Solutions for generalized interval cooperative games

Abstract

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.

Extension of generalized solidarity values to interval-valued cooperative games

“…Han et al [11] proposed the interval-valued core and the interval-valued Shapley-like value of interval-valued cooperative games by defining a new interval order relation and using the Moore's interval subtraction ( [20]). Guan et al [10] defined a new interval ranking method and hereby investigated the existence of the interval-valued core and discussed the relations between the interval-valued core and the interval-valued dominance core. Based on a partial subtraction operator, Palanci et al [27] discussed the interval-valued Shapley value and its properties and also introduced the interval-valued Banzhaf value and the interval-valued egalitarian rule.…”