DocumentCode :
1754905
Title :
The Notion of Weak-Contradiction: Definition and Measures
Author :
Bustince, Humberto ; Madrid, Nicolas ; Ojeda-Aciego, Manuel
Author_Institution :
Dept. of Autom. & Comput., Public Univ. of Navarra, Pamplona, Spain
Volume :
23
Issue :
4
fYear :
2015
fDate :
Aug. 2015
Firstpage :
1057
Lastpage :
1069
Abstract :
In this paper, we present a way to represent contradiction between fuzzy sets. This representation is given in terms of the notion of f-weak-contradiction. Unlike other approaches, we do not define contradiction just by using one of the relations of f-weak-contradiction but by considering the whole set of relations. This consideration avoids the need to fix an operator beforehand in order to take into account all the information between two fuzzy sets. As a result, we characterize the contradiction between fuzzy sets and define a family of measures of contradiction satisfying four interesting properties: symmetry; antitonicity; if the intersection is empty, then the measure is one; and if there is an element in the intersection with degree of membership 1, then the measure is zero.
Keywords :
fuzzy set theory; antitonicity property; contradiction measures; f-weak-contradiction; fuzzy sets; membership degree; symmetry property; Databases; Electronic mail; Fuzzy sets; Lattices; Noise; TV; Upper bound; Fuzzy sets; measure of contradiction, N-contra-diction;
fLanguage :
English
Journal_Title :
Fuzzy Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
1063-6706
Type :
jour
DOI :
10.1109/TFUZZ.2014.2337934
Filename :
6851922
Link To Document :
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