The invention of new sequences through classifying and counting fuzzy matrices

S. R. Kannan; Rajesh Kumar Mohapatra; Tzung Pei Hong

doi:10.1007/s00500-020-05320-w

The invention of new sequences through classifying and counting fuzzy matrices

S. R. Kannan, Rajesh Kumar Mohapatra, Tzung Pei Hong

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

1 Scopus citations

Abstract

The novelty of this paper is to construct several explicit formulas for the number of distinct fuzzy matrices of a finite order which leads us to invent new integer sequences and helps to develop fuzzy subgroups of some finite groups of matrices. In order to achieve the sequences, we analyze the behavioral study of a natural equivalence relation on the set of all fuzzy matrices of a given order. In addition, this paper derives some important relevant results by enumerating non-equivalent class of fuzzy matrices. We achieve these results by incorporating the notion of k-level fuzzy matrices, α-cuts and chains.

Original language	English
Pages (from-to)	9663-9676
Number of pages	14
Journal	Soft Computing
Volume	25
Issue number	15
DOIs	https://doi.org/10.1007/s00500-020-05320-w
State	Published - 1 Aug 2021
Externally published	Yes

Keywords

Binomial numbers
Chains of crisp matrices
Flags
Fuzzy matrices
k-level fuzzy matrices
α-cuts

ASJC Scopus subject areas

Theoretical Computer Science
Software
Geometry and Topology

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title = "The invention of new sequences through classifying and counting fuzzy matrices",

abstract = "The novelty of this paper is to construct several explicit formulas for the number of distinct fuzzy matrices of a finite order which leads us to invent new integer sequences and helps to develop fuzzy subgroups of some finite groups of matrices. In order to achieve the sequences, we analyze the behavioral study of a natural equivalence relation on the set of all fuzzy matrices of a given order. In addition, this paper derives some important relevant results by enumerating non-equivalent class of fuzzy matrices. We achieve these results by incorporating the notion of k-level fuzzy matrices, α-cuts and chains.",

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AU - Hong, Tzung Pei

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AB - The novelty of this paper is to construct several explicit formulas for the number of distinct fuzzy matrices of a finite order which leads us to invent new integer sequences and helps to develop fuzzy subgroups of some finite groups of matrices. In order to achieve the sequences, we analyze the behavioral study of a natural equivalence relation on the set of all fuzzy matrices of a given order. In addition, this paper derives some important relevant results by enumerating non-equivalent class of fuzzy matrices. We achieve these results by incorporating the notion of k-level fuzzy matrices, α-cuts and chains.

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KW - Chains of crisp matrices

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The invention of new sequences through classifying and counting fuzzy matrices

Abstract

Keywords

ASJC Scopus subject areas

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