Convex Interval Games

A new solution of core for interval-valued cooperative game

In this paper, we give a further discussion on the core solution for cooperative games with fuzzy payoffs. Some notions and results from classical games are extended to fuzzy cooperative games. Using an example, we point out that the theorem about the nonempty of I-core proposed in 2008 was not sufficient. Furthermore, the equivalence relation between balanced game and nonempty core, which play...

An interval-valued programming approach to matrix games with payoffs of triangular intuitionistic fuzzy numbers

The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payoffs of TIFNs is introduced. A pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...

Measuring Interval Efficiency in Convex Hull of Data Using DEA

M-FUZZIFYING INTERVAL SPACES

In this paper,  we introduce  the notion of $M$-fuzzifying interval spaces, and discuss the relationship between $M$-fuzzifying interval spaces and $M$-fuzzifying convex structures.It is proved that  the category  {bf MYCSA2}  can be embedded in  the category  {bf  MYIS}  as a reflective subcategory, where  {bf MYCSA2} and   {bf  MYIS} denote  the category of $M$-fuzzifying convex structures of...

Bankruptcy Assessment with the Interval Programming and Games Theory

Some of the parameters in issues of the reality world are uncertainty. One of the uncertain problems with the qualitative parameters is economic problems such as bankruptcy problem. In this case, there is a probability of dealing with imprecise concepts including the intervals regarding the official’s viewpoint, organizations’ managers. Accordingly, this article uses the concepts of data envelo...

Cooperative games under interval uncertainty: on the convexity of the interval undominated cores

Uncertainty is a daily presence in the real world. It affects our decision making and may have influence on cooperation. Often uncertainty is so severe that we can only predict some upper and lower bounds for the outcome of our actions, i.e., payoffs lie in some intervals. A suitable game theoretic model to support decision making in collaborative situations with interval data is that of cooper...