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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2024/8465775 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849739643174518784 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-eee517b0e78d441fbd4efccb32157439 |
| institution | DOAJ |
| issn | 1687-711X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| 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 |
| work_keys_str_mv | AT sanjithar onthecardinalityandpowersetoffuzzysetsandmultiplesets AT baijut onthecardinalityandpowersetoffuzzysetsandmultiplesets AT sandhyaspai onthecardinalityandpowersetoffuzzysetsandmultiplesets |