尽管可以将这些系统视为通用的2型FLS(GT2 FLS)的范围,但GT2 FLS的实际实施传统上要求次级MF为凸型和标准1型模糊集(T1 FS)。此外,类型缩减操作由于其计算复杂性,仍然对GT2 FLS构成挑战。在本文中,我们提供了一个使用最新的IT2 FS感知的2型FLS完整框架(所谓的间隔2型模糊集的一般形式,gfIT2 FS),其次级等级可以是非凸T1 FS。 。该框架包括用于gfIT2 FS的满足和连接操作的新方程式,以及涉及gfIT2 FS的2型FLS的新类型简化程序。此外,我们介绍了用于单例和非单例模糊化的2型FLS操作。我们将介绍gfIT2 FLS中采用的各种操作,从模糊化(包括单例和非单例)到推理,类型减少和反模糊化。我们还将提供两个示例,其中在对声纳传感器输入噪声和来自包括不同用户的调查得出的先验结果进行建模时,这些gfIT2 FS会自然出现。

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