Shapley value of simple cooperative games with fuzzy coalitions applied on the real voting data

The main aim of this article is to compare the results of classical Shapley value concept with results of the Shapley value extended to the cooperative games with fuzzy coalitions applied on the real data of the cooperative simple game – in this case the data from the voting in the Lower House of the Czech Parliament 20022012. One of the most intriguing tasks is to describe real system problems using mathematical tools. As the real systems are full of an uncertainty, there are several tools incorporating the uncertainty into the classical models, for example the theory of probability, the theory of fuzzy sets, or the theory of rough sets. In this article, the probabilistic approach to the Shapley value was chosen. Results indicate the improvement in predictability of the real power of existing political coalitions comparing to the values based on the classical Shapley value. .