doiSerbia

Fuzzy soft games

Deli Irfan (Kilis Aralık University, Muallim Rıfat Faculty of Education, Kilis, Turkey)
Çağman Naim (Gaziosmanpaşa University, Faculty of Arts and Sciences, Department of Mathematics, Tokat, Turkey)

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.

Keywords: soft sets, fuzzy set, fuzzy soft payoff, nash equilibrium, probabilistic equilibrium solution