Abstract
This article provides new application-independent perspectives about the performance potential of an intuitionistic (I-) fuzzy system over a (classical) Takagi-Sugeno-Kang (TSK) fuzzy system. It does this by extending sculpting the state-space works from a TSK fuzzy system to an I-fuzzy system. It demonstrates that, for piecewise-linear membership functions (trapezoids and triangles), an I-fuzzy system always has significantly more first-order rule partitions of the state space-the coarse sculpting of the state space-than does a TSK fuzzy system, and that some I-fuzzy systems also have more second-order rule partitions of the state space-the fine sculpting of the state space-than does a TSK fuzzy system. It is the author's conjecture that for piecewise-linear membership functions (trapezoids and triangles): it is the always significantly greater coarse (and possibly fine) sculpting of the state space that provides an I-fuzzy system with the potential to outperform a TSK fuzzy system, and that a type-1 I-fuzzy system has the potential to outperform an interval type-2 fuzzy system.
Highlights
RECENTLY, Mendel [1], [2] explained the performance potential1 of type-1 (T1), interval type-2 (IT2) and general type-2 (GT2) rule-based fuzzy systems that use a singleton fuzzifier and piecewise-linear membership functions as a greater sculpting of the state space
A T1 I-fuzzy system is described by two subsets of rules, one for the membership function (MF) and the other for the non-membership function (NMF); its output can be obtained in either of two ways [5], [6]: (1) the MF and NMF sub-systems are coupled by taking a linear combination of their outputs, or (2) the two subsets of rules are viewed as one larger set of rules, and their outputs are aggregated in the usual way by means of some defuzzification method
This means that, as Q increases, there will be a factor of approximately 2p more first-order rule partitions of X1 × !× X p in an I-fuzzy system than the number of such partitions in a TSK fuzzy system, which leads to our conjecture that the hugely-greater coarse sculpting of the state space by an I-fuzzy system provides it with the potential to outperform a TSK fuzzy system
Summary
RECENTLY, Mendel [1], [2] explained the performance potential of type-1 (T1), interval type-2 (IT2) and general type-2 (GT2) rule-based fuzzy systems (fuzzy systems, for short) that use a singleton fuzzifier and piecewise-linear membership functions (trapezoids and triangles) as a greater sculpting of the state space. The goal of this paper is to provide further understanding of the performance improvement potential of a T1 I-fuzzy system over a T1 fuzzy system, because it is only if such performance improvement potential exists should one even consider using a T1 I-fuzzy system This goal is accomplished by providing new additional explanations for the improved performance in terms of sculpting the state space due to using I-FSs. The author’s conjecture is that, for piecewise-linear MFs (trapezoids and triangles): It is the always significantly greater coarse (and possibly finer) sculpting of the state space accomplished by using I-FSs that. TFS-2019-0288R.1 provides a T1 I-fuzzy system with the potential to outperform a T1 fuzzy system
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