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Advances in Fuzzy Systems
Volume 2018, Article ID 3502949, 9 pages
https://doi.org/10.1155/2018/3502949
Research Article

Solidarity Value and Solidarity Share Functions for TU Fuzzy Games

1Department of Mathematics, Dibrugarh University, Dibrugarh, India
2Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia
3Faculty of Science, Palacký University Olomouc, No. 12, 77146 Olomouc, Czech Republic

Correspondence should be addressed to Surajit Borkotokey; moc.oohay@robtijarus

Received 29 November 2017; Accepted 8 March 2018; Published 15 April 2018

Academic Editor: Amit Kumar

Copyright © 2018 Rajib Biswakarma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

TU games under both crisp and fuzzy environments describe situations where players make full (crisp) or partial (fuzzy) binding agreements and generate worth in return. The challenge is then to decide how to distribute the profit among them in a rational manner: we call this a solution. In this paper, we introduce the notion of solidarity value and the solidarity share function as a suitable solution to TU fuzzy games. Two special classes of TU fuzzy games, namely, TU fuzzy games in Choquet integral form and in multilinear extension form, are studied and the corresponding solidarity value and the solidarity share functions are characterized.