descriptionPublicationkeyboard_double_arrow_right Article 24 Oct 2019 English Publisher:Springer Science and Business Media LLCJournal:Journal of Global Optimization, volume 77, pages 27-52 (issn: 0925-5001, eissn: 1573-2916,

Authors: Manuel Arana-Jiménez; Carmen Sánchez-Gil;

doi: 10.1007/s10898-019-00841-7

handle: 10498/25369

On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers

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Abstract

The paper presents a new method for solving fully fuzzy linear programming problems with inequality constraints and parameterized fuzzy numbers, by means of solving multiobjective linear programming problems. The equivalence is proven between the set of nondominated solutions of the fully fuzzy linear programming problem and the set of weakly efficient solutions of the considered and related multiobjective linear problem. The whole set of nondominated solutions for a fully fuzzy linear programming problem is explicitly obtained by means of a finite generator set.

The first author was partially supported by the research project MTM2017-89577-P (MINECO, Spain), and the second author was partially supported by Spanish Ministry of Economy and Competitiveness through grants AYA2016-75931-C2-1-P, AYA2015-68012-C2-1, AYA2014-57490-P, AYA2013-40611-P, and from the Consejería de Educación y Ciencia (Junta de Andalucía) through TIC-101, TIC-4075 and TIC-114.

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University of Cádiz
Spain

Keywords

fully fuzzy linear programming problem, multiobjective optimization, Fuzzy and other nonstochastic uncertainty mathematical programming, Fully fuzzy linear programming problem, Parameterized fuzzy numbers, Multi-objective and goal programming, parameterized fuzzy numbers, Multiobjective optimization

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