On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences

Rajesh Kumar Mohapatra and Tzung-Pei Hong
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Rajesh Kumar Mohapatra: Department of Mathematics, Kalasalingam Academy of Research and Education, Krishnankoil 626126, India
Tzung-Pei Hong: Department of Computer Science and Information Engineering, National University of Kaohsiung, Kaohsiung 811726, Taiwan

Mathematics, 2022, vol. 10, issue 7, 1-19

Abstract: This paper solves the issues of determining the number F n 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 F n , which is the sum of a finite series in the product of binomial numbers or the sum of k -level fuzzy subsets F n , 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 F n , k and F n .

Keywords: finite fuzzy subsets; ? -cuts; chains of crisp subsets; binomial numbers; integer sequences (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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