  Evolutionarily stable strategy (ESS) is a key concept in evolutionary game
theory. ESS provides an evolutionary stability criterion for biological, social
and economical behaviors. In this paper, we develop a new approach to evaluate
ESS in symmetric two player games with fuzzy payoffs. Particularly, every
strategy is assigned a fuzzy membership that describes to what degree it is an
ESS in presence of uncertainty. The fuzzy set of ESS characterize the nature of
ESS. The proposed approach avoids loss of any information that happens by the
defuzzification method in games and handles uncertainty of payoffs through all
steps of finding an ESS. We use the satisfaction function to compare fuzzy
payoffs, and adopts the fuzzy decision rule to obtain the membership function
of the fuzzy set of ESS. The theorem shows the relation between fuzzy ESS and
fuzzy Nash quilibrium. The numerical results illustrate the proposed method is
an appropriate generalization of ESS to fuzzy payoff games.
