Atanassov’s Intuitionistic Fuzzy Sets as a Promising Tool for Extended Fuzzy Decision Making Models

  • Eulalia Szmidt
  • Janusz Kacprzyk


Since decision making is omnipresent in any human activity, it is quite clear that not much later after the concept of a fuzzy set was introduced as a tool for a description and handling of imprecise concepts, a next rational step was an attempt to devise a general framework for dealing with decision making under fuzziness. Since intuitionistic fuzzy sets (in the sense of Atanassov, to be called A-IFSs, for short) provide a richer apparatus to grasp imprecision than the conventional fuzzy sets, they seem to be a promising tool for extended decision making models. We will present some of the extended models and try to show why A-IFSs make it possible to avoid some more common cognitive biases, the decision makers are prone to do, which call into question the correctness of a decision.


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  1. 1.
    Aamodt A. and Plaza E. (1994) Case-based reasoning: foundational issues, methodological variations, and system. Artificial Intelligence Communications, IOS Press, 7, 1, 39–59.Google Scholar
  2. 2.
    Anderson J.R. (1983) The architecture of cognition. Harvard University Press, Cambridge.Google Scholar
  3. 3.
    Atanassov K. (1983), Intuitionistic Fuzzy Sets. VII ITKR Session. Sofia (Deposed in Centr. Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian).Google Scholar
  4. 4.
    Atanassov K. (1986) Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 20, 87–96.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Atanassov K. (1999), Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag.Google Scholar
  6. 6.
    Atanassov K. and Gargov G. (1989), Interval-valued intuitionistic fuzzy sets. Fuzzy sets and Systems, 31 (3), 343–349.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Bellman, R.E. and Zadeh, L.A. (1970). Decision making in a fuzy environment, Management Science, 17, 141–164.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bezdek, J.C., Spillman, and B. Spillman, R. (1978) A fuzzy relation space for group decision theory. Fuzzy Sets and Systems, 1, 255–268.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Bezdek, J.C., Spillman, B. and Spillman, R. (1979) Fuzzy relation space for group decision theory: An application. Fuzzy Sets and Systems 2, 5–14.MATHCrossRefGoogle Scholar
  10. 10.
    Blin, J.M. (1974) Fuzzy relations in group decision theory. J. of Cybernetics, 4, 17–22.MathSciNetGoogle Scholar
  11. 11.
    Blin, J.M. and Whinston, A.P. (1973) Fuzzy sets and social choice. J. of Cybernetics, 4, 17–22.MathSciNetGoogle Scholar
  12. 12.
    Chen S.M. and Tan J.M. (1994) Handling multi-criteria fuzzy decision making problems based on vague set theory. Fuzzy Sets and Systems 67 (2), 163–172.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Dubois D., Gottwald S., Hájek P., Kacprzyk J., Prade H. (2005) Terminological difficulties in fuzzy set theory – the case of “intuitionistic fuzzy sets”. Fuzzy Sets and Systems 156 (3), 485–491.Google Scholar
  14. 14.
    Dubois D. and Prade H. (1994) Fuzzy set modelling in case-based reasoning. International Journal of Intelligent Systems, 13, 345–373.CrossRefGoogle Scholar
  15. 15.
    Fodor, J. and Roubens, M. (1994) Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht.MATHGoogle Scholar
  16. 16.
    García-Lapresta, J.L. and Llamazares, B. (2000). Aggregation of fuzzy preferences: Some rules of the mean. Social Choice and Welfare, 17, 673–690.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Kacprzyk, J. (1985) 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, 16, 119–129 (Part I), 131–144 (Part II).Google Scholar
  18. 18.
    Kacprzyk, J. (1986) Group decision making with a fuzzy linguistic majority. Fuzzy Sets and Systems, 18, 105–118.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    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, 119–130.Google Scholar
  20. 20.
