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Distributivity Equations Between Semi-t-operators Over Semi-uninorms

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 367))

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Abstract

The problem of distributivity was posed many years ago and investigated in families of certain operations, for example, t-norms, t-conorms, uninorms and nullnorms. In this paper, we continue to investigate the same topic as the above by focusing on semi-t-operators over semi-uninorms, which are generalizations of t-operators and uninorms by omitting commutativity, and associativity and commutativity, respectively. The obtained results are the full characterizations, and extend the previous ones about distributivity between nullnorms over uninorms, and also between semi-nullnorms over semi-uninorms.

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References

  1. Aczél, J.: Lectures on Functional Equations and Their Applications. Acad. Press, New York (1966)

    MATH  Google Scholar 

  2. Baczyński, M., Jayaram, B.: Fuzzy Implications, Studies in Fuzziness and Soft Computing, vol. 231. Springer, Berlin (2008)

    Google Scholar 

  3. Bustince, H., Burillo, P., Soria, F.: Automorphisms, negations and implication operators. Fuzzy Sets Syst. 134, 209–229 (2003)

    Article  MathSciNet  MATH  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)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. Drygaś, P.: Distributivity between semi-t-operators and semi-nullnorms. Fuzzy Sets. Syst. 264, 100–109 (2015)

    Google Scholar 

  7. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht (1994)

    Book  MATH  Google Scholar 

  8. Liu, H.W.: Distributivity and conditional distributivity of semi-uninorms over continuous t-conorms and t-norms. Fuzzy Sets Syst. 268, 27–43 (2015)

    Google Scholar 

  9. Jayaram, B., Rao, C.J.M.: On the distributivity of implication operators over \(T\)- and \(S\)-norms. IEEE Trans. Fuzzy Syst. 12, 194–198 (2004)

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

  11. Marichal, J.L.: On the associativity functional equation. Fuzzy Sets Syst. 114, 381–389 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mas, M., Mayor, G., Torrens, J.: t-Operators. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 7, 31–50 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. 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 

  14. Qin, F., Baczyński, M.: Distributivity equations of implications based on continuous triangular norms (I). IEEE Trans. Fuzzy Syst. 20, 153–167 (2012)

    Article  Google Scholar 

  15. Qin, F., Zhao, B.: The distributivity equations for idempotent uninorms and nullnorms. Fuzzy Sets. Syst. 155, 446–458 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rak, E.: Distributivity equation for nullnorms. J. Electr. Eng. 56(12/s), 53–55 (2005)

    Google Scholar 

  17. Rak, E., Drygaś, P.: Distributivity between uninorms. J. Electr. Eng. 57(7/s), 35–38 (2006)

    Google Scholar 

  18. Ruiz, D., Torrens, J.: Distributive idempotent uninorms. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 11, 413–428 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

Thanks to the support by National Natural Science Foundation of China (Nos. 61165014 and 11161023), A Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 2007B14), Jiangxi Natural Science Foundation (No. 20122BAB201009), and the Scientific Research Foundation of Jiangxi Provincial Education Department (No. GJJ12176).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, People’s Republic of China

    Feng Qin

  2. Department of Mathematics, Nanchang Normal University, Nanchang, 330032, People’s Republic of China

    Xiao-Quan Xu

Authors
  1. Feng Qin
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  2. Xiao-Quan Xu
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Corresponding author

Correspondence to Xiao-Quan Xu .

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Editors and Affiliations

  1. Guangzhou University, Guangzhou, China

    Bing-Yuan Cao

  2. Foreign Affairs Office, National Defense University, Beijing, China

    Zeng-Liang Liu

  3. Higher Education Mega Center, Guangzhou University, Guangzhou, China

    Yu-Bin Zhong

  4. Zhuhai Campus, Beijing Normal University, Zhuhai, China

    Hong-Hai Mi

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Qin, F., Xu, XQ. (2016). Distributivity Equations Between Semi-t-operators Over Semi-uninorms. In: Cao, BY., Liu, ZL., Zhong, YB., Mi, HH. (eds) Fuzzy Systems & Operations Research and Management. Advances in Intelligent Systems and Computing, vol 367. Springer, Cham. https://doi.org/10.1007/978-3-319-19105-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-19105-8_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19104-1

  • Online ISBN: 978-3-319-19105-8

  • eBook Packages: EngineeringEngineering (R0)

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