Coalitional fuzzy preferences

Milan Mareš

Kybernetika (2002)

  • Volume: 38, Issue: 3, page [339]-352
  • ISSN: 0023-5954

Abstract

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The paper deals with the concept of coalitional preferences in the 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., [6]) can serve for 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, also the coalitional preferences have to be fuzzy. 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.

How to cite

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Mareš, Milan. "Coalitional fuzzy preferences." Kybernetika 38.3 (2002): [339]-352. <http://eudml.org/doc/33587>.

@article{Mareš2002,
abstract = {The paper deals with the concept of coalitional preferences in the 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., [6]) can serve for 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, also the coalitional preferences have to be fuzzy. 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.},
author = {Mareš, Milan},
journal = {Kybernetika},
keywords = {coalitional preferences; fuzzy game; optimization; coalitional preferences; fuzzy game; optimization},
language = {eng},
number = {3},
pages = {[339]-352},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Coalitional fuzzy preferences},
url = {http://eudml.org/doc/33587},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Mareš, Milan
TI - Coalitional fuzzy preferences
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 3
SP - [339]
EP - 352
AB - The paper deals with the concept of coalitional preferences in the 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., [6]) can serve for 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, also the coalitional preferences have to be fuzzy. 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.
LA - eng
KW - coalitional preferences; fuzzy game; optimization; coalitional preferences; fuzzy game; optimization
UR - http://eudml.org/doc/33587
ER -

References

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  1. Dubois D., Kerre E. E., Mesiar, R., Prade H., Fuzzy interval analysis, In: Fundamentals of Fuzzy Sets (D. Dubois and H. Prade, eds.), Kluwer, Dordrecht 2000, pp. 483–581 Zbl0988.26020MR1890240
  2. Kerre E. E., Wang X., Reasonable properties for the ordering of fuzzy quantities, Part I. Fuzzy Sets and Systems 118 (2001), 375–383 Zbl0971.03055MR1809386
  3. Kerre E. E., Wang X., Reasonable properties for the ordering of fuzzy quantities, Part II. Fuzzy Sets and Systems 118 (2001), 387–405 Zbl0971.03055MR1809387
  4. Luce J. R., Raiffa H., Games and Decisions, Wiley, London 1957 Zbl1233.91002
  5. Mareš M., Computation Over Fuzzy Quantities, CRC–Press, Boca Raton 1994 Zbl0859.94035MR1327525
  6. Mareš M., 10.1016/S0165-0114(97)00136-X, Fuzzy Sets and Systems 91 (1997), 143–154 (1997) MR1480041DOI10.1016/S0165-0114(97)00136-X
  7. Mareš M., Fuzzy Cooperative Games, Physica–Verlag, Heidelberg 2001 Zbl1037.91007MR1841340
  8. Neuman J. von, Morgenstern O., Theory of Games and Economic Behaviour, Princeton Univ. Press, Princeton, N.J. 1953 
  9. Rosenmüller J., The Theory of Games and Markets, North Holland, Amsterdam 1982 Zbl0464.90089MR0632834

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