Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius
The circular intuitionistic fuzzy set (CIFS) extends the concept of IFS, representing each set element with a circular area on the IFS interpretation triangle (IFIT). Each element in CIFS is characterized not only by membership and non-membership degrees but also by a radius, indicating the imprecis...
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| Format: | Article |
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American Institute of Mathematical Sciences
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/112900/ |
| _version_ | 1848866070665887744 |
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| author | Pratama, Dian Yusoff, Binyamin Abdullah, Lazim Kilicman, Adem Kamis, Nor Hanimah |
| author_facet | Pratama, Dian Yusoff, Binyamin Abdullah, Lazim Kilicman, Adem Kamis, Nor Hanimah |
| author_sort | Pratama, Dian |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The circular intuitionistic fuzzy set (CIFS) extends the concept of IFS, representing each set element with a circular area on the IFS interpretation triangle (IFIT). Each element in CIFS is characterized not only by membership and non-membership degrees but also by a radius, indicating the imprecise areas of these degrees. While some basic operations have been defined for CIFS, not all have been thoroughly explored and generalized. The radius domain has been extended from [0, 1] to [0,√2]. However, the operations on the radius domain are limited to min and max. We aimed to address these limitations and further explore the theory of CIFS, focusing on operations for membership and nonmembership degrees as well as radius domains. First, we proposed new radius operations on CIFS with a domain [0, ψ], where ψ ∈ [1,√2], called a radius algebraic product (RAP) and radius algebraic sum (RAS). Second, we developed basic operators for generalized union and intersection operations on CIFS based on triangular norms and conorms, investigating their algebraic properties. Finally, we explored negation and modal operators based on proposed radius conditions and examined their characteristics. This research contributes to a more explicit understanding of the properties and capabilities of CIFS, providing valuable insights into its potential applications, particularly in decision-making theory. © 2024 the Author(s), licensee AIMS Press. |
| first_indexed | 2025-11-15T14:14:46Z |
| format | Article |
| id | upm-112900 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T14:14:46Z |
| publishDate | 2024 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1129002024-10-28T07:50:41Z http://psasir.upm.edu.my/id/eprint/112900/ Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius Pratama, Dian Yusoff, Binyamin Abdullah, Lazim Kilicman, Adem Kamis, Nor Hanimah The circular intuitionistic fuzzy set (CIFS) extends the concept of IFS, representing each set element with a circular area on the IFS interpretation triangle (IFIT). Each element in CIFS is characterized not only by membership and non-membership degrees but also by a radius, indicating the imprecise areas of these degrees. While some basic operations have been defined for CIFS, not all have been thoroughly explored and generalized. The radius domain has been extended from [0, 1] to [0,√2]. However, the operations on the radius domain are limited to min and max. We aimed to address these limitations and further explore the theory of CIFS, focusing on operations for membership and nonmembership degrees as well as radius domains. First, we proposed new radius operations on CIFS with a domain [0, ψ], where ψ ∈ [1,√2], called a radius algebraic product (RAP) and radius algebraic sum (RAS). Second, we developed basic operators for generalized union and intersection operations on CIFS based on triangular norms and conorms, investigating their algebraic properties. Finally, we explored negation and modal operators based on proposed radius conditions and examined their characteristics. This research contributes to a more explicit understanding of the properties and capabilities of CIFS, providing valuable insights into its potential applications, particularly in decision-making theory. © 2024 the Author(s), licensee AIMS Press. American Institute of Mathematical Sciences 2024 Article PeerReviewed Pratama, Dian and Yusoff, Binyamin and Abdullah, Lazim and Kilicman, Adem and Kamis, Nor Hanimah (2024) Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius. AIMS Mathematics, 9 (5). pp. 12259-12286. ISSN 2473-6988 http://www.aimspress.com/article/doi/10.3934/math.2024599 10.3934/math.2024599 |
| spellingShingle | Pratama, Dian Yusoff, Binyamin Abdullah, Lazim Kilicman, Adem Kamis, Nor Hanimah Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius |
| title | Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius |
| title_full | Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius |
| title_fullStr | Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius |
| title_full_unstemmed | Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius |
| title_short | Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius |
| title_sort | extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: exploring a domain radius |
| url | http://psasir.upm.edu.my/id/eprint/112900/ http://psasir.upm.edu.my/id/eprint/112900/ http://psasir.upm.edu.my/id/eprint/112900/ |