Ebook: Fuzzy Solution Concepts for Non-cooperative Games. Interval, Fuzzy and Intuitionistic Fuzzy Payoffs

In the last decades, several methods have been proposed in the literature to find the solution of non-cooperative games with interval/fuzzy/intuitionistic fuzzy payoffs. However, after a deep study, it is observed that some mathematically incorrect assumptions have been considered in all these methods. Therefore, it is scientifically incorrect to use the existing methods to find the solution of real-life non-cooperative games with interval/fuzzy/intuitionistic fuzzy payoffs. The aim of this book is to provide the valid methods for solving different types of non-cooperative games with interval/fuzzy/intuitionistic fuzzy payoffs and to make the researchers aware about those mathematically incorrect assumptions which are considered in the existing methods. The contents of the book are divided into six chapters. In Chap. 1, a new method (named as Gaurika method) is proposed to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for matrix games (or two-person zero-sum games) with interval payoffs (matrix games in which payoffs are represented by intervals). Furthermore, to illustrate the proposed Gaurika method, some existing numerical problems of matrix games with interval payoffs are solved by the proposed Gaurika method. In Chap. 2, the method (named as Mehar method) to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for matrix games with fuzzy payoffs (matrix games in which payoffs are represented as fuzzy numbers) is proposed. Furthermore, to illustrate the proposed Mehar method, the existing numerical problems of matrix games with fuzzy payoffs are solved by the proposed Mehar method. In Chap. 3, a new method (named as Vaishnavi method) is proposed to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for constrained matrix games with fuzzy payoffs (constrained matrix games in which payoffs are represented by fuzzy numbers). In Chap. 4, new methods (named as Ambika method-I, Ambika method-II, Ambika method-III and Ambika method-IV) are proposed to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for matrix games with intuitionistic fuzzy payoffs (matrix games in which payoffs are represented by intuitionistic fuzzy numbers). Furthermore, to illustrate proposed Ambika methods, some existing numerical problems of matrix games with intuitionistic fuzzy payoffs are solved by proposed Ambika methods. In Chap. 5, a new method (named as Mehar method) is proposed for solving such bimatrix games or two-person non-zero sum games (matrix games in which gain of one player is not equal to the loss of other player) in which payoffs are represented by intuitionistic fuzzy numbers. In Chap. 6, based on the present study future work has been suggested.

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In the last decades, several methods have been proposed in the literature to find the solution of non-cooperative games with interval/fuzzy/intuitionistic fuzzy payoffs. However, after a deep study, it is observed that some mathematically incorrect assumptions have been considered in all these methods. Therefore, it is scientifically incorrect to use the existing methods to find the solution of real-life non-cooperative games with interval/fuzzy/intuitionistic fuzzy payoffs. The aim of this book is to provide the valid methods for solving different types of non-cooperative games with interval/fuzzy/intuitionistic fuzzy payoffs and to make the researchers aware about those mathematically incorrect assumptions which are considered in the existing methods. The contents of the book are divided into six chapters. In Chap. 1, a new method (named as Gaurika method) is proposed to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for matrix games (or two-person zero-sum games) with interval payoffs (matrix games in which payoffs are represented by intervals). Furthermore, to illustrate the proposed Gaurika method, some existing numerical problems of matrix games with interval payoffs are solved by the proposed Gaurika method. In Chap. 2, the method (named as Mehar method) to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for matrix games with fuzzy payoffs (matrix games in which payoffs are represented as fuzzy numbers) is proposed. Furthermore, to illustrate the proposed Mehar method, the existing numerical problems of matrix games with fuzzy payoffs are solved by the proposed Mehar method. In Chap. 3, a new method (named as Vaishnavi method) is proposed to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for constrained matrix games with fuzzy payoffs (constrained matrix games in which payoffs are represented by fuzzy numbers). In Chap. 4, new methods (named as Ambika method-I, Ambika method-II, Ambika method-III and Ambika method-IV) are proposed to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for matrix games with intuitionistic fuzzy payoffs (matrix games in which payoffs are represented by intuitionistic fuzzy numbers). Furthermore, to illustrate proposed Ambika methods, some existing numerical problems of matrix games with intuitionistic fuzzy payoffs are solved by proposed Ambika methods. In Chap. 5, a new method (named as Mehar method) is proposed for solving such bimatrix games or two-person non-zero sum games (matrix games in which gain of one player is not equal to the loss of other player) in which payoffs are represented by intuitionistic fuzzy numbers. In Chap. 6, based on the present study future work has been suggested.