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.
Bigdeli, H., & Tayyebi, J. (2024). Cooperative games with multiple scenarios in intuitionistic fuzzy environment. Caspian Journal of Mathematical Sciences, 13(1), 171-188. doi: 10.22080/cjms.2021.21385.1583
MLA
Hamid Bigdeli; javad Tayyebi. "Cooperative games with multiple scenarios in intuitionistic fuzzy environment", Caspian Journal of Mathematical Sciences, 13, 1, 2024, 171-188. doi: 10.22080/cjms.2021.21385.1583
HARVARD
Bigdeli, H., Tayyebi, J. (2024). 'Cooperative games with multiple scenarios in intuitionistic fuzzy environment', Caspian Journal of Mathematical Sciences, 13(1), pp. 171-188. doi: 10.22080/cjms.2021.21385.1583
VANCOUVER
Bigdeli, H., Tayyebi, J. Cooperative games with multiple scenarios in intuitionistic fuzzy environment. Caspian Journal of Mathematical Sciences, 2024; 13(1): 171-188. doi: 10.22080/cjms.2021.21385.1583
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