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Coalitional fuzzy preferences. (English) Zbl 1265.91012
Summary: The paper deals with the concept of coalitional preferences in group decision-making situations in which the agents and coalitions have only vague idea about the comparative acceptability of particular outcomes. The coalitional games with vague utilities (see, e. g., [M. Mareš, Fuzzy cooperative games. Cooperation with vague expectations. Heidelberg: Physica-Verlag (2001; Zbl 1005.91013)]) can serve as a good example when some types of the game solutions (e. g., the von Neumann-Morgenstern one) are to be extended to the fuzzy game case. In this paper, we consider the fuzzy analogies of coalitional preferences and coalitional domination concepts known from the deterministic optimization models. These coalitional preferences are derived from the individual preferences of the coalition members. In the fuzzy extension of the model, the input individual preferences are represented by fuzzy relations and, consequently, the coalitional preferences have to be fuzzy, too. The general properties of these coalitional preferences are discussed in this contribution, and they are compared with the situation in the deterministic model. Finally, the case when the fuzziness of the individual preferences follows from fuzziness of the utility functions over the outcomes of the decision-making is mentioned and discussed.
91A12 Cooperative games
91A35 Decision theory for games
91B06 Decision theory
91B08 Individual preferences
91B10 Group preferences
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