Paper Info
Title
A survey on fuzzy relational equations, part I: classification and solvability
Abstract
Fuzzy relational equations play an important role in fuzzy set theory and fuzzy logic systems, from both of the theoretical and practical viewpoints. The notion of fuzzy relational equations is associated with the concept of "composition of binary relations." In this survey paper, fuzzy relational equations are studied in a general lattice-theoretic framework and classified into two basic categories according to the duality between the involved composite operations. Necessary and sufficient conditions for the solvability of fuzzy relational equations are discussed and solution sets are characterized by means of a root or crown system under some specific assumptions.
Year
DOI
Venue
2009
10.1007/s10700-009-9059-0
FO & DM
Keywords
Field
DocType
Fuzzy relational equation,Solvability,Duality,Adjointness,Triangular norm
Discrete mathematics,Fuzzy classification,Defuzzification,Fuzzy set operations,Fuzzy logic,Fuzzy mathematics,Fuzzy set,Type-2 fuzzy sets and systems,Fuzzy number,Mathematics
Journal
Volume
Issue
ISSN
8
2
1568-4539
Citations 
PageRank 
References 
44
1.34
91
Authors
2
Name
Order
Citations
PageRank
Pingke Li119310.03
Shu-Cherng Fang2115395.41