Complex Atanassov's Intuitionistic Fuzzy Relation
This paper presents distance measure between two complex Atanassov's intuitionistic fuzzy sets (CAIFSs). This distance measure is used to illustrate an application of CAIFSs in solving one of the most core application areas of fuzzy set theory, which is multiattributes decision-making (MADM) pr...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/287382 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832550040809242624 |
|---|---|
| author | Abd Ulazeez M. Alkouri Abdul Razak Salleh |
| author_facet | Abd Ulazeez M. Alkouri Abdul Razak Salleh |
| author_sort | Abd Ulazeez M. Alkouri |
| collection | DOAJ |
| description | This paper presents distance measure between two complex Atanassov's intuitionistic fuzzy sets (CAIFSs). This distance measure is used to illustrate an application of CAIFSs in solving one of the most core application areas of fuzzy set theory, which is multiattributes decision-making (MADM) problems, in complex Atanassov's intuitionistic fuzzy realm. A new structure of relation between two CAIFSs, called complex Atanassov's intuitionistic fuzzy relation (CAIFR), is obtained. This relation is formally generalised from a conventional Atanassov's intuitionistic fuzzy relation, based on complex Atanassov's intuitionistic fuzzy sets, in which the ranges of values of CAIFR are extended to the unit circle in complex plane for both membership and nonmembership functions instead of [0, 1] as in the conventional Atanassov's intuitionistic fuzzy functions. Definition and some mathematical concepts of CAIFS, which serve as a foundation for the creation of complex Atanassov's intuitionistic fuzzy relation, are recalled. We also introduce the Cartesian product of CAIFSs and derive two properties of the product space. The concept of projection and cylindric extension of CAIFRs are also introduced. An example of CAIFR in real-life situation is illustrated in this paper. Finally, we introduce the concept of composition of CAIFRs. |
| format | Article |
| id | doaj-art-fa2af4e199914fe898d96daee5e4dc79 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-fa2af4e199914fe898d96daee5e4dc792025-02-03T06:08:02ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/287382287382Complex Atanassov's Intuitionistic Fuzzy RelationAbd Ulazeez M. Alkouri0Abdul Razak Salleh1School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MalaysiaSchool of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MalaysiaThis paper presents distance measure between two complex Atanassov's intuitionistic fuzzy sets (CAIFSs). This distance measure is used to illustrate an application of CAIFSs in solving one of the most core application areas of fuzzy set theory, which is multiattributes decision-making (MADM) problems, in complex Atanassov's intuitionistic fuzzy realm. A new structure of relation between two CAIFSs, called complex Atanassov's intuitionistic fuzzy relation (CAIFR), is obtained. This relation is formally generalised from a conventional Atanassov's intuitionistic fuzzy relation, based on complex Atanassov's intuitionistic fuzzy sets, in which the ranges of values of CAIFR are extended to the unit circle in complex plane for both membership and nonmembership functions instead of [0, 1] as in the conventional Atanassov's intuitionistic fuzzy functions. Definition and some mathematical concepts of CAIFS, which serve as a foundation for the creation of complex Atanassov's intuitionistic fuzzy relation, are recalled. We also introduce the Cartesian product of CAIFSs and derive two properties of the product space. The concept of projection and cylindric extension of CAIFRs are also introduced. An example of CAIFR in real-life situation is illustrated in this paper. Finally, we introduce the concept of composition of CAIFRs.http://dx.doi.org/10.1155/2013/287382 |
| spellingShingle | Abd Ulazeez M. Alkouri Abdul Razak Salleh Complex Atanassov's Intuitionistic Fuzzy Relation Abstract and Applied Analysis |
| title | Complex Atanassov's Intuitionistic Fuzzy Relation |
| title_full | Complex Atanassov's Intuitionistic Fuzzy Relation |
| title_fullStr | Complex Atanassov's Intuitionistic Fuzzy Relation |
| title_full_unstemmed | Complex Atanassov's Intuitionistic Fuzzy Relation |
| title_short | Complex Atanassov's Intuitionistic Fuzzy Relation |
| title_sort | complex atanassov s intuitionistic fuzzy relation |
| url | http://dx.doi.org/10.1155/2013/287382 |
| work_keys_str_mv | AT abdulazeezmalkouri complexatanassovsintuitionisticfuzzyrelation AT abdulrazaksalleh complexatanassovsintuitionisticfuzzyrelation |