cooperative games with multiple scenarios in intuitionistic fuzzy environment

‎the main aim of this paper is to introduce the core and nucleolus notions of cooperative games with multiple scenarios in uncertain environment‎. ‎taking imprecision of information into account‎, ‎we incorporate fuzzy coalition values‎, ‎which are represented by intuitionistic fuzzy numbers‎. ‎they can be applied as an appropriate approach to define a fuzzy set in the case that available information is not sufficient for defining an imprecise concept by means of a conventional fuzzy set‎. ‎the characteristic function of such games associates a coalition with a vector containing the intuitionistic fuzzy components‎. ‎the notion of expected interval is defined and computed for the intuitionistic fuzzy numbers‎. ‎then‎, ‎an approach is proposed to transform the problem into a single-objective cooperative game with interval-valued payoffs‎. ‎the concepts of core and nucleolus are considered‎. ‎it is shown that the core is nonempty in these games‎. ‎a method is proposed to compute the nucleolus of such the problems‎. ‎finally‎, ‎the validity and applicability of the approach are illustrated by a numerical example.