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On the Migrativity Property for Uninorms and Nullnorms

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Book cover Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 853))

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Abstract

In this paper the notions of \(\alpha \)-migrative uninorms over a fixed nullnorm and \(\alpha \)-migrative nullnorms over a fixed uninorm are introduced and studied. All solutions of the migrativity equation for all possible combinations of uninorms and nullnorms are investigated. So, \((\alpha ,T)\)-migrative nullnorm and \((\alpha ,T)\)-migrative uninorm (\((\alpha ,S)\)-migrative nullnorm and \((\alpha ,S)\)-migrative uninorm) for a given t-norm (t-conorm) are extended to a more general form.

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References

  1. Aşıcı, E.: On the properties of the \( F \)-partial order and the equivalence of nullnorms. Fuzzy Sets Syst. (in press). https://doi.org/10.1016/j.fss.2017.11.008

  2. Aşıcı, E.: Some remarks on \( F \)-partial order and properties. Rom. J. Math. Comput. Sci. 7, 72–79 (2017)

    MathSciNet  Google Scholar 

  3. Aşıcı, E.: Some remarks on an order induced by uninorms. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT -2017. AISC, vol. 641, pp. 69–77. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66830-7_7

    Chapter  Google Scholar 

  4. 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). https://doi.org/10.1016/S0165-0114(99)00125-6

    Article  MathSciNet  MATH  Google Scholar 

  5. Casasnovas, J., Mayor, G.: Discrete t-norms and operations on extended multisets. Fuzzy Sets Syst. 159, 1165–1177 (2008). https://doi.org/10.1016/j.fss.2007.12.005

    Article  MathSciNet  MATH  Google Scholar 

  6. 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 

  7. Çaylı, G.D.: On a new class of t-norms and t-conorms on bounded lattices. Fuzzy Sets Syst. 332, 129–143 (2018). https://doi.org/10.1016/j.fss.2017.07.015

    Article  MathSciNet  MATH  Google Scholar 

  8. Çaylı, G.D., Drygaś, P.: Some properties of idempotent uninorms on a special class of bounded lattices. Inf. Sci. 422, 352–363 (2018). https://doi.org/10.1016/j.ins.2017.09.018

    Article  MathSciNet  Google Scholar 

  9. Drewniak, J., Drygaś, P., Rak, E.: Distributivity between uninorms and nullnorms. Fuzzy Sets Syst. 159, 1646–1657 (2008). https://doi.org/10.1016/j.fss.2007.09.015

    Article  MathSciNet  MATH  Google Scholar 

  10. Durante, F., Sarkoci, P.: A note on the convex combinations of triangular norms. Fuzzy Sets Syst. 159, 77–80 (2008). https://doi.org/10.1016/j.fss.2007.07.005

    Article  MathSciNet  MATH  Google Scholar 

  11. Durante, F., Fern\(\acute{a}\)ndez-S\(\acute{a}\)nchez, J., Quesada-Molina, J.J.: On the \(\alpha \)-migrativity of multivariate semi-copulas. Inf. Sci. 187, 216–223 (2012). https://doi.org/10.1016/j.ins.2011.10.026

  12. Durante, F., Ricci, R.G.: Supermigrative semi-copulas and triangular norms. Inf. Sci. 179, 2689–2694 (2009). https://doi.org/10.1016/j.ins.2009.04.001

    Article  MathSciNet  MATH  Google Scholar 

  13. Fern\(\acute{a}\)ndez-S\(\acute{a}\)nchez, F., Quesada-Molina, J.J., \(\acute{U}\)beda-Flores, M.: On \((\alpha ,\beta )\)-homogeneous copulas. Inf. Sci. 221, 181–191 (2013). https://doi.org/10.1016/j.ins.2012.09.048

  14. Fodor, J., Rudas, I.J.: An extension of the migrative property for triangular norms. Fuzzy Sets Syst. 168, 70–80 (2011). https://doi.org/10.1016/j.fss.2010.09.020

    Article  MathSciNet  MATH  Google Scholar 

  15. Fodor, J., Rudas, I.J.: On continuous triangular norms that are migrative. Fuzzy Sets Syst. 158, 1692–1697 (2007). https://doi.org/10.1016/j.fss.2007.02.020

