JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (2): 7-16.doi: 10.6040/j.issn.1671-9352.0.2020.418

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Hesitant fuzzy ideals in non-involutive residuated lattices

LIU Chun-hui   

  1. School of Mathematics and Computer Science, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Published:2021-01-21

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Abstract: In this paper, the problem of ideals in non-involutive residuated lattices is studied by using the method and principle of hesitant fuzzy sets. The notion of hesitant fuzzy ideals of non-involutive residuated lattices is introduced. Some properties of hesitant fuzzy ideals are investigated. Some equivalent characterizations of hesitant fuzzy ideals are obtained. The relation between hesitant fuzzy ideals and ideals is discussed. It is proved that the hesitant fuzzy intersection of some hesitant fuzzy ideals, homomorphism image and inverse image of a hesitant fuzzy ideal are also hesitant fuzzy ideals. At the same time, a sufficient condition which makes the hesitant fuzzy union of some hesitant fuzzy ideals to be a hesitant fuzzy ideal is given. This work further expands the way for revealing the structural characteristics of non-involutive residuated lattices.

Key words: fuzzy logic, logical algebra, non-involutive residuated lattice, hesitant fuzzy ideal, homomorphism

CLC Number: 

  • O141.1
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