On fuzzy relational equations and the covering problem

Previous studies have shown that fuzzy relational equations (FREs) based on either the max-continuous Archimedean t-norm or the max-arithmetic mean composition can be transformed into the covering problem, which is an NP-hard problem. Exploiting the properties common to the continuous Archimedean t-...

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Bibliographic Details
Published in:Information sciences 2011-07, Vol.181 (14), p.2951-2963
Main Authors: Lin, Jun-Lin, Wu, Yan-Kuen, Guu, Sy-Ming
Format: Article
Language:English
Subjects:
Arithmetic
Covering
Covering problem
Fuzzy
Fuzzy logic
Fuzzy relational equations
Fuzzy set theory
Gold
Mathematical analysis
Max-Archimedean t-norm composition
Max-arithmetic mean composition
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Summary:Previous studies have shown that fuzzy relational equations (FREs) based on either the max-continuous Archimedean t-norm or the max-arithmetic mean composition can be transformed into the covering problem, which is an NP-hard problem. Exploiting the properties common to the continuous Archimedean t-norm and the arithmetic mean, this study proposes a generalization of them as the “ u-norm”, enabling FREs that are based on the max-continuous u-norm composition also to be transformed into the covering problem. This study also proposes a procedure for transforming the covering problem into max-product FREs. Consequently, max-continuous u-norm FREs can be solved by extending any procedure for solving either the covering problem or max-product FREs.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2011.03.004