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Some Remarks on the Fuzzy Linguistic Model Based on Discrete Fuzzy Numbers

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Intelligent Systems'2014

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 322))

Abstract

In this article, some possible interpretations of the computational model based on discrete fuzzy numbers are given. In particular, some advantages of this model based on the aggregation process as well as on a greater flexibilization of the linguistic expressions are analysed. Finally, a fuzzy decision making model based on this kind on fuzzy subsets is proposed.

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References

  1. Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets and SystemsĀ 79, 175ā€“190 (1994)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  2. Herrera, F., Alonso, S., Chiclana, F., Herrera-Viedma, E.: Computing with words in decision making: Foundations, trends and prospects. Fuzzy Optimization and Decision MakingĀ 8(4), 337ā€“364 (2009)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  3. Herrera, F., MartĆ­nez, L.: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy SystemsĀ 8(6), 746ā€“752 (2000)

    ArticleĀ  Google ScholarĀ 

  4. TĆ¼rksen, I.: Type 2 representation and reasoning for CWW. Fuzzy Sets and SystemsĀ 127(1), 17ā€“36 (2002)

    ArticleĀ  MATHĀ  MathSciNetĀ  Google ScholarĀ 

  5. Wang, J.-H., Hao, J.: A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy SystemsĀ 14(3), 435ā€“445 (2006)

    ArticleĀ  Google ScholarĀ 

  6. Cabrerizo, F.J., Herrera-Viedma, E., Pedrycz, W.: A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. European Journal of Operational ResearchĀ 230(3), 624ā€“633 (2013)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  7. RodrĆ­guez, R., MartĆ­nez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy SystemsĀ 20(1), 109ā€“119 (2012)

    ArticleĀ  Google ScholarĀ 

  8. RodrĆ­guez, R., MartĆ­nez, L., Herrera, F.: A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Information SciencesĀ 241, 28ā€“42 (2013)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  9. Casasnovas, J., Riera, J.V.: Extension of discrete t-norms and t-conorms to discrete fuzzy numbers. Fuzzy Sets and SystemsĀ 167(1), 65ā€“81 (2011)

    ArticleĀ  MATHĀ  MathSciNetĀ  Google ScholarĀ 

  10. Casasnovas, J., Riera, J.V.: Weighted means of subjective evaluations. In: Seising, R., Sanz GonzĆ”lez, V. (eds.) Soft Computing in Humanities and Social Sciences. STUDFUZZ, vol.Ā 273, pp. 331ā€“354. Springer, Heidelberg (2012)

    ChapterĀ  Google ScholarĀ 

  11. Massanet, S., Riera, J.V., Torrens, J., Herrera-Viedma, E.: A new linguistic computational model based on discrete fuzzy numbers for computing with words. Information SciencesĀ 258, 277ā€“290 (2014)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  12. Riera, J.V., Torrens, J.: Aggregation of subjective evaluations based on discrete fuzzy numbers. Fuzzy Sets and SystemsĀ 191, 21ā€“40 (2012)

    ArticleĀ  MATHĀ  MathSciNetĀ  Google ScholarĀ 

  13. Riera, J.V., Torrens, J.: Aggregation functions on the set of discrete fuzzy numbers defined from a pair of discrete aggregations. Fuzzy Sets and SystemsĀ 241, 76ā€“93 (2014)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  14. Voxman, W.: Canonical representations of discrete fuzzy numbers. Fuzzy Sets and SystemsĀ 118(3), 457ā€“466 (2001)

    ArticleĀ  MATHĀ  MathSciNetĀ  Google ScholarĀ 

  15. Mayor, G., Torrens, J.: Triangular norms in discrete settings. In: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, pp. 189ā€“230. Elsevier (2005)

    Google ScholarĀ 

  16. De Baets, B., Mesiar, R.: Triangular norms on product lattices. Fuzzy Sets and SystemsĀ 104, 61ā€“75 (1999)

    ArticleĀ  MATHĀ  MathSciNetĀ  Google ScholarĀ 

  17. Mas, M., Monserrat, M., Torrens, J.: Kernel aggregation functions on finite scales, Constructions from their marginals. Fuzzy Sets and SystemsĀ 241, 27ā€“40 (2014)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  18. Godo, L., Torra, V.: On aggregation operators for ordinal qualitative information. IEEE Transactions on Fuzzy SystemsĀ 8, 143ā€“154 (2000)

    ArticleĀ  Google ScholarĀ 

  19. Mas, M., Mayor, G., Torrens, J.: t-Operators and uninorms on a finite totally ordered set. International Journal of Intelligent SystemsĀ 14, 909ā€“922 (1999)

    ArticleĀ  MATHĀ  Google ScholarĀ 

  20. Yager, R.R.: Aggregation of ordinal information. Fuzzy Optimization and Decision MakingĀ 6, 199ā€“219 (2007)

    ArticleĀ  MATHĀ  MathSciNetĀ  Google ScholarĀ 

  21. Casasnovas, J., Riera, J.V.: Lattice properties of discrete fuzzy numbers under extended min and max. In: Proceedings of IFSA-EUSFLAT-2009, Lisbon (2009)

    Google ScholarĀ 

  22. De Baets, B., Fodor, J.C., Ruiz-Aguilera, D., Torrens, J.: Idempotent uninorms on Finite Ordinal Scales. International Journal of Uncertainty, Fuzziness and Knowledge-Based SystemsĀ 17(1), 1ā€“14 (2009)

    ArticleĀ  MATHĀ  MathSciNetĀ  Google ScholarĀ 

  23. Herrera, F., Herrera-Viedma, E., MartĆ­nez, L.: A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets and SystemsĀ 114, 43ā€“58 (2000)

    ArticleĀ  MATHĀ  Google ScholarĀ 

  24. Alonso, S., PĆ©rez, I.J., Cabrerizo, F.J., Herrera-Viedma, E.: A linguistic consensus model for Web 2.0 communities. Applied Soft ComputingĀ 13(1), 149ā€“157 (2013)

    ArticleĀ  Google ScholarĀ 

  25. Chen, L.H., Lu, H.W.: An approximate approach for ranking fuzzy numbers based on left and right dominance. Computers and Mathematics with ApplicationsĀ 41(12), 1589ā€“1602 (2001)

    ArticleĀ  MATHĀ  MathSciNetĀ  Google ScholarĀ 

  26. Herrera, F., Herrera-Viedma, E., MartĆ­nez, L.: A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Transactions on Fuzzy SystemsĀ 16(2), 354ā€“370 (2008)

    ArticleĀ  Google ScholarĀ 

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Correspondence to Enrique Herrera-Viedma .

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Herrera-Viedma, E., Riera, J.V., Massanet, S., Torrens, J. (2015). Some Remarks on the Fuzzy Linguistic Model Based on Discrete Fuzzy Numbers. In: Angelov, P., et al. Intelligent Systems'2014. Advances in Intelligent Systems and Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-11313-5_29

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  • DOI: https://doi.org/10.1007/978-3-319-11313-5_29

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11312-8

  • Online ISBN: 978-3-319-11313-5

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