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Representation by cuts in the framework of relational valued fuzzy sets | IEEE Conference Publication | IEEE Xplore
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Representation by cuts in the framework of relational valued fuzzy sets

Publisher: IEEE

Abstract:

Generalized or relational-valued fuzzy sets are mappings from a set X to a relational system S = (S, p). Representation of collections of subsets by relational-valued fuz...View more

Abstract:

Generalized or relational-valued fuzzy sets are mappings from a set X to a relational system S = (S, p). Representation of collections of subsets by relational-valued fuzzy sets in the cutworthy framework is presented. It is proved that for every collection F of subsets of a set X there is a relational system S = (S, p) and a fuzzy set μ : X → S, such that the collection of cuts of μ coincides with F.
Date of Conference: 20-24 August 2009
Date Added to IEEE Xplore: 02 October 2009
ISBN Information:
Print ISSN: 1098-7584
Publisher: IEEE
Conference Location: Jeju, Korea (South)

I. Introduction

In the classical fuzzy set theory, it is known that the family of cut-sets uniquely determines the starting fuzzy structure. Therefore, from the beginning of fuzzy era, identification of a fuzzy set by the collection of its cuts has been an important problem. For [0, 1]- valued fuzzy sets, as well as for particular lattice-valued ones, known relevant results were obtained by Negoita and Ralescu ([7], [8], [9], [10], [11]). Recently, many problems connected with the representation of collections of subsets as cuts of fuzzy sets (still for [0, 1]-valued fuzzy sets) have been formulated and solved by Jaballah and Saidi (see e.g., [4], [12], [13], [14]).

References

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