Optimal Solution of Nonlinear Fuzzy Optimization Problem under Linear Order Relation

2018/02/23 by Umme Salma M. Pirzada, Pirzada, Umme Salma M.
Decision Sciences · Engineering · Mathematics · #FOS: Mathematics #Fuzzy Systems and Optimization #General Mathematics (math.GM) #Multi-Criteria Decision Making #Optimization and Mathematical Programming

paper · pdf · doi:10.48550/arxiv.1802.09909

openalex publication_date 2018/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Multi-variable nonlinear fuzzy optimization problem is considered under linear order relation on fuzzy numbers. Using gH-differentiability of a fuzzy-valued function f, new necessary and sufficient optimality conditions are proposed. The optimality conditions are obtained without putting additional conditions on fuzzy-valued functions like, convexity, quasi-convexity, pseudo-convexity. Optimum solution of the fuzzy optimization problem is obtained based on the optimality conditions. Illustrations and a case study are given to explain the numerical applications of the proposed results. Comparison of optimality conditions from existing literature is given.

Citations

• Differentials of fuzzy functions

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