A normalized distribution mechanism under multi-criteria situations and fuzzy behavior

In general, agents always face an increasing need to focus on multiple aims efficiently under their operational processes. However, agents might take different activity levels to participate and might represent administrative areas of different scales. Therefore, this paper proposes a normalized index considering multi-criteria situations and supreme-utilities among fuzzy activity level (decision, strategy) vectors. Three existing notions of traditional game theory are reinterpreted in the framework of multi-criteria fuzzy transferable utility games. First, the normalized index could be represented as an alternative formulation in terms of excess functions. Second, an axiomatic result is proposed to present the rationality of this normalized index based on the reduced game and related consistency. Finally, two dynamic processes are introduced to illustrate that this normalized index could be reached by agents who start from an arbitrary efficient payoff vector and make successive adjustments.