General form of lattice-valued fuzzy sets under the cutworthy approach

  • Authors:

  • Marijana Gorjanac-Ranitović;Andreja Tepavčević

  • Affiliations:

  • Faculty of Education, University of Novi Sad, 25000 Sombor, Serbia;Faculty of Science, Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

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Abstract

In this note a new solution of problem of Synthesis of fuzzy sets is presented. In other words, necessary and sufficient conditions are formulated, under which for a given family of subsets F of a set X and a fixed complete lattice L there is a fuzzy set @m:X-L, such that the collection of cuts of @m coincides with F. Moreover, it is proved that the general form of lattice-valued fuzzy sets (considering families of cuts) are the type of fuzzy sets having the codomain {0,1}^c for a suitable chosen cardinal c.