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

Rajesh Kumar Mohapatra; Tzung Pei Hong

doi:10.3390/math10071161

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

Rajesh Kumar Mohapatra, Tzung Pei Hong

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Article number	1161
Journal	Mathematics
Volume	10
Issue number	7
DOIs	https://doi.org/10.3390/math10071161
State	Published - 1 Apr 2022
Externally published	Yes

Keywords

binomial numbers
chains of crisp subsets
finite fuzzy subsets
integer sequences
α-cuts

ASJC Scopus subject areas

General Mathematics

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10.3390/math10071161

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title = "On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences",

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.",

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N2 - 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.

AB - 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.

KW - binomial numbers

KW - chains of crisp subsets

KW - finite fuzzy subsets

KW - integer sequences

KW - α-cuts

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

Abstract

Keywords

ASJC Scopus subject areas

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