Matrix Games under an Intuitionistic Fuzzy Duality Approach with Exponential Functions: MRI-Related Cochlear Implant Analysis

Sandeep Kumar; Aashish; Parth Parashar

doi:10.31181/sdmap41202767

Authors

Sandeep Kumar Department of Mathematics, Chaudhary Charan Singh University, Meerut, 250004, Uttar Pradesh, India Author https://orcid.org/0000-0001-6169-4606
Aashish Department of Mathematics, Chaudhary Charan Singh University, Meerut, 250004, Uttar Pradesh, India Author https://orcid.org/0009-0008-8842-6255
Parth Parashar Department of Mathematics, Chaudhary Charan Singh University, Meerut, 250004, Uttar Pradesh, India Author https://orcid.org/0009-0007-4148-4776

DOI:

https://doi.org/10.31181/sdmap41202767

Keywords:

Two-person zero sum matrix game, Intuitionistic fuzzy goals, Exponential functions

Abstract

Game theory has evolved to incorporate various forms of uncertainty. The intuitionistic fuzzy (I-Fuzzy) framework is a powerful tool for modeling such uncertainties, particularly in two-person zero-sum matrix games (TZMGs) with imprecise goals. This study addresses TZMGs where goals are represented in I-Fuzzy form under pessimistic, optimistic, and mixed approaches. By applying exponential functions, optimization problems are constructed for each player. These problems are then transformed into crisp linear programming problems (LPPs) using logarithmic functions, enabling the derivation of optimal strategies. The role and impact of the shape parameter in exponential functions are analyzed, highlighting its influence through comparative insights. To illustrate the effectiveness and real-world relevance of the proposed approach, a practical healthcare problem evaluating adverse MRI effects on cochlear implant (CI) users is solved, showcasing both the methodology's applicability and its potential for decision-making under uncertainty.

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