Fractional Programming for Stackelberg Game Under Type-2 Fuzzy Environment

Sumit Kumar Maiti; Sankar Kumar Roy; Chinmay Saha; Gora Das

doi:10.2298/YJOR230915049M

Authors

Sumit Kumar Maiti Department of Applied Science & Humanities, Haldia Institute of Technology Haldia, India https://orcid.org/0000-0002-1022-2083
Sankar Kumar Roy Department of Applied Mathematics, Vidyasagar University, Midnapore, India https://orcid.org/0000-0003-4478-1534
Chinmay Saha Department of Applied Science & Humanities, Haldia Institute of Technology Haldia, India https://orcid.org/0009-0009-0416-8875
Gora Das Department of Applied Science & Humanities, Haldia Institute of Technology Haldia, India https://orcid.org/0009-0007-9972-6467

DOI:

https://doi.org/10.2298/YJOR230915049M

Keywords:

Bi-level fractional programming, Taylor series, GA and PSO, type-2 fuzzy number, Stackelberg game, intuitionistic fuzzy programming

Abstract

This study intends to present a Stackelberg game model for design of the fractional type-2 fuzzy programming. In achieving this aspiration, we develop a probabilistic fuzzy multi-objective fractional linear programming where the entire parameters are of type-2 fuzzy numbers apart from the right-hand side of the constraints are follow Weibull distribution. In the projected approach, the membership function allied with each objective function is generated by using the first-order Taylor series approximation and converted into a single objective function by assuming the weights of the objective functions are equal. Type conversion is made in two ways by existing methods, and using stochastic programming, the probabilistic constraints are transformed into a deterministic form. The accessible model incorporates the non-linear programming viewpoint of the decision-maker and is solved with the help of intuitionistic fuzzy programming (IFS). A comparison study on the optimum results by genetic algorithm (GA) and particle swarm optimization (PSO) with the LINGO 15.0 iterative scheme is offered to resolve the created bi-level programming problem (BLPP) in the course of the Stackelberg game. To make obvious the feasibility of the projected representation and solution methodology, realistic data are measured and results are presented through several discussions.

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Fractional Programming for Stackelberg Game Under Type-2 Fuzzy Environment

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