A New Technique to Solve Game Matrix with Neutrosophic Payoffs
Matrix games are extensively applied to conflicting situations that frequently arise in real world since it gives the ability to the decision maker to make more informed decisions. However, modeling of such situations often cannot be done by conventional techniques as the payoffs may not be concrete...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of New Mexico
2025-07-01
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| Series: | Neutrosophic Sets and Systems |
| Subjects: | |
| Online Access: | https://fs.unm.edu/NSS/13GameMatrix.pdf |
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| Summary: | Matrix games are extensively applied to conflicting situations that frequently arise in real world since it gives the ability to the decision maker to make more informed decisions. However, modeling of such situations often cannot be done by conventional techniques as the payoffs may not be concretely determined due to uncertainty present in the system. This uncertainty can be handled in numerous ways but neutrosophic set theory plays an important role in examining intricacy, inadequacy, enigma and self-contradictory parameters in real life problems. This article develops a more structured technique to solve neutrosophic game matrix with payoffs as Single Valued Trapezoidal Neutrosophic (SVTrN) numbers. This method converts the considered game matrix to interval valued game matrix problem by using (α, β, γ)- cut on SVTrN numbers. This interval valued game matrix problem is further converted to a crisp game matrix (pessimistic, optimistic and moderate )problem by using a ranking function. Then, these problems are solved by maxmin theorem if saddle point exist. In case of no saddle point or many saddle points, the problem is solved by converting it to linear programming primal-dual problem. The proposed technique can be applied to a wider range of game theory problems existing in practical, as the data encountered in practice is often imprecise with some level of hesitation, inconsistent or incompleteness which can best be described using single valued neutrosophic number. Numerical illustrations are provided to demonstrate the methodology and to prove the vitality of the proposed method. |
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| ISSN: | 2331-6055 2331-608X |