On the properties of subsethood measures

被引：14

作者：

Hu, Mengjun ^{[1
]}

Deng, Xiaofei ^{[1
]}

Yao, Yiyu ^{[1
]}

机构：

[1] Univ Regina, Dept Comp Sci, Regina, SK S4S 0A2, Canada

来源：

INFORMATION SCIENCES | 2019年 / 494卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Inclusion degree; Subsethood measure; Quantitative inclusion; FUZZY SUBSETHOOD; INCLUSION DEGREE; ROUGH; SIMILARITY; ENTROPY; SETS; COMONOTONICITY; DISTANCE;

D O I：

10.1016/j.ins.2019.04.038

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper explores the properties of subsethood measures, including boundary conditions, monotonicity, duality, and additivity. These properties can be used as candidates of axioms to define specific subsethood measures. The standard set theory introduces the set inclusion relation with a qualitative nature, that is, a set is either a subset of the other or not. As a quantitative generalization, a subsethood measure considers the degree of inclusion. It should keep essential characteristics of the qualitative set-inclusion and satisfy generalized properties with the qualitative set-inclusion relation as a special case. A systematic study of the relationships between the qualitative and quantitative frameworks results in the four types of properties of subsethood measures presented in this paper. A combination of different types of properties helps in constructing an appropriate subset hood measure in real-world applications. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：208 / 232

页数：25

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