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Uninorms and Non-contradiction

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5285))

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Abstract

This paper studies the satisfaction of the well-known Non-Contradiction Principle within the class of uninorm aggregation functions, taking into account that this principle may be interpreted in two different ways (a strong one, based on falsity, and a weaker one, relying on self-contradiction). The logical negation is represented by means of strong negation functions, and the most important classes of uninorms are examined.

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References

  1. Yager, R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80, 111–120 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dombi, J.: Basic concepts for a theory of evaluation: the aggregative operator. Europ. J. Oper. Research 10, 282–293 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Klement, E., Mesiar, R., Pap, E.: On the relationship of associative compensatory operators to triangular norms and conorms. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 4, 129–144 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fodor, J., Yager, R., Rybalov, A.: Structure of uninorms. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 5, 411–427 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. De Baets, B.: Idempotent uninorms. Europ. J. Oper. Research 118, 631–642 (1999)

    Article  MATH  Google Scholar 

  6. Martín, J., Mayor, G., Torrens, J.: On locally internal monotonic operations. Fuzzy Sets and Systems 137, 27–42 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hu, S.K., Li, Z.F.: The structure of continuous uni-norms. Fuzzy Sets and Systems 124, 43–52 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Drygaś, P.: On the structure of continuous uninorms. Kybernetika 43(2), 183–196 (2007)

    MathSciNet  MATH  Google Scholar 

  9. Calvo, T., De Baets, B., Fodor, J.: The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets and Systems 120, 385–394 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mas, M., Mayor, G., Torrens, J.: The modularity condition for uninorms and t-operators. Fuzzy Sets and Systems 126, 207–218 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mas, M., Mayor, G., Torrens, J.: The distributivity condition for uninorms and t-operators. Fuzzy Sets and Systems 128, 209–225 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Drewniak, J., Drygaś, P., Rak, E.: Distributivity between uninorms and nullnorms. Fuzzy Sets and Systems 159(13), 1646–1657 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. De Baets, B., Fodor, J.: Van Melle’s combining function in MYCIN is a representable uninorm: An alternative proof. Fuzzy Sets and Systems 104, 133–136 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tsadiras, A., Margaritis, K.: The MYCIN certainty factor handling function as uninorm operator and its use as a threshold function in artificial neurons. Fuzzy Sets and Systems 93, 263–274 (1999)

    Article  MathSciNet  Google Scholar 

  15. Yager, R.: Uninorms in fuzzy systems modeling. Fuzzy Sets and Systems 122, 167–175 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yager, R., Kreinovich, V.: Universal approximation theorem for uninorm-based fuzzy systems modeling. Fuzzy Sets and Systems 140, 331–339 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. De Baets, B., Fodor, J.: Residual operators of uninorms. Soft Comput. 3(2), 89–100 (1999)

    Article  MATH  Google Scholar 

  18. Ruiz-Aguilera, D., Torrens, J.: Residual implications and co-implications from idempotent uninorms. Kybernetika 40(1), 21–38 (2004)

    MathSciNet  MATH  Google Scholar 

  19. Mas, M., Monserrat, M., Torrens, J.: Two types of implications derived from uninorms. Fuzzy Sets Syst. 158(23), 2612–2626 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ruiz-Aguilera, D., Torrens, J.: Distributivity of residual implications over conjunctive and disjunctive uninorms. Fuzzy Sets and Systems 158(1), 23–37 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gabbay, D.M., Metcalfe, G.: Fuzzy logics based on [0, 1]-continuous uninorms. Arch. Math. Log. 46(5-6), 425–449 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. Marchioni, E., Montagna, F.: On triangular norms and uninorms definable in Ł \(\Pi \frac{1}{2}\). Int. J. Approx. Reasoning 47(2), 179–201 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Pedrycz, W.: Logic-based fuzzy neurocomputing with unineurons. IEEE T. Fuzzy Systems 14(6), 860–873 (2006)

    Article  Google Scholar 

  24. Pedrycz, W., Hirota, K.: Uninorm-based logic neurons as adaptive and interpretable processing constructs. Soft Comput. 11(1), 41–52 (2007)

    Article  MATH  Google Scholar 

  25. Fodor, J., De Baets, B.: Uninorm basics. In: Wang, P., Ruan, D., Kerre, E. (eds.) Fuzzy Logic. A Spectrum of Theoretical & Practical Issues, pp. 49–64. Springer, Berlin (2007)

    Chapter  Google Scholar 

  26. Trillas, E., Alsina, C., Pradera, A.: Searching for the roots of Non-Contradiction and Excluded-Middle. International Journal of General Systems 31, 499–513 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  27. Pradera, A., Trillas, E.: Aggregation operators from the ancient NC and EM point of view. Kybernetika 42, 243–260 (2006)

    MathSciNet  MATH  Google Scholar 

  28. Pradera, A., Trillas, E.: Aggregation, Non-Contradiction and Excluded-Middle. Mathware & Soft Computing XIII, 189–201 (2006)

    MathSciNet  MATH  Google Scholar 

  29. Klement, E., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)

    Book  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  31. Trillas, E.: Sobre funciones de negación en la teoría de los subconjuntos difusos. In: Stochastica, vol. III, pp. 47–59 (in Spanish) (1979); Reprinted (English version) S. Barro et al. (eds.): Advances of Fuzzy Logic, Universidad de Santiago de Compostela, pp. 31–43 (1998)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Departamento de Ciencias de la Computación, Universidad Rey Juan Carlos, C. Tulipán s/n, Móstoles, 28933, Madrid, Spain

    Ana Pradera

Authors
  1. Ana Pradera
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Editor information

Editors and Affiliations

  1. IIIA, Artificial Intelligence Research Institute CSIC, Spanish National Research Council,, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen,, 3-1-10 Naka, Kunitachi, 186-0004, Tokyo, Japan

    Yasuo Narukawa

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© 2008 Springer-Verlag Berlin Heidelberg

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Pradera, A. (2008). Uninorms and Non-contradiction. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2008. Lecture Notes in Computer Science(), vol 5285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88269-5_6

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  • DOI: https://doi.org/10.1007/978-3-540-88269-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88268-8

  • Online ISBN: 978-3-540-88269-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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