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| 广义区间值模糊粗糙集模型及其公理化特性 | |
| 引用本文： | 张海东,贺艳平.广义区间值模糊粗糙集模型及其公理化特性[J].山东大学学报(理学版),2013,48(9):56-63. |
| 作者姓名： | 张海东 贺艳平 |
| 作者单位： | 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 |
| 基金项目： | 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) |
| 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 |
| 收稿时间： | 2012-10-22 |
Generalized interval-valued fuzzy rough sets and axiomatic characterizations |
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| ZHANG Hai-dong,HE Yan-ping.Generalized interval-valued fuzzy rough sets and axiomatic characterizations[J].Journal of Shandong University,2013,48(9):56-63. | |
| Authors: | ZHANG Hai-dong HE Yan-ping |
| Institution: | 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 |
| 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. |
| Keywords: | interval-valued fuzzy sets interval-valued fuzzy relation interval-valued fuzzy rough approximation operators axiomatic approach |
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