BulDML at Institute of Mathematics and Informatics >
International Journal ITA >
2005 >
Volume 12 Number 2 >

Please use this identifier to cite or link to this item:

Title: A Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets
Authors: Torres, Carmen
CastiƱeira, Elena
Cubillo, Susana
Zarzosa, Victoria
Keywords: Fuzzy Sets
Fuzzy Strong Negations
Measures of Contradiction
Issue Date: 2005
Publisher: Institute of Information Theories and Applications FOI ITHEA
Abstract: For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1]2. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.
ISSN: 1313-0463
Appears in Collections:Volume 12 Number 2

Files in This Item:

File Description SizeFormat
ijita12-2-p04.pdf212.71 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License