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.

Solutions for generalized interval cooperative games

“…For simplification, we denote this ranking method by the symbol (I(R), λ, ∼ ), the advantage of it can be shown in the following Example. 4,9]. Please give the size relation between them.…”

“…In recent years, many scholars have conducted extensive researches on its solution concepts, related properties, and relations among so many solutions. Some success has been achieved, for example, [7] defined S-core for interval cooperative games, and gave the sufficient condition for a non-empty S-core; [8] studied some interval-type solution concepts for interval-valued cooperative games like the interval core, the interval dominance core and stable sets; [9] proposed a generalized form of cooperative fuzzy games with a coalition structure and interval payoffs based on the extension Hukuhara difference between interval numbers; [10] discussed the characteristics of convex interval cooperative games; [11] gave the axiom characteristics of interval Shapley function and proved its existence and uniqueness; [12][13][14][15] proposed many concepts such as interval dominance core, square interval core and interval nondominated core and discussed their properties respectively. All these research works necessitate onto the following two important points: 1) Using an effective ranking method of interval numbers is very important.…”

The Large-Small Group-Based Evolutionary Game on Knowledge Sharing in Uncertain Environment under the Background of Telemedicine Service

“…Moreover, it has almost become the basic analytical tool and study language of economists and management experts in the entire field. So far, it has been successfully applied to many areas: oligopoly games [21], cooperative games [22][23][24], fuzzy games [25][26][27], and so on [28,29]. erefore, game theory has been widely applied in the study of knowledge sharing.…”

Cooperative fuzzy games with interval characteristic functions

“…Alparslan Gök et al (2014b) studied the relationship between the interval core, the interval dominance core, the square interval dominance core and the interval stable sets for cooperative interval games. Meanwhile, Meng et al (2013b) discussed fuzzy games with a coalition structure and interval payoffs. Furthermore, the comparison of interval numbers was investigated by Chanas and Zieliński (1999), and Sengupta and Pal (2000).…”