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

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

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.

Citation

Mendel, J. M., Eyoh, I., & John, R. (2020). Comparing Performance Potentials of Classical and Intuitionistic Fuzzy Systems in Terms of Sculpting the State Space. IEEE Transactions on Fuzzy Systems, 28(9), 2244-2254. https://doi.org/10.1109/TFUZZ.2019.2933786

• Journal Article Type: Article
• Acceptance Date: Jul 30, 2019
• Online Publication Date: Aug 7, 2019
• Publication Date: 2020-09
• Deposit Date: Aug 6, 2019
• Publicly Available Date: Aug 6, 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
• Volume: 28
• Issue: 9
• Pages: 2244-2254
• DOI: https://doi.org/10.1109/TFUZZ.2019.2933786
• Keywords: Control and Systems Engineering; Computational Theory and Mathematics; Applied Mathematics; Artificial Intelligence
• Public URL: https://nottingham-repository.worktribe.com/output/2397308
• 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.