On the Cardinality and Power Set of Fuzzy Sets and Multiple Sets

A multiple set is a generalized version of a fuzzy set that deals with the uncertainty of an object along with its multiplicity. This work is a comparative analysis of the fundamental conclusions based on the cardinality of the classical set and fuzzy set. Several classical results based on fuzzy ca...

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Main Authors: Sanjitha R., Baiju T., Sandhya S. Pai
Format: Article
Language:English
Published: Wiley 2024-01-01
Series:Advances in Fuzzy Systems
Online Access:http://dx.doi.org/10.1155/2024/8465775
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author Sanjitha R.
Baiju T.
Sandhya S. Pai
author_facet Sanjitha R.
Baiju T.
Sandhya S. Pai
author_sort Sanjitha R.
collection DOAJ
description A multiple set is a generalized version of a fuzzy set that deals with the uncertainty of an object along with its multiplicity. This work is a comparative analysis of the fundamental conclusions based on the cardinality of the classical set and fuzzy set. Several classical results based on fuzzy cardinality are then generalized to multiple set theory. An introduction to the concept of the power set of a multiple set is made, along with some basic results that support it. Furthermore, an extensive analysis of the power set properties of the fuzzy set is also carried out.
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spelling doaj-art-eee517b0e78d441fbd4efccb321574392025-08-20T03:06:13ZengWileyAdvances in Fuzzy Systems1687-711X2024-01-01202410.1155/2024/8465775On the Cardinality and Power Set of Fuzzy Sets and Multiple SetsSanjitha R.0Baiju T.1Sandhya S. Pai2Department of MathematicsDepartment of MathematicsDepartment of MathematicsA multiple set is a generalized version of a fuzzy set that deals with the uncertainty of an object along with its multiplicity. This work is a comparative analysis of the fundamental conclusions based on the cardinality of the classical set and fuzzy set. Several classical results based on fuzzy cardinality are then generalized to multiple set theory. An introduction to the concept of the power set of a multiple set is made, along with some basic results that support it. Furthermore, an extensive analysis of the power set properties of the fuzzy set is also carried out.http://dx.doi.org/10.1155/2024/8465775
spellingShingle Sanjitha R.
Baiju T.
Sandhya S. Pai
On the Cardinality and Power Set of Fuzzy Sets and Multiple Sets
Advances in Fuzzy Systems
title On the Cardinality and Power Set of Fuzzy Sets and Multiple Sets
title_full On the Cardinality and Power Set of Fuzzy Sets and Multiple Sets
title_fullStr On the Cardinality and Power Set of Fuzzy Sets and Multiple Sets
title_full_unstemmed On the Cardinality and Power Set of Fuzzy Sets and Multiple Sets
title_short On the Cardinality and Power Set of Fuzzy Sets and Multiple Sets
title_sort on the cardinality and power set of fuzzy sets and multiple sets
url http://dx.doi.org/10.1155/2024/8465775
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