Bi-cooperative games in bipolar fuzzy settings. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Hazarika, Pankaj; Borkotokey, Surajit; Mesiar, Radko
• Is Part Of: International journal of general systems. Volume 47:Issue 1(2018)
• Page Start: 51
• Page End: 66
• Publication Date: 2018-01-02
• Subjects: Bi-cooperative games -- bipolar fuzzy bi-coalition -- shapley function; System theory -- Periodicals; 003
• DOI: 10.1080/03081079.2017.1388800
• Languages: English
• ISSNs: 0308-1079

Abstract

Abstract: In this paper, we introduce the notion of a bi-cooperative game with Bipolar Fuzzy Bi-coalitions and discuss the related properties. In many decision-making situations, players show bipolar motives while cooperating among themselves. This is modelled in both crisp and fuzzy environments. Bi-cooperative games with fuzzy bi-coalitions have already been proposed under the product order of bi-coalitions where one had memberships in [0, 1]. In the present paper, we adopt the alternative ordering: ordering by monotonicity and account for players' memberships in[ - 1, 1 ], a break from the previous formulation. This simplifies the model to a great extent. The corresponding Shapley axioms are proposed. An explicit form of the Shapley value to a particular class of such games is also obtained. Our study is supplemented with an illustrative example.