Simplified Interval Type-2 Fuzzy Logic Systems

Author

Mendel, Jerry M. ; Xinwang Liu

Author_Institution

Ming Hsieh Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA

Volume

21

Issue

6

fYear

2013

fDate

Dec. 2013

Firstpage

1056

Lastpage

1069

Abstract

Type reduction (TR) followed by defuzzification is commonly used in interval type-2 fuzzy logic systems (IT2 FLSs). Because of the iterative nature of TR, it may be a computational bottleneck for the real-time applications of an IT2 FLS. This has led to many direct approaches to defuzzification that bypass TR, the simplest of which is the Nie-Tan direct defuzzification method (NT method). This paper provides some theoretical analyses of the NT method that answer the question “Why is the NT method good to use?” This paper also provides a direct relationship between TR followed by defuzzification (using KM algorithms) and the NT method. It also provides an improved NT method. Numerical examples illustrate our theoretical results and suggest that the NT method is a very good way to simplify an interval type-2 fuzzy set.

Keywords

approximation theory; fuzzy set theory; IT2 FLS; KM algorithms; Karnik-Mendel algorithms; NT method; Nie-Tan direct defuzzification method; TR; interval type-2 fuzzy set; simplified interval type-2 fuzzy logic systems; type reduction; Algorithm design and analysis; Approximation methods; Computer architecture; Frequency selective surfaces; Fuzzy logic; Real-time systems; Uncertainty; Defuzzification; Karnik–Mendel (KM) algorithms; Nie–Tan (NT) method; interval type-2 fuzzy set (IT2 FS); type reduction (TR);

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/TFUZZ.2013.2241771

Filename

6416036