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  | abstract        = The determination of solutions in group decision making via intuitionistic fuzzy sets is considered. The point of departure is a collection of individual intuitionistic fuzzy preference relations. We also assume a (traditional) fuzzy majority equated with a fuzzy linguistic quantifier. A solution is derived either directly from the individual intuitionistic fuzzy preference relations or by constructing first a social intuitionistic fuzzy preference relation. Two solution concepts are proposed, the intuitionistic fuzzy core and consensus winner.
  | abstract        = The determination of solutions in group decision making via intuitionistic fuzzy sets is considered. The point of departure is a collection of individual intuitionistic fuzzy preference relations. We also assume a (traditional) fuzzy majority equated with a fuzzy linguistic quantifier. A solution is derived either directly from the individual intuitionistic fuzzy preference relations or by constructing first a social intuitionistic fuzzy preference relation. Two solution concepts are proposed, the intuitionistic fuzzy core and consensus winner.
  | keywords        = Group decision making, fuzzy preference relations, intuitionistic fuzzy preference relations, core, consensus winner.
  | keywords        = Group decision making, fuzzy preference relations, intuitionistic fuzzy preference relations, core, consensus winner.
  | ams = ОЗЕ72
  | ams =           0ЗЕ72
  | references      =  
  | references      =  


Revision as of 13:37, 7 July 2017

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Title of paper: Intuitionistic fuzzy sets in group decision making
Author(s):
Eulalia Szmidt
Systems Research Institute, Polish Academy of Sciences
Janusz Kacprzyk
Systems Research Institute, Polish Academy of Sciences
kacprzyk@ibspan.waw.pl
Published in: "Notes on IFS", Volume 2 (1996) Number 1, pages 15—32
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Abstract: The determination of solutions in group decision making via intuitionistic fuzzy sets is considered. The point of departure is a collection of individual intuitionistic fuzzy preference relations. We also assume a (traditional) fuzzy majority equated with a fuzzy linguistic quantifier. A solution is derived either directly from the individual intuitionistic fuzzy preference relations or by constructing first a social intuitionistic fuzzy preference relation. Two solution concepts are proposed, the intuitionistic fuzzy core and consensus winner.
Keywords: Group decision making, fuzzy preference relations, intuitionistic fuzzy preference relations, core, consensus winner.
AMS Classification: 0ЗЕ72
References:
  1. Atanassow K.T. (1986). Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 20, 87-96.
  2. Atanassov K.T. (1988). Review and new results on intuitionistic fuzzy sets. IM-MFAIS-1.
  3. Atanassov K.T. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33, 3-45.
  4. Barrett, C.R. and Pattanaik, P.K. (1990). Aggregation of fuzzy preferences. In J. Kacprzyk and M. Fedrizzi, (Eds.): Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 155—162.
  5. Blin, J.M. and Whinston, A.P. (1973). Fuzzy sets and social choice. J. of Cybernetics 4, 17-22.
  6. Bustince H., Burillo P. (1996). Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems, 3, 293-303.
  7. Dubois D., Prade H. (1980). Fuzzy sets and Systems. New York.
  8. Fedrizzi, M., Kacprzyk, J. and Nurmi, H. (1993). Consensus degrees under fuzzy majorities and fuzzy preferences using OWA (ordered weighted average) operators, Control and Cybernetics, 22, 71—80.
  9. Kacprzyk, J. (1984). Collective decision making with a fuzzy majority rule, Proc. WOGSC Congress, AFCET, Paris, pp. 153-159.
  10. Kacprzyk, J. (1985a). Some 'commonsense solution concepts in group decision making via fuzzy linguistic quantifiers. In J. Kacprzyk and R.R. Yager (Eds.): Management Decision Support Systems Using Fuzzy Sets and Possibility Theory, Verlag TV*{U}V Rheinland, Cologne, pp. 125-135.
  11. Kacprzyk, J. (1985b). Group decision-making with a fuzzy majority via linguistic quantifiers. Part I: A consensory-like pooling; Part II: A competitive-like pooling, Cybernetics and Systems: an Int. J., 16, 119—129 (Part I), 131-144 (Part II).
  12. Kacprzyk, J. (1986). Group decision making with a fuzzy linguistic majority, Fuzzy Sets and Systems, 18, 105—118.
  13. Kacprzyk, J. (1987). On some fuzzy cores and 'soft' consensus measures in group decision making. In J.C. Bezdek (Ed.): The Analysis of Fuzzy Information, Vol. 2, CRC Press, Boca Raton, pp. 119-130.
  14. Kacprzyk, J. and Fedrizzi,M., Eds. (1990). Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht.
  15. Kacprzyk, J. and Fedrizzi, M. (1995). A fuzzy majority in group DM and consensus via the OWA operators with importance qualification, Proc. of dFT'95 — Current Issues in Fuzzy Technologies (Trento, Italy), pp. 128—137.
  16. Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1990). Group decision making with fuzzy majorities represented by linguistic quantifiers. In J.L. Verdegay and M. Delgado (Eds.): Approximate Reasoning Tools for Artificial Intelligence, Verlag TV*{U}V Rheinland, Cologne, pp. 126-145.
  17. Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1992). Group decision making and consensus under fuzzy preferences and fuzzy majority, Fuzzy Sets and Systems, 49,21-31.
  18. Kacprzyk, J. and Nurmi, H. (1989). Linguistic quantifiers and fuzzy majorities for more realistic and human-consistent group decision making. In G. Evans, W. Karwowski and M. Wilhelm (Eds.): Fuzzy Methodologies for Industrial and Systems Engineering, Elsevier, Amsterdam, pp. 267-281.
  19. Kacprzyk, J., Nurmi, H. and Fedrizzi, M., Eds. (1996). Consensus under Fuzziness, Kluwer, Boston.
  20. Kacprzyk, J. and Roubens, M., Eds. (1988). Non-Conventional Preference Relations in Decision Making, Springer—Verlag, Heidelberg.
  21. Nurmi, H. (1981). Approaches to collective decision making with fuzzy preference relations, Fuzzy Sets and Systems, 6, 249—259.
  22. Nurmi, H., Fedrizzi, M. and Kacprzyk, J. (1990). Vague notions in the theory of voting. In J. Kacprzyk and M. Fedrizzi (Eds.): Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 43-52.
  23. Nurmi, H. and Kacprzyk, J. (1991). On fuzzy tournaments and their solution concepts in group decision making, Europ. J. of Operational Research, 51, 223-232.
  24. Tanino, T. (1984). Fuzzy preference orderings in group decision making, Fuzzy Sets and Systems, 12, 117-131.
  25. Tanino, T. (1990). On group decision making under fuzzy preferences. In J. Kacprzyk and M. Fedrizzi (Eds.): Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 172—185.
  26. Zadeh, L.A. (1983). A computational approach to fuzzy quantifiers in natural languages. Computers and Maths with Appls, 9, 149—184.
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