JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (5): 88-98.doi: 10.6040/j.issn.1671-9352.0.2018.386

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Bipolar fuzzy ideals in negative non-involutive residuated lattices

LIU Chun-hui, LI Yu-mao, ZHANG Hai-yan   

  1. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Published:2019-05-09

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Abstract: Based on the theory of bipolar fuzzy sets, the problem of ideals in negative non-involutive residuated lattices is studied. Firstly, the concept of bipolar fuzzy ideals in negative non-involutive residuated lattices is introduced, and some their basic properties and equivalent characterizations are discussed. Secondly, the relationships between bipolar fuzzy ideals and ideals are investigated by using the concepts of positive t-cut and negative s-cut set of bipolar valued fuzzy sets. Finally, some equivalence relations are constructed on the set of all bipolar fuzzy ideals in a negative non-involutive residuated lattice, and the properties of corresponding quotient sets are obtained. It further expands the way for revealing the structural characteristics of negative non-involutive residuated lattices.

Key words: fuzzy logic, logical algebra, negative non-involutive residuated lattice, ideal, bipolar fuzzy ideal

CLC Number: 

  • O141.1
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