Abstract
Single-valued neutrosophic set (SVNS) is considered as generalization and extension of fuzzy set, intuitionistic fuzzy set (IFS), and crisp set for expressing the imprecise, incomplete, and indeterminate information about real-life decision-oriented models. The theme of this research is to develop a solution approach to solve constrained bimatrix games with payoffs of single-valued trapezoidal neutrosophic numbers (SVTNNs). In this approach, the concepts and suitable ranking function of SVTNNs are defined. Hereby, the equilibrium optimal strategies and equilibrium values for both players can be determined by solving the parameterized mathematical programming problems, which are obtained from two novel auxiliary SVTNNs programming problems based on the proposed ranking approach of SVTNNs. Moreover, an application example is examined to verify the effectiveness and superiority of the developed algorithm. Finally, a comparison analysis between the proposed and the existing approaches is conducted to expose the advantages of our work.
Highlights
Constrained bimatrix games are nonzero-sum two-player noncooperative games which play a dominant role in many real-life applications such as in military, finance, economy, strategic welfares, cartel behaviour, management models, social problems or auctions, political voting systems, races, and development research [1, 2]
Zadeh [3] introduced the fuzzy set concept and since various researchers have extended it to the different sets such as interval intuitionistic fuzzy set, IFS, linguistic interval IFS, and cubic IFS
We introduce the basic concepts of fuzzy sets, IFSs, neutrosophic set (NS), Single-valued neutrosophic set (SVNS), and single-valued neutrosophic numbers (SVNNs)
Summary
Constrained bimatrix games are nonzero-sum two-player noncooperative games which play a dominant role in many real-life applications such as in military, finance, economy, strategic welfares, cartel behaviour, management models, social problems or auctions, political voting systems, races, and development research [1, 2]. (1) To propose a novel constrained bimatrix games model with SVTNNs payoffs (2) To develop an effective algorithm for SVTNN constrained bimatrix games to obtain the optimal strategies for such games (3) To formulate crisp linear optimization problems from the neutrosophic models based on the defined ambiguity and value indexes of SVTNN (4) To present an application example to demonstrate the effectiveness and applicability of the proposed method (5) To compare our results with other existing approaches e remainder of the manuscript is summarized as follows.
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