Abstract
Based on the extension Hukuhara difference between interval numbers, a generalized form of cooperative fuzzy games with a coalition structure and interval payoffs is proposed, which can be seen as an extension of crisp case. The interval Owen value for this kind of fuzzy games is studied, and its explicit form is given. When the fuzzy games are convex, the proposed interval Owen value is an interval population monotonic allocation function (IPMAF), and belongs to the associated core. Furthermore, we discuss a special kind of fuzzy games with a coalition structure and interval payoffs, and study the interval Owen value and the core of it. Some properties are also examined, which are coincided with the crisp case.
Highlights
The Shapley value is a well-known solution concept in cooperative game theory
Inspired by Sprumont [24], we show the given interval Owen value is an IPMAF when the fuzzy games are convex
If there is no fear of confliction, we still use a H b to denote the extension Hukuhara difference between the interval numbers in
Summary
The Shapley value (see [1]) is a well-known solution concept in cooperative game theory. Researched games with crisp coalitions and fuzzy payoffs. Owen [20] gave another payoff index for games with a coalition structure, which is called the Banzhaf-Owen value, and discussed its axiomatic system. In this paper, based on the extension Hukuhara difference between interval numbers, we will research cooperative fuzzy games with a coalition structure and interval payoffs.
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