Nash - Equilibrium solutions for Fuzzy Rough Continuous Static Games

Abstract

Fuzzy rough is used to measure the various uncertainties with high vagueness and imprecision in continuous static games.In this article we develop a new class de ned as fuzzy rough continuous static games (FRGSG) in which the objective functions and the constraints have fuzzy rough nature.The fuzzy part is converted into deterministic ones by utilizing the -cut methodology and the roughness part is transformed into two problems corresponding to the upper and lower approximation models thus, the result is four cases.The necessary conditions for determining Nash- Equilibrium points of fuzzy rough continuousstatic games are achieved and a numerical example is performed to support the theoretical claims.