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A New Proposal of Parametric Similarity Measures with Application in Decision Making

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Intelligent Computing

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 284))

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Abstract

We introduce a general equality index for two fuzzy values, proposing a parametric family of similarity measures between two fuzzy vectors, and investigating the mathematical properties. Subsequently we construct a class of parametric similarity measures, showing how the proposed approach extends and generalizes previously proposed framework in the context of decision making problem. The proposed approach can support decision maker under complex situations. An application of the proposed method is also given.

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Notes

  1. 1.

    The probabilistic sum is the dual t-conorm of t-norm product \(T_P(a,b)=ab\).

References

  1. Alsina, C., Schweizer, B., Frank, M.: Associative Functions: Triangular Norms and Copulas. World Scientific, Singapore (2006)

    Book  Google Scholar 

  2. Bien, Z., Chun, M.-G.: An inference network for bidirectional approximate reasoning based on an equality measure. IEEE Trans. Fuzzy Syst. 2(2), 177–180 (1994)

    Article  Google Scholar 

  3. Chun, M.-G.: A similarity-based bidirectional approximate reasoning method for decision-making systems. Fuzzy Sets Syst. 117(2), 269–278 (2001)

    Article  MathSciNet  Google Scholar 

  4. Dubois, D., Prade, H.: New results about properties and semantics of fuzzy set-theoretic operators. In: Fuzzy Sets: Theory and Applications to Policy Analysis and Information Systems, pp. 59–75. Plenum Press, New York (1980)

    Google Scholar 

  5. Dubois, D., Prade, H.: A class of fuzzy measures based on triangular norms a general framework for the combination of uncertain information. Int. J. Gener. Syst. 8(1), 43–61 (1982)

    Article  MathSciNet  Google Scholar 

  6. Dubois, D., Prade, H.: Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions. Fuzzy Sets Syst. 40(1), 143–202 (1991)

    Article  Google Scholar 

  7. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation functions: means. Inf. Sci. 181(1), 1–22 (2011)

    Article  MathSciNet  Google Scholar 

  8. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications (1996)

    Google Scholar 

  9. Pedrycz, W.: Direct and inverse problem in comparison of fuzzy data. Fuzzy Sets Syst. 34(2), 223–235 (1990)

    Article  MathSciNet  Google Scholar 

  10. Pedrycz, W.: Neurocomputations in relational systems. IEEE Trans. Pattern Anal. Mach. Intell. 13(3), 289–297 (1991)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Management, Economics, Mathematics and Statistics, University of Salento, Lecce, Italy

    Luca Anzilli

  2. Department of Economics, University Ca’ Foscari of Venice, Venice, Italy

    Silvio Giove

Authors
  1. Luca Anzilli
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  2. Silvio Giove
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Corresponding author

Correspondence to Luca Anzilli .

Editor information

Editors and Affiliations

  1. Faculty of Science and Engineering, Saga University, Saga, Japan

    Kohei Arai

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Anzilli, L., Giove, S. (2021). A New Proposal of Parametric Similarity Measures with Application in Decision Making. In: Arai, K. (eds) Intelligent Computing. Lecture Notes in Networks and Systems, vol 284. Springer, Cham. https://doi.org/10.1007/978-3-030-80126-7_16

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