On Solving Two Person Zero Sum Game with Uncertainty

Abstract

In this research work we considered the theories like the theory of fuzzy sets, newlinethe theory of intuitionistic fuzzy sets, the theory of soft sets, the theory of rough sets newlineto handle different types of uncertainties that arise in decision making problem in newlinecompetitive situations with two persons. Here we focused on two-person zero sum newlinegame with different types of uncertainties. We proposed TOPSIS (Technique for newlineorder preference by similarity to ideal solution) to solve a two person zero sum fuzzy newlinegame when the relative importance of strategies are not the same, that is weights are newlineassigned to the strategies. We have introduced octagonal intuitionistic fuzzy number newlineand generalized octagonal intutionistic fuzzy number and solved the fuzzy game newlineproblem with Octagonal Intuitionistic fuzzy number as payoffs using ranking method newlinebased on and#61537; -cuts and using the function defining the degree of favour of element newlinebelonging to the set and the function defining the degree of against of element newlinebelonging to the set, the intuitionistic fuzzy number is converted to crisp numbers and newlineare solved in the view of Player I and Player II respectively. We proposed a method to newlinefind the best strategies for the two players using heavy ordered weighted averaging newline(HOWA) operator on the generalized triangular, trapezoidal and octagonal newlineintutionistic fuzzy numbers with weights given to the strategies. Also we have defined newlineoctagonal neutrsophic number (ONN) and operations on it. We proposed a method to newlinefind the best strategies for the two players using heavy ordered weighted averaging newline(HOWA) operator on the generalized triangular, trapezoidal and octagonal newlineneutrosophic fuzzy numbers with weights given to the strategies. We have introduced newlinetwo-person zero sum intuitionistic fuzzy soft game and two-person zero sum neutrosophic newlinesoft game as an extension of fuzzy soft games defined by Cagman and Deli [12] and newlinesolved it in view of Player I and in view of Player II separately using the function defining the newlinedegree of favour of element and degree of against of element belonging to the set. newlineThroughout this work, we focused on two-person zero sum game with newlinedifferent types of uncertainties. As a future study this may be extended to n-person newlinezero sum games, bimatrix games and rectangular games with different types of newlineuncertainties. We used rough sets in solving a two person zero sum game which can newlinebe extended by fuzzy rough sets, intuitionistic fuzzy rough sets. newline