What is it about?
In this paper, we discuss the notion of Share functions for cooperative games with fuzzy coalitions or simply fuzzy cooperative games. We obtain the Share functions for some special classes of fuzzy games, namely the fuzzy games in proportional value form and the fuzzy games in Choquet integral form. The Shapley Share and Banzhaf Share functions for these classes are derived.
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Why is it important?
Share functions are alternative solution concepts of TU games. Their extensions to fuzzy counterparts open new areas of studies and wide application possibilities. Nature is not binary, so are our behavior. Therefore, modelling human behavior in a binary setting has been attracted widespread criticisms from both the theorists and practitioners. Therefore our paper addresses some of the open problems related to the solution concepts of TU games under fuzzy environment.
Perspectives
Writing this article was a pleasant experience. We have been co-authoring a number of papers each of which is a distinct and enlightened experience. This, we feel that will continue in the future also as our paper has opened up a completely new domain of research.
Surajit Borkotokey
Dibrugarh University
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This page is a summary of: A Simplified Expression of Share Functions for Cooperative Games with Fuzzy Coalitions, Tatra Mountains Mathematical Publications, June 2017, De Gruyter,
DOI: 10.1515/tmmp-2017-0011.
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