Cooperative Fuzzy Games with a Coalition Structure and Interval Payoffs

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.

Keywords

• Cooperative fuzzy game
• Coalition structure
• Interval Owen value
• Extension Hukuhara difference