A New Decomposition Linear Programming Model to Solve Zero Sum Two Person Matrix Game in Fully Fuzzy Trapezoidal Environment

G. Sharma, Ganesh Kumar
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Abstract

This article targets to unriddle the problem of a non-cooperative fully fuzzified ’Zero Sum Two Person Matrix Game’ (ZSTPMG) with payoff matrix equipped with Trapezoidal fuzzy numbers (TrFNs). To achieve the target a unique and novel decomposition technique has been introduced. First, we develop two auxiliaries fully fuzzified linear programming problem (FFLPP) models for both the players and then we decompose these two FFLPP models into four linear programming (LP) models each, for both the players. These eight LP models are then solved by using the software TORA-2.0. The solutions of these eight LP models ascertain the optimal strategies and the optimal value of the fully fuzzified ZSTPMG for both the players. Our technique has an advantage over the existing ones as it can solve fully fuzzified ZSTPMG with all kind of TrFNs such as symmetric, asymmetric, positive or negative TrFNs. To establish this fact, the proposed methodology has been illustrated by taking three numericals equipped with various kinds of TrFNs.
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全模糊梯形环境下求解零和二人矩阵对策的一种新的分解线性规划模型
本文旨在揭示具有梯形模糊数(TrFNs)的收益矩阵的非合作完全模糊“零和二人矩阵博弈”问题。为了实现这一目标,引入了一种独特而新颖的分解技术。首先,我们为两个参与者建立了两个辅助的完全模糊线性规划问题(FFLPP)模型,然后我们将这两个FFLPP模型分解为四个线性规划(LP)模型,分别用于两个参与者。然后利用TORA-2.0软件对这8个LP模型进行求解。这8个LP模型的解确定了两方的最优策略和全模糊ZSTPMG的最优值。与现有的方法相比,我们的方法具有一定的优势,可以解决对称、不对称、正、负TrFNs等各种TrFNs的完全模糊ZSTPMG。为了确定这一事实,所提出的方法已通过采用配备各种TrFNs的三个数字来说明。
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来源期刊
CiteScore
3.80
自引率
6.20%
发文量
57
审稿时长
20 weeks
期刊介绍: IJMEMS is a peer reviewed international journal aiming on both the theoretical and practical aspects of mathematical, engineering and management sciences. The original, not-previously published, research manuscripts on topics such as the following (but not limited to) will be considered for publication: *Mathematical Sciences- applied mathematics and allied fields, operations research, mathematical statistics. *Engineering Sciences- computer science engineering, mechanical engineering, information technology engineering, civil engineering, aeronautical engineering, industrial engineering, systems engineering, reliability engineering, production engineering. *Management Sciences- engineering management, risk management, business models, supply chain management.
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