Jornal article

Butnariu D., Kroupa T.

European Journal of Operational Research

2008

1 (2008)

288-299

0377-2217

Ing. Tomáš Kroupa, Ph.D. (ÚTIA - Oddělení matematické teorie rozhodování)

coalition, fuzzy coalition, Shapley value

We prove existence and uniqueness of the so-called Shapley mapping, which is a solution concept for a class of n-person games with fuzzy coalitions whose elements are defined by the specific structure of their characteristic functions. The Shapley mapping associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency, the symmetry, and the null-player conditions. It determines a cumulative value that is the sum of all coalitional allocations for whose computation we provide an explicit formula.