﻿ 剩余格上的交软滤子与交软同余 Int-Soft Filters and Their Congruences on Residuated Lattices

Operations Research and Fuzziology
Vol.07 No.02(2017), Article ID:20487,8 pages
10.12677/ORF.2017.72005

Int-Soft Filters and Their Congruences on Residuated Lattices

Chunxin Lin, Zhenming Ma

School of Mathematics and Statistics, Linyi University, Linyi Shandong

Received: Apr. 19th, 2017; accepted: May 7th, 2017; published: May 10th, 2017

ABSTRACT

The aim of this paper is to study filters on residuated lattices associated with soft sets. By introducing the notion of tip-extended pair of soft sets, a bounded distributive lattice based on the sets of all int-soft filters is formed, a one-to-one correspondence between the set of all int-soft filters and the set of all int-soft congruences is established, and a quotient residuated lattice with respect to int-soft filter is induced.

Keywords:Residuated Lattice, Int-Soft Filter, Int-Soft Congruence, Distributive Lattice

1. 引言

2. 预备知识

(1)是有界格；

(2)是交换幺半群；

(3)构成伴随对，即当且仅当，则称为剩余格。

(1)

(2)

(3) 如果，那么

(4)

(5)

(6)

(7)

(8)

(9)

(10)，其中

3. 交软滤子及其格结构

(1)

(2)

,

，定义满足，则容易验证为交软滤子。

(1)蕴含

(2)

。考虑如下情形：

，容易验证，则上式可表示为

4. 交软同余

(1)

(2)

(3)

(4)，其中

。所以为交软滤子。

5. 结束语

Int-Soft Filters and Their Congruences on Residuated Lattices[J]. 运筹与模糊学, 2017, 07(02): 37-44. http://dx.doi.org/10.12677/ORF.2017.72005

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