R0-代数的（∈, ∈ ∨ qk)-模糊滤子格

doi:10.13371/j.cnki.chin.q.j.m.2018.02.005

数学季刊 ›› 2018, Vol. 33 ›› Issue (2): 144-155.doi: 10.13371/j.cnki.chin.q.j.m.2018.02.005

R₀-代数的（∈, ∈ ∨ q_k)-模糊滤子格

Department of Mathematics and Statistics, Chifeng University

接受日期:2016-03-16 出版日期:2018-06-30 发布日期:2020-10-09
作者简介:LIU Chun-hui (1982-), male, native of Chifeng, Inner Mongolia, an associate professor of Chifeng University, M.S.D., engages in domain theory, non-Classical Mathematical Logic and Topology.
基金资助:
Department of Mathematics and Statistics, Chifeng University

The Lattice of （∈, ∈ ∨ q_k)-fuzzy Filters in a Given R₀-algebra

Department of Mathematics and Statistics, Chifeng University

Accepted:2016-03-16 Online:2018-06-30 Published:2020-10-09
About author:LIU Chun-hui (1982-), male, native of Chifeng, Inner Mongolia, an associate professor of Chifeng University, M.S.D., engages in domain theory, non-Classical Mathematical Logic and Topology.
Supported by:
Department of Mathematics and Statistics, Chifeng University

摘要/Abstract

摘要：

The purpose of this paper is to further study the（∈, ∈ ∨ q_k)-fuzzy filter theory in R0-algebras. Some new properties of （∈, ∈ ∨ q_k)-fuzzy filters are given. Representation theorem of（∈, ∈ ∨ q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all（∈, ∈ ∨ q_k)-fuzzy filters on a given R0-algebra, under the partial order, forms a complete distributive lattice.

关键词: Fuzzy logic, R₀-algebra;（∈, ∨ q_k)-fuzzy filter, Lattice

Abstract: The purpose of this paper is to further study the（∈, ∈ ∨ q_k)-fuzzy filter theory in R0-algebras. Some new properties of （∈, ∈ ∨ q_k)-fuzzy filters are given. Representation theorem of（∈, ∈ ∨ q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all（∈, ∈ ∨ q_k)-fuzzy filters on a given R0-algebra, under the partial order, forms a complete distributive lattice.

Key words: Fuzzy logic, R₀-algebra;（∈, ∨ q_k)-fuzzy filter, Lattice

中图分类号:

O159
O141

刘春辉. R₀-代数的（∈, ∈ ∨ q_k)-模糊滤子格[J]. 数学季刊, 2018, 33(2): 144-155.

LIU Chun-hui. The Lattice of （∈, ∈ ∨ q_k)-fuzzy Filters in a Given R₀-algebra[J]. Chinese Quarterly Journal of Mathematics, 2018, 33(2): 144-155.

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R₀-代数的（∈, ∈ ∨ q_k)-模糊滤子格

The Lattice of （∈, ∈ ∨ q_k)-fuzzy Filters in a Given R₀-algebra

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