Revisiting separation properties of convex fuzzy sets

被引：0

作者：

Gomez-Acevedo, Horacio ^{[1
,2
]}

机构：

[1] Univ Arkansas Med Sci, Arkansas Childrens Nutr Ctr, Little Rock, AR 72202 USA

[2] Univ Arkansas Med Sci, Dept Pediat, Little Rock, AR 72202 USA

来源：

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS | 2015年 / 29卷 / 02期

关键词：

Basic concepts; fuzzy convexity; separation of convex fuzzy sets;

D O I：

10.3233/IFS-151613

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Separation of convex sets by hyperplanes has been extensively studied on crisp sets. In a seminal paper from L. A. Zadeh [1] separability and convexity are investigated, however there is a flaw on the definition of degree of separation. We revisited separation on convex fuzzy sets that have level-wise (crisp) disjointness with non-empty interior at certain level and introduced the concept of minimal level of separation for such fuzzy sets. On this context, the smallest level in which a separation by a hyperplane occurs coincides with the maximal degree of the (fuzzy) intersection. Moreover, this property suggests an algorithm for finding the maximal grade of a (fuzzy) intersection based on hyperplane separability level-wise of fuzzy sets.

引用

页码：845 / 849

页数：5