Fuzzy soft games

Abstract

In this work, after introduce the definition of fuzzy soft sets and their basic operations we define two person fuzzy soft games which can apply to problems contain vagueness and uncertainty. We then give four different types solution methods of the games which are fuzzy soft saddle points, fuzzy soft lower and upper values, fuzzy soft dominated strategies and fuzzy soft Nash equilibrium. We also give a probabilistic equilibrium solution method for the two persons fuzzy soft games (tp f s-games) which show that every finite tp f s-game with probabilistic strategies has one solution. Finally, we give an application which shows that the methods can be successfully applied to a financial problem and extended the two person fuzzy soft games to n-person fuzzy soft games.