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Pseudo General Overlap Functions and Weak Inflationary Pseudo BL-Algebras

Author

Listed:
  • Rong Liang

    (Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China
    Current address: School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China.)

  • Xiaohong Zhang

    (Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China
    Shaanxi Joint Laboratory of Artificial Intelligence, Shaanxi University of Science & Technology, Xi’an 710021, China
    Current address: School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China.)

Abstract

General overlap functions are generalized on the basis of overlap functions, which have better application effects in classification problems, and the (weak) inflationary BL-algebras as the related algebraic structure were also studied. However, general overlap functions are a class of aggregation operators, and their commutativity puts certain restrictions on them. In this article, we first propose the notion of pseudo general overlap functions as a non-commutative generalization of general overlap functions, so as to extend their application range, then illustrate their relationship with several other commonly used aggregation functions, and characterize some construction methods. Secondly, the residuated implications induced by inflationary pseudo general overlap functions are discussed, and some examples are given. Then, on this basis, we show the definitions of inflationary pseudo general residuated lattices (IPGRLs) and weak inflationary pseudo BL-algebras, and explain that the weak inflationary pseudo BL-algebras can be gained by the inflationary pseudo general overlap functions. Moreover, they are more extensive algebraic structures, thus enriching the content of existing non-classical logical algebra. Finally, their related properties and their relations with some algebraic structures such as non-commutative residuated lattice-ordered groupoids are investigated. The legend reveals IPGRLs include all non-commutative algebraic structures involved in the article.

Suggested Citation

  • Rong Liang & Xiaohong Zhang, 2022. "Pseudo General Overlap Functions and Weak Inflationary Pseudo BL-Algebras," Mathematics, MDPI, vol. 10(16), pages 1-15, August.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:3007-:d:893193
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    References listed on IDEAS

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    1. Nan Sheng & Xiaohong Zhang, 2022. "Regular Partial Residuated Lattices and Their Filters," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
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    Cited by:

    1. Mingdi Hu & Yixuan Li & Jiulun Fan & Bingyi Jing, 2022. "Joint Semantic Deep Learning Algorithm for Object Detection under Foggy Road Conditions," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    2. Xiaohong Zhang & Rong Liang & Benjamín Bedregal, 2022. "Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices," Mathematics, MDPI, vol. 10(18), pages 1-21, September.

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