In this paper, by a new ranking method of interval numbers which has a total order, interval cooperative games and some relevant definitions are firstly redefined, two important theorems are presented respectively to discuss the existence of the interval core and to prove the relations between the interval core and the interval dominance core. Then on the condition that the profit value of any coalition is not fully used to allocate, a generalized interval cooperative game and its solution concepts, such as generalized interval core, generalized interval dominance core are proposed. Further more, some extended theorems to discuss the existence and the relations about its solution concepts are developed. Finally, by a specific example, the reasonableness and validity of the above theoretical notions are verified.
Interval cooperative game is a kind of model focusing on how to distribute the profit reasonably when payoffs of any alliance are interval numbers. In recent years, the existence and reasonableness of its solution have aroused widespread concern. In this paper, based on the conceptual analyses of various solutions of interval cooperative games, S-core is further researched. The concepts of weak balanced interval cooperative games and minimal weak balanced interval cooperative games are firstly proposed. The necessary and sufficient condition which guarantees S-core is nonempty is proven, furthermore, the inequalities can be simplified on the condition that the left endpoints of interval numbers satisfy the superadditivity. Then this paper analyzes the whole solution space of S-core and the solution method of S-core is converted into the method solving a linear programming problem. After that the concept of S-dominance core is put forward and the equivalent conditions of S-core and S-dominance core are proved. Finally, the reasonableness and validity of S-core are verified through a specific example.
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