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

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