Fuzzy logic based game theory applications in multi-criteria decision making process

Abstract

Decision process can be summarized as a process that helps for choosing the optimal alternatives according to suggested objectives by evaluating all environmental effects in problem solving. Nowadays, since environmental effects are more complex, imprecise and multilateral, fuzzy set theory and game theory are widely preferred instruments in decision making process. The aim of this study is to present a hybrid multi-criteria decision making approach which uses artificial intelligence techniques such as fuzzy logic and game theory. This process is considered in two person non-constant sum game theory perspective. The methods in literature about related topics (such as scenario planning and fuzzy TOPSIS) are examined and a hybrid decision making methodology that comprises many decision methods is formed. All phases of this approach are executed in game theory perspective by evaluating mutual strategies of players. In the study, the methodology is explained and a fictitious international disagreement case is used as a numerical example to demonstrate the validity and applicability.

D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment

“…Let us compare the result obtained by the proposed DNT based framework or method with that by a TOPSIS based method developed in [29]. On the basis of the same data, a real-valued payoff matrix for the application is also derived by using the TOPSIS based method [29], which is shown in At first, from Table 8 the equilibrium point is also (AS 5 , BS 3 ) by using the TOPSIS based method, which is the same as the result of this paper that uses the DNT based method. Both of these two methods have obtained correct result.…”

“…United Nations send and located international peace support force to control the area. Regarding to this situation, the conflict between countries is formalized in two-person non-constant game theory and analyzed by the Figure 4: An example of adversarial decision making about territorial dispute [29] proposed DNT based game-theoretic framework. Before the analysis, it is assumed a DMG consisting of ten decision makers (DM) is established in advance.…”

“…In the phase of strategy assessment, at first we identify key criteria so as to evaluate the strategies for players. In previous study [29], six key criteria have been identified, including "Management", "Protection", "Mobility", "Logistic", "Flexibility", "Simplicity", and a fuzzy weigh for every criterion has been also determined, as shown in Table 3.…”

“…Case for Alpha, and AS 1 Case, AS 2 Case, AS 3 Case, AS 4 Case, AS 5 Case for Beta. In this paper, all of the evaluation matrices are from literature [29].…”

“…In a perspective of game theory, it constitutes a two-person zero sum or non-constant sum game [40]. Therefore, game theory is feasibly used in researching the adversarial decision making problem [29,30,41]. Based on two aspects of considerations, the representation of human being's uncertain evaluations and methods for decision making, in this paper we suggest a D numbers theory (DNT) based game-theoretic framework for two persons' adversarial decision making under fuzzy environment, where DNT [42,43] is a new uncertainty reasoning theory which generalizes Dempster-Shafer theory [44,45] and already has some applications [46][47][48][49][50].…”