Cooperative game theory is concerned with situations where a group of agents coordinate their actions to get a common benefit. An allocation rule for these situations is a way to share the common benefit among the agents. The search for a fair allocation rule may depend on the information one has about these agents. A formal context represents information about certain attributes of a set of objects in a table, and they have been used in the literature to describe information about the agents in a game. More recently, formal contexts are extended to the fuzzy setting. Now in this paper we establish a methodology to share the profits of a group of agents that have some information about them collected in a fuzzy formal context when those benefits depend on a set of attributes.

In a cooperative game with transferable utility, it is usually assumed that all coalitions are equally feasible. However, if we deal with cooperative games with coalition configuration, only some coalitions are a priori feasible, due to the preferences of the agents. In this paper, we propose a generalization of games with coalition configuration. In our model, the feasibility of a coalition is determined by the cohesion of its members, and obviously, this cohesion does not have to be equal for all coalitions. The cohesion of each coalition will be determined by a cohesion index. We introduce the class of games with cohesion index and propose an allocation rule, which is characterized by using reasonable properties. The cohesion idea is not only a concept related to social groups. In software design, this concept explains the relationships among all the elements of a module. Our value can be applied in this way as we show in the paper.