JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (11): 71-80.doi: 10.6040/j.issn.1671-9352.0.2019.245

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Bipolar fuzzy prime ideals in negative non-involutive residuated lattices

LIU Chun-hui   

  1. School of Mathematics and Computer Science, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Published:2019-11-06

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Abstract: The problem of bipolar fuzzy ideals is further studied in negative non-involutive residuated lattices. The concept of bipolar fuzzy prime ideal(BF-prime ideal for short)is introduced and its properties are investigated. Some equivalent characterizations of BF-prime ideal are obtained. The BF-prime ideal theorem in a prelinearity negative non-involutive residuated lattice is established. It is proved that the NRL-homomorphism image and the inverse image of a BF-prime ideal are also BF-prime ideals. This work 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, bipolar fuzzy ideal, bipolar fuzzy prime ideal

CLC Number: 

  • O141.1
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