Gradual elements in a fuzzy set

Publication Type:
Journal Article
Citation:
Soft Computing, 2008, 12 (2), pp. 165 - 175
Issue Date:
2008-01-01
Full metadata record
Files in This Item:
Filename Description Size
Thumbnail2013007839OK.pdfPublished Version227.75 kB
Adobe PDF
The notion of a fuzzy set stems from considering sets where, in the words of Zadeh, the "transition from non-membership to membership is gradual rather than abrupt". This paper introduces a new concept in fuzzy set theory, that of a gradual element. It embodies the idea of fuzziness only, thus contributing to the distinction between fuzziness and imprecision. A gradual element is to an element of a set what a fuzzy set is to a set. A gradual element is as precise as an element, but the former is flexible while the latter is fixed. The gradual nature of an element may express the idea that the choice of this element depends on a parameter expressing some relevance or describing some concept. Applications of this notion to fuzzy cardinality, fuzzy interval analysis, fuzzy optimization, and defuzzification principles are outlined. © Springer-Verlag 2007.
Please use this identifier to cite or link to this item: