m-polar generalization of fuzzy T-ordering relations: an approach to group decision making
Recently, T-orderings, defined based on a t-norm T and infimum operator (for infinite case) or minimum operator (for finite case), have been applied as a generalization of the notion of crisp orderings to fuzzy setting. When this concept is extending to m-polar fuzzy data, it is questioned whether t...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Published: |
MDPI
2020
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/94280/ |
| _version_ | 1848861954864578560 |
|---|---|
| author | Khameneh, Azadeh Zahedi Kilicman, Adem |
| author_facet | Khameneh, Azadeh Zahedi Kilicman, Adem |
| author_sort | Khameneh, Azadeh Zahedi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Recently, T-orderings, defined based on a t-norm T and infimum operator (for infinite case) or minimum operator (for finite case), have been applied as a generalization of the notion of crisp orderings to fuzzy setting. When this concept is extending to m-polar fuzzy data, it is questioned whether the generalized definition can be expanded for any aggregation function, not necessarily the minimum operator, or not. To answer this question, the present study focuses on constructing m-polar T-orderings based on aggregation functions A, in particular, m-polar T-preorderings (which are reflexive and transitive m-polar fuzzy relations w.r.t T and A) and m-polar T-equivalences (which are symmetric m-polar T-preorderings). Moreover, the construction results for generating crisp preference relations based on m-polar T-orderings are obtained. Two algorithms for solving ranking problem in decision-making are proposed and validated by an illustrative example. |
| first_indexed | 2025-11-15T13:09:20Z |
| format | Article |
| id | upm-94280 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:09:20Z |
| publishDate | 2020 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-942802023-05-08T04:34:21Z http://psasir.upm.edu.my/id/eprint/94280/ m-polar generalization of fuzzy T-ordering relations: an approach to group decision making Khameneh, Azadeh Zahedi Kilicman, Adem Recently, T-orderings, defined based on a t-norm T and infimum operator (for infinite case) or minimum operator (for finite case), have been applied as a generalization of the notion of crisp orderings to fuzzy setting. When this concept is extending to m-polar fuzzy data, it is questioned whether the generalized definition can be expanded for any aggregation function, not necessarily the minimum operator, or not. To answer this question, the present study focuses on constructing m-polar T-orderings based on aggregation functions A, in particular, m-polar T-preorderings (which are reflexive and transitive m-polar fuzzy relations w.r.t T and A) and m-polar T-equivalences (which are symmetric m-polar T-preorderings). Moreover, the construction results for generating crisp preference relations based on m-polar T-orderings are obtained. Two algorithms for solving ranking problem in decision-making are proposed and validated by an illustrative example. MDPI 2020-12-30 Article PeerReviewed Khameneh, Azadeh Zahedi and Kilicman, Adem (2020) m-polar generalization of fuzzy T-ordering relations: an approach to group decision making. Symmetry, 13 (1). art. no. 51. pp. 1-21. ISSN 2073-8994 https://www.mdpi.com/2073-8994/13/1/51 10.3390/sym13010051 |
| spellingShingle | Khameneh, Azadeh Zahedi Kilicman, Adem m-polar generalization of fuzzy T-ordering relations: an approach to group decision making |
| title | m-polar generalization of fuzzy T-ordering relations: an approach to group decision making |
| title_full | m-polar generalization of fuzzy T-ordering relations: an approach to group decision making |
| title_fullStr | m-polar generalization of fuzzy T-ordering relations: an approach to group decision making |
| title_full_unstemmed | m-polar generalization of fuzzy T-ordering relations: an approach to group decision making |
| title_short | m-polar generalization of fuzzy T-ordering relations: an approach to group decision making |
| title_sort | m-polar generalization of fuzzy t-ordering relations: an approach to group decision making |
| url | http://psasir.upm.edu.my/id/eprint/94280/ http://psasir.upm.edu.my/id/eprint/94280/ http://psasir.upm.edu.my/id/eprint/94280/ |