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Distributivity for 2-Uninorms over Semi-uninorms

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Quantitative Logic and Soft Computing 2016

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 510))

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Abstract

This paper is devoted to solving the distributivity equations for 2-uninorms over semi-uninorms. Our investigations are motivated by the couple of distributive logical connectives and their generalizations, such as t-norms, t-conorms, uninorms, nullnorms, and fuzzy implications, which are often used in fuzzy set theory. There are two generalizations of them. One is a 2-uninorm covering both a uninorm and a nullnorm, which forms a class of commutative, associative and increasing operators on the unit interval with an absorbing element that separates two subintervals with neutral elements. Another is a semi-uninorm, which generalizes a uninorm by omitting commutativity and associativity. In this work, all possible solutions of the distributivity equation for the three defined subclasses of 2-uninorms over semi-uninorms are characterized.

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Acknowledgments

This research is supported by the National Natural Science Foundation of China (No. 61563020) and Jiangxi Natural Science Foundation (No. 20151BAB201019).

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Authors and Affiliations

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

    Ya-Ming Wang & Feng Qin

Authors
  1. Ya-Ming Wang
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  2. Feng Qin
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Corresponding author

Correspondence to Feng Qin .

Editor information

Editors and Affiliations

  1. Zhejiang, Zhejiang Sci-Tech University Zhejiang, Hangzhou, China

    Tai-He Fan

  2. Fujian, Jimei University Fujian, Xiamen, China

    Shui-Li Chen

  3. Zhejiang, Zhejiang Sci-Tech University Zhejiang, Hangzhou, China

    San-Min Wang

  4. Yanta, Shaanxi Normal University Yanta, Xi’an, China

    Yong-Ming Li

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Wang, YM., Qin, F. (2017). Distributivity for 2-Uninorms over Semi-uninorms. In: Fan, TH., Chen, SL., Wang, SM., Li, YM. (eds) Quantitative Logic and Soft Computing 2016. Advances in Intelligent Systems and Computing, vol 510. Springer, Cham. https://doi.org/10.1007/978-3-319-46206-6_31

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  • DOI: https://doi.org/10.1007/978-3-319-46206-6_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46205-9

  • Online ISBN: 978-3-319-46206-6

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