JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (9): 29-35.doi: 10.6040/j.issn.1671-9352.0.2019.131

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Lattice of bipolar fuzzy ideals in negative non-involutive residuated lattices

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

  1. School of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Online:2019-09-20 Published:2019-07-30

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Abstract: In this paper, the problem of bipolar fuzzy ideals is further studied in negative non-involutive residuated lattices. The definition of bipolar fuzzy ideal which is generated by a bipolar fuzzy set is given and its two representation theorems are established. It is proved that the set BFI(L)which containing of all bipolar fuzzy ideals in a negative non-involutive residuated lattice L, under the partial order, forms a complete Heyting algebra. 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, complete Heyting algebra

CLC Number: 

  • O141.1
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