Interval Type-2 Fuzzy Logic Systems Made Simple

Interval Type-2 Fuzzy Logic Systems Made Simple

VOL. 14, NO. 6, DECEMBER 2006 | Jerry M. Mendel, Life Fellow, IEEE, Robert I. John, Member, IEEE, and Feilong Liu, Student Member, IEEE
This paper addresses the computational complexity and educational burden associated with using interval type-2 fuzzy logic systems (IT2 FLSs), which are often preferred over general type-2 fuzzy logic systems (T2 FLSs) due to their practicality. The authors argue that the complexity of T2 FS mathematics is a significant barrier to the adoption of IT2 FLSs. They demonstrate that all necessary results for implementing an IT2 FLS can be derived using type-1 fuzzy set (T1 FS) mathematics, making IT2 FLSs more accessible. The paper provides a tutorial on IT2 FSs, including their representation, set-theoretic operations, and the derivation of formulas for union, intersection, and complement. It also discusses the structure of an IT2 FLS, focusing on single-rule scenarios with crisp or T1 FS inputs, and extends these results to multiple antecedents and rules. The authors conclude that their approach significantly simplifies the implementation of IT2 FLSs, making them more widely applicable.This paper addresses the computational complexity and educational burden associated with using interval type-2 fuzzy logic systems (IT2 FLSs), which are often preferred over general type-2 fuzzy logic systems (T2 FLSs) due to their practicality. The authors argue that the complexity of T2 FS mathematics is a significant barrier to the adoption of IT2 FLSs. They demonstrate that all necessary results for implementing an IT2 FLS can be derived using type-1 fuzzy set (T1 FS) mathematics, making IT2 FLSs more accessible. The paper provides a tutorial on IT2 FSs, including their representation, set-theoretic operations, and the derivation of formulas for union, intersection, and complement. It also discusses the structure of an IT2 FLS, focusing on single-rule scenarios with crisp or T1 FS inputs, and extends these results to multiple antecedents and rules. The authors conclude that their approach significantly simplifies the implementation of IT2 FLSs, making them more widely applicable.
Reach us at info@study.space