Generalized convexity in fuzzy vector optimization through a linear ordering

In this article we study efficiency and weakly efficiency in fuzzy vector optimization. After formulating the problem, we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized Hukuhara differentiability, pseudoinvexity-I and pseudoinvexity-II. We prov...

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Bibliographic Details
Published in:Information sciences 2015-08, Vol.312, p.13-24
Main Authors: Arana-Jiménez, M., Rufián-Lizana, A., Chalco-Cano, Y., Román-Flores, H.
Format: Article
Language:English
Subjects:
Computational efficiency
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy vector optimization
Generalized Hukuhara differentiability
Mathematical analysis
Mathematical models
Necessary and sufficient conditions of optimality
Optimization
Vectors (mathematics)
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Summary:In this article we study efficiency and weakly efficiency in fuzzy vector optimization. After formulating the problem, we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized Hukuhara differentiability, pseudoinvexity-I and pseudoinvexity-II. We prove that pseudoinvexity is the necessary and sufficient condition for a stationary point to be a solution of a fuzzy vector optimization problem. We give conditions to insure that a fuzzy vector mapping is invex and pseudoinvex (I and II). Moreover, we present some examples to illustrate the results. Lastly, we use these results to study the class of problems which have uncertainty and inaccuracies in the objective function coefficients of mathematical programming models.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2015.03.045