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Some aspects of intuitionistic fuzzy sets

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Abstract

We first discuss the significant role that duality plays in many aggregation operations involving intuitionistic fuzzy subsets. We then consider the extension to intuitionistic fuzzy subsets of a number of ideas from standard fuzzy subsets. In particular we look at the measure of specificity. We also look at the problem of alternative selection when decision criteria satisfaction is expressed using intuitionistic fuzzy subsets. We introduce a decision paradigm called the method of least commitment. We briefly look at the problem of defuzzification of intuitionistic fuzzy subsets.

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References

  • Atanassov K.T. (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20: 87–96

    Article  MATH  MathSciNet  Google Scholar 

  • Atanassov K.T. (1989) More on intuitionistic fuzzy sets. Fuzzy Sets and Systems 33: 37–459

    Article  MATH  MathSciNet  Google Scholar 

  • Atanassov K.T. (1999) Intuitionistic fuzzy sets. Heidelberg, Springer-Verlag

    MATH  Google Scholar 

  • Bellman R.E., Zadeh L.A. (1970) Decision-making in a fuzzy environment. Management Science 17(4): 141–164

    Article  MathSciNet  Google Scholar 

  • Cornelis, C., Atanassov, K. T., & Kerre, E. E. (2003). Intuitionistic fuzzy sets and interval valued fuzzy sets: A critical comparison. Proceedings Third European Conference (pp. 227–235). Germany: Fuzzy Logic Technology (EUSFLAT) Zittau.

  • Deschrijver G., Kerre E.E. (2003) On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems 133: 227–235

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D., Gottwald S., Hajek P., Kacprzyk J., Prade H. (2005) Terminological difficulties in fuzzy set theory—The case of Intuitionistic fuzzy sets. Fuzzy Sets and Systems 156: 485–491

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D., Prade H. (1985) A note on measures of specificity for fuzzy sets. International Journal of General Systems 10: 279–283

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D., Prade H. (1987) The principle of minimum specificity as a basis for evidential reasoning. In: Bouchon B., Yager R.R. (eds) Uncertainty in knowledge-based systems. Springer-Verlag, Berlin, pp 75–84

    Google Scholar 

  • Dubois D., Prade H. (1991) Fuzzy sets in approximate reasoning Part I: Inference with possibility distributions. Fuzzy Sets and Systems 40: 143–202

    Article  MATH  MathSciNet  Google Scholar 

  • Klement E.P., Mesiar R., Pap E. (2000) Triangular norms. Kluwer Academic Publishers, Dordrecht

    MATH  Google Scholar 

  • Klir G.J. (2006) Uncertainty and information. John Wiley & Sons, New York

    Google Scholar 

  • Pedrycz W., Gomide F. (2007) Fuzzy systems engineering: Toward human-centric computing. John Wiley & Sons, New York

    Google Scholar 

  • Yager R.R. (1982) Measuring tranquility and anxiety in decision making: An application of fuzzy sets. International Journal of General Systems 8: 139–146

    Article  MATH  MathSciNet  Google Scholar 

  • Yager R.R. (1983) Entropy and specificity in a mathematical theory of evidence. International Journal of General Systems 9: 249–260

    Article  MATH  MathSciNet  Google Scholar 

  • Yager R.R. (1984) Measuring the quality of linguistic forecasts. International Journal of Man-Machine Studies 21: 253–257

    Article  Google Scholar 

  • Yager R.R. (1986) A characterization of the extension principle. Fuzzy Sets and Systems 18: 205–217

    Article  MATH  MathSciNet  Google Scholar 

  • Yager R.R. (1992a) On the specificity of a possibility distribution. Fuzzy Sets and Systems 50: 279–292

    Article  MATH  MathSciNet  Google Scholar 

  • Yager R.R. (1992b) Default knowledge and measures of specificity. Information Sciences 61: 1–44

    Article  MATH  MathSciNet  Google Scholar 

  • Yager R.R. (1994) On the RAGE aggregation method with applications to neural networks and decision making. International Journal of Approximate Reasoning 11: 175–204

    Article  MATH  Google Scholar 

  • Yager R.R. (1998) On measures of specificity. In: Kaynak O., Zadeh L.A., Turksen B., Rudas I.J. (eds) Computational intelligence: Soft computing and fuzzy-neuro integration with applications. Springer-Verlag, Berlin, pp 94–113

    Google Scholar 

  • Yager R.R. (2007a) Owa aggregation of intuitionistic fuzzy sets. Technical report# MII–2717. Machine Intelligence Institute, Iona College, New Rochelle, NY

    Google Scholar 

  • Yager R.R. (2007b) On the soundness of altering granular information. International Journal of Approximate Reasoning 45: 43–67

    Article  MATH  MathSciNet  Google Scholar 

  • Yager R.R. (2008) Measures of specificity over continuous spaces under similarity relations. Fuzzy Sets and Systems 159: 2193–2210

    Article  MathSciNet  Google Scholar 

  • Yager R.R., Filev D.P. (1994) Essentials of fuzzy modeling and control. John Wiley, New York

    Google Scholar 

  • Yager R.R., Kikuchi S. (2004) On the role of anxiety in decisions under possibilistic uncertainty. IEEE Transactions on Systems, Man and Cybernetics: Part B 34: 1224–1234

    Article  Google Scholar 

  • Zadeh L.A. (1965) Fuzzy sets. Information and Control 8: 338–353

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh L. (1975) The concept of a linguistic variable and its application to approximate reasoning: Part 1. Information Sciences 8: 199–249

    Article  MathSciNet  Google Scholar 

  • Zadeh L.A. (2005) Toward a generalized theory of uncertainty (GTU)-An outline. Information Sciences 172: 1–40

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Ronald R. Yager.

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Yager, R.R. Some aspects of intuitionistic fuzzy sets. Fuzzy Optim Decis Making 8, 67–90 (2009). https://doi.org/10.1007/s10700-009-9052-7

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