Decomposition and resolution of fuzzy relation equations (II) based on boolean-type implications

Authors:
Yanbin Luo;Chunjie Yang;Yongming Li;Daoying Pi
Affiliations:
National Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China;National Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China;Institute of Fuzzy Systems, College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an, China;National Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China
Venue:
AI'05 Proceedings of the 18th Australian Joint conference on Advances in Artificial Intelligence
Year:
2005

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Abstract

The problem of solving fuzzy relation equations (II) based on Boolean-type implications is studied in the present paper. Decomposition of fuzzy relation equations (II) based on Boolean-type implications is first presented in a finite case. Then, the solution existence of fuzzy relation equations (II) based on Boolean-type implications is discussed, and for nice Boolean-type implications, some new solvability criteria based upon the notion of ”solution matrices” are given. It is also shown that for each solution a of a fuzzy relation equation (II) based on Boolean-type implication, there exists a minimal solution a* of this equation, such that a* is less than or equal to a, whenever the solution set of this equation is nonempty. The complete solution set of fuzzy relation equation (II) based on Boolean-type implication can be determined by all minimal solutions of this equation. Finally, an effective method to solve fuzzy relation equations (II) based on Boolean-type implications is proposed.