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.