Abstract
This paper solves the issues of determining the number Fn of fuzzy subsets of a nonempty finite set X. To solve this, this paper incorporates the equivalence relation on the collection of all fuzzy subsets of X. We derive two closed explicit formulas for Fn, which is the sum of a finite series in the product of binomial numbers or the sum of k-level fuzzy subsets Fn,k by introducing a classification technique. Moreover, these explicit formulas enable us to find the number of the maximal chains of crisp subsets of X. Further, this paper presents some elementary properties of Fn,k and Fn.
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.
