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Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making

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An Erratum to this article was published on 07 June 2012

Abstract

Atanassov (1986) defined the notion of intuitionistic fuzzy set, which is a generalization of the notion of Zadeh’ fuzzy set. In this paper, we first develop some similarity measures of intuitionistic fuzzy sets. Then, we define the notions of positive ideal intuitionistic fuzzy set and negative ideal intuitionistic fuzzy set. Finally, we apply the similarity measures to multiple attribute decision making under intuitionistic fuzzy environment.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K. (1989a). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems 33: 37–46

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K. (1989b). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 31: 343–349

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K. (1994a). New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems 61: 137–142

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K. (1994b). Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 64: 159–174

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K. (1999). Intuitionistic fuzzy sets: theory and applications. Physica-Verlag, Heidelberg

    Book  MATH  Google Scholar 

  • Atanassov K. (2000). Two theorems for intuitionistic fuzzy sets. Fuzzy Sets and Systems 110: 267–269

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K., Georgiev C. (1993). Intuitionistic fuzzy prolog. Fuzzy Sets and Systems 53: 121–128

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov K., Pasi G., Yager R.R. (2005). Intuitionistic fuzzy interpretations of multi-criteria multi- person and multi-measurement tool decision making. International Journal of Systems Science 36: 859–868

    Article  MathSciNet  MATH  Google Scholar 

  • Bustine H., Burillo P. (1996). Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems 79: 403–405

    Article  MathSciNet  MATH  Google Scholar 

  • Bustince H., Kacprzyk J., Mohedano V. (2000). Intuitionistic fuzzy generators: Application to intuitionistic fuzzy complementation. Fuzzy Sets and Systems 114: 485–504

    Article  MathSciNet  MATH  Google Scholar 

  • Chen S.M. (1988). A new approach to handling fuzzy decisionmaking problems. IEEE Transactions on Systems, Man, and Cybernetics-18: 1012–1016

    Article  MATH  Google Scholar 

  • Chen S.M., Yeh S.M., Hsiao P.H. (1995). A comparison of similarity measures of fuzzy values. Fuzzy Sets and Systems 72: 79–89

    Article  MathSciNet  Google Scholar 

  • Chen S.M., Tan J.M. (1994) Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 67: 163–172

    Article  MathSciNet  MATH  Google Scholar 

  • De S.K., Biswas R., Roy A.R. (2000). Some operations on intuitionistic fuzzy sets. Fuzzy Sets and Systems 114: 477–484

    Article  MathSciNet  MATH  Google Scholar 

  • S.K. De R. Biswas A.R. Roy (2001) ArticleTitleAn application of intuitionistic fuzzy sets in medical diagnosis Fuzzy Sets and Systems 117 209–213 Occurrence Handle10.1016/S0165-0114(98)00235-8 Occurrence Handle0980.92013

    Article  MATH  Google Scholar 

  • Deschrijver G., Kerre E. (2003). On the composition of intuitionistic fuzzy relations. Fuzzy Sets and Systems 136: 333–361

    Article  MathSciNet  MATH  Google Scholar 

  • Gau W.L., Buehrer D.J. (1993). Vague Sets. IEEE Transactions on Systems, Man, and Cybernetics 23: 610–614

    Article  MATH  Google Scholar 

  • Grzegorzewski P. (2004). Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems 148: 319–328

    Article  MathSciNet  MATH  Google Scholar 

  • Hong D.H., Choi C.H. (2000). Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 114: 103–113

    Article  MATH  Google Scholar 

  • Hung D.H., Hwang S.Y. (1994). A note on the value similarity of fuzzy systems variables. Fuzzy Sets and Systems 66: 383–386

    Article  MathSciNet  MATH  Google Scholar 

  • Hyung L.K., Song Y.S., Lee K.M. (1994). Similarity measure between fuzzy sets and between elements. Fuzzy Sets and Systems 62: 291–293

    Article  MathSciNet  Google Scholar 

  • Kacprzyk J. (1997). Multistage fuzzy control. Chichester: Wiley

    MATH  Google Scholar 

  • Kaufmann A. (1973). Introduction a La Theorie Des Sous-ensembles Flous. Editeurs: Masson et Cie.

    MATH  Google Scholar 

  • Liu X. (1992). Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems 52: 305–318

    Article  MathSciNet  MATH  Google Scholar 

  • Mondal T.K., Samanta S.K. (2001). Topology of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 119: 483–494

    Article  MathSciNet  MATH  Google Scholar 

  • Mondal T.K., Samanta S.K. (2002). On intuitionistic gradation of openness. Fuzzy Sets and Systems 131: 323–336

    Article  MathSciNet  MATH  Google Scholar 

  • Pappis C.P., Karacapilidis N.I. (1993). A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems 56: 171–174

    Article  MathSciNet  MATH  Google Scholar 

  • Sanchez E. (1976). Resolution of composition fuzzy relation equations. Information and Control 30: 38–48

    Article  MathSciNet  MATH  Google Scholar 

  • Szmidt E., Kacprzyk J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems 114: 505–518

    Article  MathSciNet  MATH  Google Scholar 

  • Szmidt E., Kacprzyk J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118: 467–477

    Article  MathSciNet  MATH  Google Scholar 

  • Szmidt E., Kacprzyk J. (2002). Using intuitionistic fuzzy sets in group decision making. Control and Cybernetics 31: 1037–1053

    MATH  Google Scholar 

  • Sudkamp T. (1993). Similarity, interpolation and fuzzy rule construction. Fuzzy Sets and Systems 58: 73–86

    Article  MathSciNet  Google Scholar 

  • Wang W.J. (1997). New similarity measures on fuzzy sets and elements. Fuzzy Sets and Systems 85: 305–309

    Article  MathSciNet  MATH  Google Scholar 

  • Xu Z.S., Ronald R.R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems 35: 417–433

    Article  MathSciNet  MATH  Google Scholar 

  • Yoon K. (1989). The propagation of errors in multiple-attribute decision analysis: A practical approach. Journal of Operational Research Society 40: 681–686

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Zwick R., Carlstein E., Budescu D.V. (1987) Measures of similarity among fuzzy concepts: A comparative analysis. International Journal of Approximate Reasoning 1: 221–242

    Article  MathSciNet  Google Scholar 

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Correspondence to Zeshui Xu.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s10700-012-9135-8

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Xu, Z. Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Making 6, 109–121 (2007). https://doi.org/10.1007/s10700-007-9004-z

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