Interval Type-2 Fuzzy Logic Systems Made Simple

Interval Type-2 Fuzzy Logic Systems Made Simple

December 2006 | Jerry M. Mendel, Life Fellow, IEEE, Robert I. John, Member, IEEE, and Feilong Liu, Student Member, IEEE
This paper introduces a simplified approach to interval type-2 fuzzy logic systems (IT2 FLS). The authors argue that it is unnecessary to use general type-2 fuzzy set (T2 FS) mathematics to implement an IT2 FLS, as all required results can be obtained using type-1 (T1) FS mathematics. This simplification makes IT2 FLS more accessible to readers and practitioners. The paper provides a novel tutorial that explains the concepts of IT2 FS, including their representation, set-theoretic operations, and application in fuzzy logic systems. It also demonstrates how to derive formulas for the union, intersection, and complement of IT2 FSs using T1 FS mathematics. The paper further explains how to apply these concepts to develop IT2 FLS, starting with a single rule and one antecedent, and then extending to multiple antecedents and rules. The authors emphasize that the key to implementing an IT2 FLS lies in understanding the concept of the footprint of uncertainty (FOU), which is a bounded region that characterizes the uncertainty in the primary memberships of an IT2 FS. The paper concludes that using T1 FS mathematics allows for a more straightforward and efficient implementation of IT2 FLS, making them more practical for real-world applications.This paper introduces a simplified approach to interval type-2 fuzzy logic systems (IT2 FLS). The authors argue that it is unnecessary to use general type-2 fuzzy set (T2 FS) mathematics to implement an IT2 FLS, as all required results can be obtained using type-1 (T1) FS mathematics. This simplification makes IT2 FLS more accessible to readers and practitioners. The paper provides a novel tutorial that explains the concepts of IT2 FS, including their representation, set-theoretic operations, and application in fuzzy logic systems. It also demonstrates how to derive formulas for the union, intersection, and complement of IT2 FSs using T1 FS mathematics. The paper further explains how to apply these concepts to develop IT2 FLS, starting with a single rule and one antecedent, and then extending to multiple antecedents and rules. The authors emphasize that the key to implementing an IT2 FLS lies in understanding the concept of the footprint of uncertainty (FOU), which is a bounded region that characterizes the uncertainty in the primary memberships of an IT2 FS. The paper concludes that using T1 FS mathematics allows for a more straightforward and efficient implementation of IT2 FLS, making them more practical for real-world applications.
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