R0-代数的（∈, ∈ ∨ qk)-模糊滤子格

刘春辉

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

数学季刊 >

2018 , Vol. 33 >Issue 2: 144 - 155

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.02.005

R₀-代数的（∈, ∈ ∨ q_k)-模糊滤子格

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Department of Mathematics and Statistics, Chifeng University

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.

录用日期: 2016-03-16

网络出版日期: 2020-10-09

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Department of Mathematics and Statistics, Chifeng University

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

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Department of Mathematics and Statistics, Chifeng University

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.

Accepted date: 2016-03-16

Online published: 2020-10-09

Supported by

Department of Mathematics and Statistics, Chifeng University

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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

本文引用格式

刘春辉 . R₀-代数的（∈, ∈ ∨ q_k)-模糊滤子格[J]. 数学季刊, 2018 , 33(2) : 144 -155 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.02.005

Abstract

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

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