The starting point of this paper is the introduction of a new measure ofinclusion of fuzzy set A in fuzzy set B. Previously used inclusion measurestake values in the interval [0,1]; the inclusion measure proposed here takesvalues in a Boolean lattice. In other words, inclusion is viewed as an L-fuzzyvalued relation between fuzzy sets. This relation is re exive, antisymmetricand transitive, i.e. it is a fuzzy order relation; in addition it possesess anumber of properties which various authors have postulated as axiomaticallyappropriate for an inclusion measure. We also define an L-fuzzy valued measureof similarity between fuzzy sets and and an L-fuzzy valued distance functionbetween fuzzy sets; these possess properties analogous to the ones ofreal-valued similarity and distance functions. Keywords: Fuzzy Relations, inclusion measure, subsethood, L-fuzzy sets,similarity, distance, transitivity.
展开▼
