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Some Remarks on an Order Induced by Uninorms

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 641))

Abstract

Recently an order induced by t-norms, uninorms and nullnorms have been investigated. This paper is mainly devoted to defining and investigating the set of incomparable elements with respect to the order induced by a uninorm. Also, by defining such an order, an equivalence relation on the class of uninorms is defined and this equivalence is deeply investigated.

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References

  1. Aşıcı, E.: An order induced by nullnorms and its properties. Fuzzy Sets Syst. (in press). doi:10.1016/j.fss.2016.12.004

  2. Aşıcı, E., Karaçal, F.: On the \(T\)-partial order and properties. Inf. Sci. 267, 323–333 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aşıcı, E., Karaçal, F.: Incomparability with respect to the triangular order. Kybernetika 52, 15–27 (2016)

    MathSciNet  MATH  Google Scholar 

  4. Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society, Providence (1967)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Casasnovas, J., Mayor, G.: Discrete t-norms and operations on extended multisets. Fuzzy Sets Syst. 159, 1165–1177 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. De Baets, B., Mesiar, R.: Triangular norms on product lattices. Fuzzy Sets Syst. 104, 61–75 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. De Baets, B., Mesiar, R.: Triangular norms on the real unit square. In: Proceedings of the 1999 EUSFLAT-ESTYLF Joint Conference, Palma de Mallorca, Spain, pp. 351–354 (1999)

    Google Scholar 

  9. Çaylı, G.D., Karaçal, F., Mesiar, R.: On a new class of uninorms on bounded lattices. Inf. Sci. 367–368, 221–231 (2016)

    Article  Google Scholar 

  10. Çaylı, G.D., KaraÇal, F.: Construction of uninorms on bounded lattices. Kybernetika 53, 394–417 (2017)

    Google Scholar 

  11. Çaylı, G.D.: On a new class of t-norms and t-conorms on bounded lattices. Fuzzy Sets Syst. (in press) doi:10.1016/j.fss.2017.07.015

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Drygaś, P., Rak, E.: Distributivity equation in the class of 2-uninorms. Fuzzy Sets Syst. 291, 82–97 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dubois, D., Prade, H.: Fundamentals of Fuzzy Sets. Kluwer Acad. Publ., Boston (2000)

    Book  MATH  Google Scholar 

  15. Ertuğrul, U., Kesicioğlu, M.N., Karaçal, F.: Ordering based on uninorms. Inf. Sci. 330, 315–327 (2016)

    Article  Google Scholar 

  16. Fodor, J.C., Yager, R.R., Rybalov, A.: Structure of uninorms. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 5, 411–427 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gottwald, S.: A Treatise on Many-Valued Logic. Studies in Logic and Computation. Research Studies Press, Baldock (2001)

    MATH  Google Scholar 

  18. Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  19. Karaçal, F., Aşıcı, E.: Some notes on T-partial order. J. Inequal. Appl. 2013, 219 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Karaçal, F., Kesicioğlu, M.N.: A T-partial order obtained from t-norms. Kybernetika 47, 300–314 (2011)

    MathSciNet  MATH  Google Scholar 

  21. Karaçal, F., Mesiar, R.: Uninorms on bounded lattices. Fuzzy Sets Syst. 261, 33–43 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  22. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  23. Liang, X., Pedrycz, W.: Logic-based fuzzy networks: a study in system modeling with triangular norms and uninorms. Fuzzy Sets Syst. 160, 3475–3502 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Maes, K.C., Mesiarova-Zemankova, A.: Cancellativity properties for t-norms and t-subnorms. Inf. Sci. 179, 135–150 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Martin, J., Mayor, G., Torrens, J.: On locally internal monotonic operations. Fuzzy Sets Syst. 137, 27–42 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  27. Mitsch, H.: A natural partial order for semigroups. Proc. Am. Math. Soc. 97, 384–388 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  28. Saminger, S.: On ordinal sums of triangular norms on bounded lattices. Fuzzy Sets Syst. 157, 1403–1413 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  29. Yager, R.R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets Syst. 80, 111–120 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  30. Yager, R.R.: Uninorms in fuzzy system modeling. Fuzzy Sets Syst. 122, 167–175 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  31. Yager, R.R.: Aggregation operators and fuzzy systems modelling. Fuzzy Sets Syst. 67, 129–145 (1994)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Software Engineering, Faculty of Technology, Karadeniz Technical University, 61830, Trabzon, Turkey

    Emel Aşıcı

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  1. Emel Aşıcı
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Correspondence to Emel Aşıcı .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Sławomir Zadrożny

  4. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Aşıcı, E. (2018). Some Remarks on an Order Induced by Uninorms. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_7

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  • DOI: https://doi.org/10.1007/978-3-319-66830-7_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66829-1

  • Online ISBN: 978-3-319-66830-7

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