    Article  MathSciNet  MATH  Google Scholar 

  16. Fodor, J., Rudas, I.J.: Migrative t-norms with respect to continuous ordinal sums. Inf. Sci. 181, 4860–4866 (2011). https://doi.org/10.1016/j.ins.2011.05.014

    Article  MathSciNet  MATH  Google Scholar 

  17. Fodor, J., Rudas, I.J., Rybalov, A.: Structure of uninorms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5, 411–427 (1997). https://doi.org/10.1142/S0218488597000312

    Article  MathSciNet  MATH  Google Scholar 

  18. Karaçal, F., Aşıcı, E.: Some notes on T-partial order. J. Inequalities Appl. 2013, 219 (2013). https://doi.org/10.1186/1029-242X-2013-219

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  Google Scholar 

  20. 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). https://doi.org/10.1016/j.fss.2009.04.014

    Article  MathSciNet  MATH  Google Scholar 

  21. Mas, M., Mayor, G., Torrens, J.: t-operators. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 7, 31–50 (1999). https://doi.org/10.1142/S0218488599000039

    Article  MATH  Google Scholar 

  22. Mas, M., Monserrat, M., Ruiz-Aquilera, D., Torrens, J.: Migrative uninorms and nullnorms over t-norms and t-conorms. Fuzzy Sets Syst. 261, 20–32 (2015). https://doi.org/10.1016/j.fss.2014.05.012

    Article  MathSciNet  MATH  Google Scholar 

  23. Mas, M., Monserrat, M., Ruiz-Aquilera, D., Torrens, J.: An extension of the migrative property for uninorms. Fuzzy Sets Syst. 246, 191–198 (2013). https://doi.org/10.1016/j.ins.2013.05.024

    Article  MathSciNet  MATH  Google Scholar 

  24. Martin, J., Mayor, G., Torrens, J.: On locally internal monotonic operations. Fuzzy Sets Syst. 137, 27–42 (2003). https://doi.org/10.1016/S0165-0114(02)00430-X

    Article  MathSciNet  MATH  Google Scholar 

  25. Mesiar, R., Bustince, H., Fernandez, J.: On the \(\alpha \)-migrativity of semicopulas, quasi-copulas and copulas. Inf. Sci. 180, 1967–1976 (2010). https://doi.org/10.1016/j.ins.2010.01.024

    Article  MathSciNet  MATH  Google Scholar 

  26. Ouyang, Y.: Generalizing the migrativity of continuous t-norms. Fuzzy Sets Syst. 211, 73–83 (2013). https://doi.org/10.1016/j.fss.2012.03.008

    Article  MathSciNet  MATH  Google Scholar 

  27. Ruiz-Aquilera, D., Torrens, J.: Distributivity and conditional distributivity of a uninorm and a continuous t-conorm. IEEE Trans. Fuzzy Syst. 14, 180–190 (2006). https://doi.org/10.1109/TFUZZ.2005.864087

    Article  MATH  Google Scholar 

  28. Su, Y., Zong, W., Liu, H.W.: Migrative property for uninorms. Fuzzy Sets Syst. 287, 213–226 (2016). https://doi.org/10.1016/j.fss.2015.05.018

    Article  Google Scholar 

  29. Wu, L., Ouyang, Y.: On the migrativity of triangular subnorms. Fuzzy Sets Syst. 226, 89–98 (2013). https://doi.org/10.1016/j.fss.2012.12.013

    Article  MathSciNet  MATH  Google Scholar 

  30. Yager, R.R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets Syst. 80, 111–120 (1996). https://doi.org/10.1016/0165-0114(95)00133-6

    Article  MathSciNet  MATH  Google Scholar 

  31. Zong, W., Su, Y., Liu, H.W.: Migrative property for nullnorms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5, 749–759 (2014). https://doi.org/10.1142/S021848851450038X

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgement

We are grateful to the anonymous reviewers and editors for their valuable comments which have enabled us to improve the original version of our paper.

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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. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Aşıcı, E. (2018). On the Migrativity Property for Uninorms and Nullnorms. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_28

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  • DOI: https://doi.org/10.1007/978-3-319-91473-2_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91472-5

  • Online ISBN: 978-3-319-91473-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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