    Kacprzyk, J. (1997) Multistage Fuzzy Control (Wiley,Chichester ).Google Scholar
  21. 21.
    Kacprzyk, J. and Fedrizzi, M. (1986) ‘Soft’ consensus measures for monitoring real consensus reaching processes under fuzzy preferences. Control and Cybernetics, 15, 309–323.MathSciNetGoogle Scholar
  22. 22.
    Kacprzyk, J. and Fedrizzi, M. (1988) A ‘Soft’ measure of consensus in the setting of partial (fuzzy) preferences. Europ. J. of Operational Research, 34, 315–325.MathSciNetGoogle Scholar
  23. 23.
    Kacprzyk, J. and Fedrizzi, M. (1989) A ‘human-consistent’ degree of consensus based on fuzzy logic with linguistic quantifiers. Mathematical Social Sciences, 18, 275–290.MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Kacprzyk, J. and Fedrizzi, M., Eds. (1990) Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht.MATHGoogle Scholar
  25. 25.
    Kacprzyk J., M. Fedrizzi and H. Nurmi (1992) Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Systems, 49, 21–32.MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Kacprzyk, J. and Nurmi, H. (1998) Group decision making under fuzziness, in R. Słowiński (Ed.): Fuzzy Sets in Decision Analysis, Operations Research and Statistics, Kluwer, Boston, 103–136.Google Scholar
  27. 27.
    Kacprzyk, J., Nurmi, H. and Fedrizzi, M., Eds. (1996) Consensus under Fuzziness, Kluwer, Boston.Google Scholar
  28. 28.
    Kang W.-T. (2004) Protest voting and abstention under pluraluity rule elections, Journal of theoretical Politics, 16, 71–102.CrossRefGoogle Scholar
  29. 29.
    Kim, J.B. (1983). Fuzzy rational choice functions. Fuzzy Sets and Systems, 10, 37–43.MATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Kolodner J. (1992) An introduction to case-based reasoning. Artificial Intelligence Review, 6 (1), 3–34.CrossRefGoogle Scholar
  31. 31.
    Liu H.W. Multi-criteria decision making methods based on intuitionistic fuzzy sets. In press.Google Scholar
  32. 32.
    Loewer B. and R. Laddaga (1985) Destroying the consensus. In Loewer B. (Guest Ed.): Special Issue on Consensus. Synthese, 62 (1), 79–96.Google Scholar
  33. 33.
    Nurmi, H. (1981) Approaches to collective decision making with fuzzy preference relations, Fuzzy Sets and Systems, 6, 249–259.MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Nurmi, H. (1987) Comparing Voting Systems, Reidel, Dordrecht.Google Scholar
  35. 35.
    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.MATHCrossRefGoogle Scholar
  36. 36.
    Ros B.H. (1989) Some psychological results on case-based reasoning. Case-Based Reasoning Workshop, DARPA, 144–147.Google Scholar
  37. 37.
    Salles, M. (1996). Fuzzy utility. In S. Barberà, P.J. Hammond and C. Seidl (Eds.): Handbook of Utility Theory, Vol. I, Kluwer, Boston.Google Scholar
  38. 38.
    Schank R. (1982) Dynamic memory: a theory of reminding and learning in computers and people. Cambridge University Press.Google Scholar
  39. 39.
    Sutherland S. (1994) Irrationality. The Enemy Within. Penguin Books.Google Scholar
  40. 40.
    Szmidt E. and Baldwin J. (2005) Assigning the parameters for Intuitionistic Fuzzy Sets. Notes on IFSs, 11 (6), 1–12.Google Scholar
  41. 41.
    Szmidt E. and Baldwin J. (2006) Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms. 2006 IEEE World Congress on Computational Intelligence, 237–243.Google Scholar
  42. 42.
    Szmidt E. and Kacprzyk J. (1996a) Intuitionistic fuzzy sets in group decision making, Notes on IFS, 2, 15–32.Google Scholar
  43. 43.
    Szmidt E. and Kacprzyk J. (1996c) Remarks on some applications of intuitionistic fuzzy sets in decision making, Notes on IFS, 2 (3), 22–31.MATHMathSciNetGoogle Scholar
  44. 44.
    Szmidt E. and Kacprzyk J. (1997) On measuring distances between intuitionistic fuzzy sets, Notes on IFS, 3 (4), 1–13.MATHMathSciNetGoogle Scholar
  45. 45.
    Szmidt E. and Kacprzyk J. (1998a) Group Decision Making under Intuitionistic Fuzzy Preference Relations. IPMU’98, Paris, La Sorbonne, 172–178.Google Scholar
  46. 46.
