Solving multi-objective fuzzy matrix games via multi-objective linear programming approach

Aggarwal, Abha; Khan, Imran

doi:10.14736/kyb-2016-1-0153

Cited by 5 publications

(17 citation statements)

References 17 publications

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“…In this paper, a new game with I-fuzzy goals named MOIFG has been constructed for solving multi-criteria programming problems, which is different from MOFG that was studied by Aggarwal and Khan [33]. For the solution of such games, certain definitions of I-fuzzy POSS and I-fuzzy security level are also defined.…”

Section: Discussionmentioning

confidence: 99%

“…In this section, a review of (crisp) multi-criteria zero sum game of two persons model (given by Fernandez et al [41], while its generalized model with fuzzy goals was proposed by Aggarwal and Khan in [33]) are presented.…”

Section: Multi-criteria Zero Sum Gamementioning

confidence: 99%

“…To illustrate our multi-criteria model and show its resourcefulness, the same example is solved as taken by Cook [45], Nishizaki and Sakwaw [26] and Aggarwal and Imran [33]. The choice of this example will lead us to making a comprehensive comparison with the existing models.…”

Section: Illustrative Examplementioning

confidence: 99%

“…The solution model of Aggarwal and Khan [33] is much better, as it explicitly deals with the individual fuzzy goal related to the different criteria; in addition, their results are far better. Their solutions to Example 1 are presented in Tables 3 and 4 for Player I and Player II respectively.…”

Section: Comparison With Existing Modelsmentioning

confidence: 99%

“…• In addition, there are some other lapses in the Nishizaki and Sakwaw's model, like the slight error in the linear programming model for Player II explained in [28,33], and our model produces much better strategies with higher securities as max(α 1 , α 2 , α 3 ) ≥ 0.88 > λ = 0.33088 and max(γ 1 , γ 2 , γ 3 ) ≥ 0.9 > 1 − σ = 0.4196. • Aggarwal and Khan's model of solving zero sum game is more promising and quite better than Nishizaki and Sakwaw's model.…”

Section: Comparison With Existing Modelsmentioning

confidence: 99%

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Intuitionistic-Fuzzy Goals in Zero-Sum Multi Criteria Matrix Games

et al. 2017

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Abstract:The classical matrix theory is deficient to express the vagueness of the real life. The fuzzy set theory has been successfully applied to bridge this gap. Much work has already been done on a two-person zero sum matrix game with fuzzy goals. In continuation, this paper is dedicated to define and study a multi-criteria two-person zero sum game with intuitionistic fuzzy goals. It is shown that solving such games is equivalent to solving two crisp multi object linear programming problems. Our work generalizes the previous study on a multi-criteria game with fuzzy goals by adopting the approach of linear programming with intuitionistic fuzzy sets. Finally, an illustrative numerical example is provided to elaborate the proposed approach.

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Section: Discussionmentioning

confidence: 99%

Section: Multi-criteria Zero Sum Gamementioning

confidence: 99%

Section: Illustrative Examplementioning

confidence: 99%

Section: Comparison With Existing Modelsmentioning

confidence: 99%

Section: Comparison With Existing Modelsmentioning

confidence: 99%

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Intuitionistic-Fuzzy Goals in Zero-Sum Multi Criteria Matrix Games

et al. 2017

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Two-person game with hesitant fuzzy payoff: An application in MADM

Jana

Roy

2021

RAIRO-Oper. Res.

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Hesitant Fuzzy Set (HFS) permits the membership function having a collection of probable values which are more effective for modelling the real-life problems. Multiple Attribute Decision Making (MADM) process apparently assesses multiple conflicting attribute in decision making. In traditional decision making problems, each player is moving independently whereas in reality it is seen that each player aims to maximize personal profit which causes a negative impact on other player. MADM problem treats with candidate to the best alternative corresponding to the several attributes. Here, we present an MADM problem under hesitant fuzzy information and then transforming it into two-person matrix game, referred to herein as MADM game. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one of the prominent approach for solving the MADM problems. In this work, we develop the TOPSIS based on Ordered Weighted Aggregation (OWA) operator and hybrid hesitant fuzzy normalized Euclidean distance. Then the two approaches, namely Hybrid Hesitant Fuzzy Ordered Weighted Aggregation-TOPSIS (HHFOWA-TOPSIS) and the Linear Programming Problem (LPP) are applied to solve the formulated MADM game. For solving MADM game, we apply LPP by considering the various values of $\alpha, \psi$, and HHFOWA-TOPSIS for finding the optimal alternative according to their scores. An investment selection problem is included to explain the feasibility and superiority of our formulated approaches. A comparison analysis is drawn among the obtained results which are derived from the two approaches. LPP and HHFOWA-TOPSIS provide the best alternative for the proposed problem. Finally, conclusions about our findings and outlooks are described.

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