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A class of nonconvex fuzzy optimization problems under granular differentiability concept

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  • Shi, Fangfang
  • Ye, Guoju
  • Liu, Wei
  • Zhao, Dafang

Abstract

The aim of this paper is to study a class of nonconvex optimization problems with fuzzy objective functions under granular differentiability concept. In order to get it, we give the definition of granular preinvex fuzzy functions and discuss its fascinating characteristics. In particular, two necessary and sufficient conditions for granular differentiable fuzzy functions to be granular preinvex are proved. As an application of granular preinvex fuzzy functions, we study a class of nonconvex fuzzy optimization problems with constraints, and obtain the existence of the optimal solution by solving the fuzzy variational inequalities. In addition, the developed theory is illustrated by some numerical examples.

Suggested Citation

  • Shi, Fangfang & Ye, Guoju & Liu, Wei & Zhao, Dafang, 2023. "A class of nonconvex fuzzy optimization problems under granular differentiability concept," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 430-444.
    • Handle: RePEc:eee:matcom:v:211:y:2023:i:c:p:430-444
    DOI: 10.1016/j.matcom.2023.04.021
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    References listed on IDEAS

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    1. Wu, Hsien-Chung, 2007. "The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function," European Journal of Operational Research, Elsevier, vol. 176(1), pages 46-59, January.
    2. Hsien-Chung Wu, 2007. "The Karush-Kuhn-Tucker optimality conditions for the optimization problem with fuzzy-valued objective function," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 203-224, October.
    3. Saima Rashid & Elbaz I. Abouelmagd & Sobia Sultana & Yu-Ming Chu, 2022. "NEW DEVELOPMENTS IN WEIGHTED n-FOLD TYPE INEQUALITIES VIA DISCRETE GENERALIZED â„ Ì‚-PROPORTIONAL FRACTIONAL OPERATORS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(02), pages 1-16, March.
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