Solving Fuzzy Relational Equations Via Semitensor Product

Author

Daizhan Cheng ; Jun-e Feng ; Hongli Lv

Author_Institution

Inst. of Syst. Sci., Beijing, China

Volume

20

Issue

2

fYear

2012

fDate

4/1/2012 12:00:00 AM

Firstpage

390

Lastpage

396

Abstract

The problem of solving max-min fuzzy relational equations is investigated. First, we show that if there is a solution, then there is a corresponding solution within the set of parameters [briefly, the parameter set solution (PSS)]. Then, the semitensor product of matrices is used to convert the logical equations into algebraic equations via the vector expression of logical variables. Under this form, every PSS can be obtained. It is proved that all the solutions can be revealed from their corresponding PSS. Some examples are presented to demonstrate the algorithm to solve fuzzy relational equations.

Keywords

formal logic; fuzzy set theory; matrix algebra; minimax techniques; relational algebra; vectors; algebraic equations; logical equations; matrices; max-min fuzzy relational equations; parameter set solution; semitensor product; vector expression; Approximation algorithms; Bismuth; Educational institutions; Equations; Inference algorithms; Matrix converters; Vectors; Fuzzy relational equation (FRE); multivalued logic; parameter set solution (PSS); semitensor product;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/TFUZZ.2011.2174243

Filename

6064885