Posynomial geometric programming problem subject to max–min fuzzy relation equations

We discuss a class of posynomial geometric programming problem(PGPF), aimed at minimizing a posynomial subject to fuzzy relational equations with max–min composition. By introducing auxiliary variables, we convert the PGPF into an equivalent programming problem whose objective function is a non-decr...

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Bibliographic Details
Published inInformation sciences Vol. 328; pp. 15 - 25
Main Authors Zhou, Xue-Gang, Yang, Xiao-Peng, Cao, Bing-Yuan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 20.01.2016
Subjects
Equivalence
Fuzzy
Fuzzy logic
Fuzzy relation equation
Fuzzy set theory
Mathematical analysis
Mathematical models
Max–min composition
Optimization
Posynomial geometric programming
Programming
Max–min composition
Posynomial geometric programming
Fuzzy relation equation
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Summary:We discuss a class of posynomial geometric programming problem(PGPF), aimed at minimizing a posynomial subject to fuzzy relational equations with max–min composition. By introducing auxiliary variables, we convert the PGPF into an equivalent programming problem whose objective function is a non-decreasing function with an auxiliary variable. We show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem. In addition, we introduce some rules for simplifying the problem. Then by using a branch and bound method and fuzzy relational equations (FRE) path, we present an algorithm to obtain an optimal solution to the PGPF. Finally, numerical examples are provided to illustrate the steps of the procedure.
Bibliography:ObjectType-Article-1
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content type line 23
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2015.07.058