A novel notion of dense fuzzy lock set was introduced as an extension of fuzzy sets. Learning experiences have a vital role in this fuzzy lock set instigation. The novel fuzzy lock set reduces the fuzziness of the situation. Occasionally, the players are bound to make little changes in their game strategies to reach their goal for some matrix game problems. It may lead to some changes in payoffs. In this scenario, a matrix game's payoffs are chosen as dense fuzzy lock sets to make the problem more realistic. This paper's prime intent is to develop a mathematical model of a matrix game that represents payoffs by triangular dense fuzzy lock sets. Initially, a new defuzzification function MagD(.) is defined to find a ranking order relation of the dense fuzzy lock sets. Then a pair of auxiliary dense fuzzy programming problems is established for two players. These two problems are transformed into two equivalent crisp linear programming problems applying the proposed defuzzification function and its linearity property. The reduced problems are solved using LINGO 17.0 software to determine each player's optimal strategies and the game values. One surprising fact of this approach is that the value of the game increases with the increment of the player's learning experience. The validity, applicability, and superiority of this proposed methodology are illustrated by considering a real‐life media share problem.

中文翻译：

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具有密集模糊收益的矩阵游戏

引入了一种新的稠密模糊锁集概念，作为模糊集的扩展。学习经验在这种模糊锁集策动中起着至关重要的作用。新颖的模糊锁集减少了情况的模糊性。有时候，玩家必定会对其游戏策略进行很少的改变以达到某些矩阵游戏问题的目标。这可能会导致收益的某些变化。在这种情况下，将矩阵游戏的收益选择为密集的模糊锁定集，以使问题更加逼真。本文的主要目的是开发一个矩阵游戏的数学模型，该模型通过三角密集模糊锁集来表示收益。最初，定义了一个新的反模糊化函数MagD（。），以找到密集模糊锁集的排序顺序关系。然后为两个参与者建立了一对辅助的密集模糊规划问题。这两个问题利用拟议的去模糊函数及其线性特性转化为两个等效的清晰线性规划问题。使用LINGO 17.0软件可以解决减少的问题，从而确定每个玩家的最佳策略和游戏价值。这种方法的一个令人惊讶的事实是，游戏价值随着玩家学习经验的增加而增加。通过考虑现实生活中的媒体共享问题，说明了该方法的有效性，适用性和优越性。使用LINGO 17.0软件可以解决减少的问题，从而确定每个玩家的最佳策略和游戏价值。这种方法的一个令人惊讶的事实是，游戏价值随着玩家学习经验的增加而增加。通过考虑现实生活中的媒体共享问题，说明了该方法的有效性，适用性和优越性。使用LINGO 17.0软件可以解决减少的问题，从而确定每个玩家的最佳策略和游戏价值。这种方法的一个令人惊讶的事实是，游戏价值随着玩家学习经验的增加而增加。通过考虑现实生活中的媒体共享问题，说明了该方法的有效性，适用性和优越性。