On existence of P-valued fuzzy sets with a given collection of cuts

  • Authors:

  • Branimir Šešelja;Dragan Stojić;Andreja Tepavčević

  • Affiliations:

  • Department of Mathematics and Informatics, University of Novi Sad, Trg D.Obradovića 4, 21000 Novi Sad, Serbia;Faculty of Economics, University of Novi Sad, 24000 Subotica, Serbia;Department of Mathematics and Informatics, University of Novi Sad, Trg D.Obradovića 4, 21000 Novi Sad, Serbia

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2010

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Abstract

A representation theorem of families of subsets by poset-valued fuzzy sets is presented. Namely, necessary and sufficient conditions are given under which for a given family of subsets F of a set X and a fixed poset P there is a fuzzy set @m:X@?P, such that the collection of cuts of @m coincides with F.