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Fuzzy posets on sets

Authors
Journal
Fuzzy Sets and Systems
0165-0114
Publisher
Elsevier
Publication Date
Volume
117
Issue
3
Identifiers
DOI: 10.1016/s0165-0114(98)00249-8
Keywords
  • Foset
  • Skeleton
  • Fuzzy Order-Preserving
  • Fuzzy Intersection
  • Decidable
  • Fuzzy Dimension
Disciplines
  • Mathematics

Abstract

Abstract In this paper we introduce the notion of a fuzzy poset defined on a set X via a triplet (L,G,P) of functions with domain X × X and range [0,1] satisfying a special condition L+G+P=1. Using this approach we are able to define special classes of fuzzy posets and to prove several standard theorems for posets in the setting of fuzzy posets. Furthermore, using a rounding-off procedure we are able to define the skeleton of a fuzzy poset and to obtain results on the behavior of deformations of skeleta of fuzzy posets as it relates to the structure of these fuzzy posets. If the fuzzy dimension is defined as the intersection of the least number of fuzzy chains which yield the fuzzy poset, then it is shown that the definition makes sense and in large classes equals the dimension of the skeleton. L is the “less than” function, G is the “greater than” function, and P is the “parallel” or “incomparability” function.

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