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

✍ Scribed by A. Kehagias; M. Konstantinidou

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
303 KB
Volume
136
Category
Article
ISSN
0165-0114

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✦ Synopsis

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 re exive, 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 deΓΏne 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.

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