# Decomposition and Resolution of Fuzzy Relation Equations (II) Based on Boolean-Type Implications

• Yanbin Luo
• Chunjie Yang
• Yongming Li
• Daoying Pi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3809)

## 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.

## Keywords

Minimal Solution Resolution Problem Fuzzy Relation Great Solution Minimal Subset
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Yanbin Luo
• 1
• Chunjie Yang
• 1
• Yongming Li
• 2
• Daoying Pi
• 1
1. 1.National Laboratory of Industrial Control TechnologyZhejiang UniversityHangzhouChina
2. 2.Institute of Fuzzy Systems, College of Mathematics and Information SciencesShaanxi Normal UniversityXi’anChina