L-fuzzy valued inclusion measure, L-fuzzy similarity and L-fuzzy distance

  • Authors:

  • A. Kehagias;M. Konstantinidou

  • Affiliations:

  • Division of Mathematics, Department of Mathematics, Physical and Computational Sciences, Faculty of Engineering, Aristotle University of Thessaloniki, PB 464, Thessaloniki, GR 54124, Greece;Division of Mathematics, Department of Mathematics, Physical and Computational Sciences, Faculty of Engineering, Aristotle University of Thessaloniki, PB 464, Thessaloniki, GR 54124, Greece

  • Venue:
  • Fuzzy Sets and Systems - Theme: Basic concepts
  • Year:
  • 2003

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Abstract

The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0, 1]; the inclusion measure proposed here takes values in a Boolean lattice. In other words, an inclusion is viewed as an L-fuzzy valued relation between fuzzy sets. This relation is reflexive, antisymmetric and transitive, i.e. it is a fuzzy order relation; in addition, it possesess a number of properties which various authors have postulated as axiomatically appropriate for an inclusion measure. We also define an L-fuzzy valued measure of similarity between fuzzy sets and an L-fuzzy valued distance function between fuzzy sets; these possess properties analogous to the ones of real-valued similarity and distance functions.