Linear optimization with an arbitrary fuzzy relational inequality

In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated whereby an arbitrary function is considered as fuzzy composition. The feasible solution set is determined and compared with some common results in the literature. A necessary and s...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 206; pp. 89 - 102
Main Authors: Ghodousian, Amin, Khorram, Esmaile
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2012
Subjects:
Algorithms
Feasibility
Fuzzy
Fuzzy compositions and t-norms
Fuzzy logic
Fuzzy relational inequalities
Fuzzy relations
Fuzzy set theory
Inequalities
Linear objective function optimization
Lower bounds
Optimization
Fuzzy relational inequalities
Fuzzy relations
Fuzzy compositions and t-norms
Linear objective function optimization
ISSN:0165-0114, 1872-6801
Online Access:Get full text
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Summary:In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated whereby an arbitrary function is considered as fuzzy composition. The feasible solution set is determined and compared with some common results in the literature. A necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem. It is shown that in general a lower bound is always attainable for the optimal objective value. Moreover, we prove that the optimal solution of the problem is obtained if the problem is defined by a non-decreasing or non-increasing function. An algorithm is presented to summarize the process and an example is described to illustrate the algorithm.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2012.04.009