The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems

Type-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasonings by using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper an algorithm is provided for constructing type-2 fuzzy reasoning relations of SISO type-2 fuzzy logic systems. First, we give some properties of extended t-(co)norm and simplify the expression of type-2 fuzzy reasoning relations in accordance with different input subdomains under certain conditions. And then different techniques are discussed to solve the simplified expressions on the input subdomains by using the related methods on solving fuzzy relation equations. Besides, it is pointed out that the computation amount level of the proposed algorithm is the same as that of polynomials and the possibility of applying the proposed algorithm in the construction of type-2 fuzzy reasoning relations is illustrated on several examples. Finally, the calculation of an arbitrary extended continuous t-norm can be obtained as the special case of the proposed algorithm.

Download Full-text

Study on center-of-sets type-reduction of interval type-2 fuzzy logic systems with noniterative algorithms

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202264 ◽

2021 ◽

pp. 1-8

Author(s):

Yang Chen ◽

Jiaxiu Yang

Keyword(s):

Fuzzy Logic ◽

Fuzzy Reasoning ◽

Fuzzy Logic Systems ◽

Simulation Experiments ◽

Potential Value ◽

Type Reduction ◽

Logic Systems ◽

Interval Type ◽

Open Question

In recent years, interval type-2 fuzzy logic systems (IT2 FLSs) have become a hot topic for the capability of coping with uncertainties. Compared with the centroid type-reduction (TR), investigating the center-of-sets (COS) TR of IT2 FLSs is more favorable for applying IT2 FLSs. Actually, it is still an open question for comparing Karnik-Mendel (KM) types of algorithms and other types of alternative algorithms for COS TR. This paper gives the block of fuzzy reasoning, COS TR, and defuzzification of IT2 FLSs based on Nagar-Bardini (NB), Nie-Tan (NT) and Begian-Melek-Mendel (BMM) noniterative algorithms. Six simulation experiments are used to show the performances of three types of noniterative algorithms. The proposed noniterative algorithms can obtain much higher computational efficiencies compared with the KM algorithms, which give the potential value for designing T2 FLSs.

Download Full-text

Design of back propagation optimized Nagar-Bardini structure-based interval type-2 fuzzy logic systems for fuzzy identification

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211006635 ◽

2021 ◽

pp. 014233122110066

Author(s):

Yang Chen ◽

Jiaxiu Yang

Keyword(s):

Fuzzy Logic ◽

Back Propagation ◽

Membership Functions ◽

Identification Problems ◽

Fuzzy Logic Systems ◽

Fuzzy Identification ◽

Logic Systems ◽

Academic Topic ◽

Interval Type

In recent years, fuzzy identification based on system identification theory has become a hot academic topic. Interval type-2 fuzzy logic systems (IT2 FLSs) have become a rising technology. This paper designs a type of Nagar-Bardini (NB) structure-based singleton IT2 FLSs for fuzzy identification problems. The antecedents of primary membership functions of IT2 FLSs are chosen as Gaussian type-2 primary membership functions with uncertain standard deviations. Then, the back propagation algorithms are used to tune the parameters of IT2 FLSs according to the chain rule of derivation. Compared with the type-1 fuzzy logic systems, simulation studies show that the proposed IT2 FLSs can obtain better abilities of generalization for fuzzy identification problems.

Download Full-text