Abstract
If one considers the membership degrees of fuzzy sets as truth values of a many-valued logic there is a canonical way to define a fuzzified equality for fuzzy sets. This generalized equality relation can be used to define a degree to which some value of the unknown variable is a solution of the fuzzy equation as well as a degree of solvability of the whole equation. Furthermore there is an intimate relationship between such a degree to which some fuzzy set is a solution and the “quality” to which it is an approximate solution. The background is that the negation of the fuzzified equality measures a kind of distinctness of fuzzy sets. Formally, the definition of this fuzzified equality contains as parameter some t-norm which acts as truth functions of a conjunction connective. For some such t-norms this negation of the fuzzified equality really has the properties of a metric in the mathematical sense of the word. The paper gives a necessary and sufficient condition which characterizes all those t-norms which in that way yield a metric for fuzzy sets.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
