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Comparing Performance Potentials of Classical and Intuitionistic Fuzzy Systems in Terms of Sculpting the State Space

Mendel, Jerry M.; Eyoh, Imo; John, Robert

Authors

Jerry M. Mendel

Imo Eyoh

Robert John



Abstract

This paper provides new application-independent perspectives about the performance potential of an intuitionistic (I-) fuzzy system over a (classical) 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. Index Terms-intuitionistic fuzzy sets, intuitionistic fuzzy systems, TSK fuzzy systems, rule partitions, sculpting the state space.

Journal Article Type Article
Publication Date Aug 7, 2019
Journal IEEE Transactions on Fuzzy Systems
Print ISSN 1063-6706
Electronic ISSN 1941-0034
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
APA6 Citation Mendel, J. M., Eyoh, I., & John, R. (2019). Comparing Performance Potentials of Classical and Intuitionistic Fuzzy Systems in Terms of Sculpting the State Space. IEEE Transactions on Fuzzy Systems, doi:10.1109/TFUZZ.2019.2933786
DOI https://doi.org/10.1109/TFUZZ.2019.2933786
Keywords Control and Systems Engineering; Computational Theory and Mathematics; Applied Mathematics; Artificial Intelligence
Publisher URL https://ieeexplore.ieee.org/document/8790981
Additional Information © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

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