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Characterizations of residual implications derived from uni-nullnorms

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Abstract

Uni-nullnorms generalize both uninorms and nullnorms. In this paper, residual implications derived from uni-nullnorms are investigated. First, properties of residual implications derived from uni-nullnorms and left-continuous uni-nullnorms are studied. Then, it is characterized for which uni-nullnorms the residuated operations are fuzzy implications. Finally, an axiomatic characterization of residual implications derived from left-continuous uni-nullnorms is given and the mutual independence of the properties in this characterization is investigated.

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Acknowledgements

The authors would like to thank the editor and the anonymous referees for their valuable comments and suggestions which helped to improve the paper.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Leshan Normal University, Leshan, 614000, Sichuan, China

    Feng Sun, Xiao-bing Qu & Xue-jun Huang

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  1. Feng Sun
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  2. Xiao-bing Qu
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  3. Xue-jun Huang
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Correspondence to Feng Sun.

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Communicated by Marcos Eduardo Valle.

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This work was supported by the National Natural Science Foundation of China (No. 11701245), the Scientific Research Fund of Sichuan Provincial Education Department (Nos. 18ZA0238 and 18ZA0241), and the Research Projects of Leshan Normal University (Nos. XJR17004 and ZZ201811).

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Sun, F., Qu, Xb. & Huang, Xj. Characterizations of residual implications derived from uni-nullnorms. Comp. Appl. Math. 39, 110 (2020). https://doi.org/10.1007/s40314-020-1135-7

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  • DOI: https://doi.org/10.1007/s40314-020-1135-7

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