JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (2): 65-72.doi: 10.6040/j.issn.1671-9352.0.2017.508

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On(∈,∈∨q(λ, μ))-fuzzy LI-ideals in lattice implication algebras

LIU Chun-hui   

  1. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Received:2017-09-27 Online:2018-02-20 Published:2018-01-31

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Abstract: Firstly, the notion of (∈,∈∨q(λ, μ))-fuzzy LI-ideals in lattice implication algebras is further studied, and some new properties and equivalent characterizations of (∈,∈∨q(λ, μ))-fuzzy LI-ideals are given. Secondly, a partial order is defined on the set of all fuzzy sets in a given lattice implication algebra L, the definition of (∈,∈∨q(λ, μ))-fuzzy LI-ideal which is generated by a fuzzy set is given and its representation theorem is established by using. Finally, It is proved that the set consisting of all (∈,∈∨q(λ, μ))-fuzzy LI-ideals with respect to a fixed pair(λ, μ)in a given lattice implication algebra, under the partial order, forms a complete distributive lattice.

Key words: distributive lattice, lattice implication algebra, complete lattice, lattice-valued logic, (∈,∈∨q(λ, μ))-fuzzy LI-ideal

CLC Number: 

  • O141.1
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