    Szmidt E. and Kacprzyk J. (1998b) Applications of Intuitionistic Fuzzy Sets in Decision Making. Proc. 8th Congreso Español sobre Tecnologias y Lógica Fuzzy, Univ. de Navarra, 143–149.Google Scholar
  47. 47.
    Szmidt E. and Kacprzyk J. (2000) Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114 (3), 505–518.MATHCrossRefMathSciNetGoogle Scholar
  48. 48.
    Szmidt E. and Kacprzyk J. (2000) On Measures on Consensus Under Intuitionistic Fuzzy Relations. IPMU 2000, 1454–1461.Google Scholar
  49. 49.
    Szmidt E. and Kacprzyk J. (2001) Distance from Consensus Under Intuitionistic Fuzzy Preferences. Proc. EUROFUSE Workshop on Preference Modelling and Applications, Granada, 73–78.Google Scholar
  50. 50.
    Szmidt E., Kacprzyk J. (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118 (3), 467–477.MATHCrossRefMathSciNetGoogle Scholar
  51. 51.
    Szmidt E. and Kacprzyk J. (2001) Analysis of Consensus under Intuitionistic Fuzzy Preferences. Proc. Int. Conf. in Fuzzy Logic and Technology. De Montfort Univ. Leicester, UK, 79–82.Google Scholar
  52. 52.
    Szmidt E. and Kacprzyk J. (2002a) Analysis of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Preferences. Proc. IPMU’2002, Annecy, 1859–1865.Google Scholar
  53. 53.
    Szmidt E. and Kacprzyk J. (2002b) An Intuitionistic Fuzzy Set Based Approach to Intelligent Data Analysis (an application to medical diagnosis). In A. Abraham, L. Jain, J. Kacprzyk (Eds.): Recent Advances in Intelligent Paradigms and Applications. Springer-Verlag, 57–70.Google Scholar
  54. 54.
    Szmidt E. and Kacprzyk J. (2002c) Evaluation of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Sets. Proc. IEEE-IS’2002 – Int. IEEE Symposium: Intelligent Systems, Varna, 166–170.Google Scholar
  55. 55.
    Szmidt E., Kacprzyk J. (2003) Group Agreement Analysis via Distances and Entropy of Intuitionistic Fuzzy Sets. Int. Conference on Fuzzy Information Processing - Theories and Applications, Beijing, Springer, 631–635.Google Scholar
  56. 56.
    Szmidt E., Kacprzyk J.(2004) A Concept of Similatity for Intuitionistic Fuzzy Sets and its use in Group Decision Making. Proc. 2004 IEEE Int. Conference on Fuzzy Systems, Budapest, 1129-1134.Google Scholar
  57. 57.
    Szmidt E. and Kacprzyk J. (2004) Similarity of intuitionistic fuzzy sets and the Jaccard coefficient. Proc. IPMU 2004, Perugia, 1405–1412.Google Scholar
  58. 58.
    Szmidt E., Kacprzyk J. (2004) A Similarity Measure for Intuitionistic Fuzzy Sets and its Application in Supporting Medical Diagnostic Reasoning. LNAI, 3070, 388–393.Google Scholar
  59. 59.
    Szmidt E. and Kacprzyk J. (2005) A New Concept of a Similarity Measure for Intuitionistic Fuzzy Sets and its Use in Group Decision Making. In V. Torra, Y. Narukawa, S. Miyamoto (Eds.): Modelling Decisions for AI. LNAI 3558, Springer, 272–282.Google Scholar
  60. 60.
    Szmidt E. and Kacprzyk J. (2006) Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. 3rd Int. IEEE Conf. “Intelligent Systems”, 716–721.Google Scholar
  61. 61.
    Szmidt E. and Kacprzyk J. (2006) A Model of Case Based Reasoning Using Intuitionistic Fuzzy Sets. 2006 IEEE World Congress on Computational Intelligence, 8428–8453.Google Scholar
  62. 62.
    Szmidt E. and Kacprzyk J. (2006) An Application of Intuitionistic Fuzzy Set Similarity Measures to a Multi-criteria Decision Making Problem. ICAISC 2006, LNAI 4029, Springer-Verlag, 314–323.Google Scholar
  63. 63.
    Zadeh L.A. (1965) Fuzzy sets. Information and Control, 8, 338–353.MATHCrossRefMathSciNetGoogle Scholar
  64. 64.
    Zadeh, L.A. (1983) A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl., 9 (1), 149–184.MATHCrossRefMathSciNetGoogle Scholar
  65. 65.
    Zadrożny, S. (1997) An approach to the consensus reaching support in fuzzy environment. In: J. Kacprzyk, H. Nurmi and M. Fedrizzi (Eds.): Consensus under Fuzziness. Kluwer, Boston, 83–109.Google Scholar

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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Eulalia Szmidt
  • Janusz Kacprzyk

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