广义区间值模糊粗糙集模型及其公理化特性

J4 ›› 2013, Vol. 48 ›› Issue (09): 56-63.

广义区间值模糊粗糙集模型及其公理化特性

张海东1,贺艳平2

1.西北民族大学数学与计算机科学学院, 甘肃兰州 730030;
2.西北民族大学电气工程学院, 甘肃兰州 730030

收稿日期:2012-10-22 出版日期:2013-09-20 发布日期:2013-09-25
作者简介:张海东(1980- ), 男, 硕士, 讲师, 研究方向为模糊集和粗糙集理论. Email: lingdianstar@163. com
基金资助:
国家自然科学基金资助项目(71261022); 西北民族大学中央高校基本业务费专项资金基金资助项目(zyz2012076); 西北民族大学中青年科研基金资助项目(12XB29)

Generalized interval-valued fuzzy rough sets and axiomatic characterizations

ZHANG Hai-dong1, HE Yan-ping 2

1. School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, Gansu, China;
2. School of Electrical Engineering, Northwest University for Nationalities, Lanzhou 730030, Gansu, China

Received:2012-10-22 Online:2013-09-20 Published:2013-09-25

摘要/Abstract

摘要：

把粗糙集理论和区间值模糊集理论结合起来, 利用粗糙集理论的构造性方法, 提出了一种广义区间值模糊粗糙集理论模型。首先, 利用区间值模糊剩余蕴含算子和它的对偶算子, 定义了一种广义上下区间值模糊粗糙集近似算子。然后, 利用该蕴含算子的性质, 讨论了该模型上、下近似算子一系列有趣的性质。在公理化方法中, 通过定义一对抽象的区间值模糊近似算子, 刻画了广义区间值模糊粗糙集模型的公理化特性。

关键词: 区间值模糊集;区间值模糊关系;区间值模糊粗糙近似算子;公理化方法

Abstract:

A general framework is presented for the study of generalized interval-valued fuzzy rough sets integrating the rough set theory with the interval-valued fuzzy set theory by using constructive approach. Firstly, through employing an interval-valued fuzzy residual implicator and its dual operator, generalized upper and lower interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy approximation space are first defined. Based on properties of interval-valued fuzzy residual implicator on LI, some interesting properties of interval-valued fuzzy rough approximation operators are then examined. In the axiomatic approach, interval-valued fuzzy rough approximation operators are further defined by axioms. And different axiom sets can characterize the essential properties of interval-valued fuzzy rough approximation operators.

Key words: interval-valued fuzzy sets; interval-valued fuzzy relation; interval-valued fuzzy rough approximation operators; axiomatic approach

张海东1,贺艳平2. 广义区间值模糊粗糙集模型及其公理化特性[J]. J4, 2013, 48(09): 56-63.

ZHANG Hai-dong1, HE Yan-ping 2. Generalized interval-valued fuzzy rough sets and axiomatic characterizations[J]. J4, 2013, 48(09): 56-63.

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