Consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments
Fuzzy orders, especially T-preorders, can express the vague priority over a list of alternatives. The cardinal consistency of such relations is achieved through the T-transitivity condition, while the ordinal consistency of the final decision at a given threshold α ϵ (0,1) is not guaranteed by the T...
| Main Authors: | , , , |
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| Format: | Article |
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Elsevier
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/100787/ |
| _version_ | 1848863414963666944 |
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| author | Khameneh, Azadeh Zahedi Kilicman, Adem Khameneh, Hamed Zahedi Alcantud, José Carlos R. |
| author_facet | Khameneh, Azadeh Zahedi Kilicman, Adem Khameneh, Hamed Zahedi Alcantud, José Carlos R. |
| author_sort | Khameneh, Azadeh Zahedi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Fuzzy orders, especially T-preorders, can express the vague priority over a list of alternatives. The cardinal consistency of such relations is achieved through the T-transitivity condition, while the ordinal consistency of the final decision at a given threshold α ϵ (0,1) is not guaranteed by the T-consistency. This paper investigates the problem of ordinal consistency, as the minimum requirement for a reliable judgment, of a partial preference induced by a fuzzy relation at a given level α ϵ (0,1), so-called α-preference relation. We first define new concepts of T - L-cyclic and T-consistency at a given level α for fuzzy relations. Based on digraph theory, a new methodology is designed for finding the locations of all consistent and inconsistent L-cycles of an α -preference. An algorithm is proposed to eliminate the ordinal inconsistency through the TM-transitivity. Meanwhile, a new T-consistency index is introduced to measure the acceptable consistency level of fuzzy relations. Furthermore, some results concerning the ordinal consistency of T-preorders are applied to design another algorithm for creating a consistent collective judgment based on initial fuzzy assessments of alternatives in a group ranking problem. The proposed method constructs the consistent fuzzy order matrix for each case (expert), then calculates the group consensus by aggregating these matrices. The collective fuzzy order is then checked for consistency level. Finally, a numerical example with a real dataset is given to illustrate the application of the proposed method in a ranking problem. |
| first_indexed | 2025-11-15T13:32:33Z |
| format | Article |
| id | upm-100787 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:32:33Z |
| publishDate | 2022 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1007872023-08-22T03:56:39Z http://psasir.upm.edu.my/id/eprint/100787/ Consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments Khameneh, Azadeh Zahedi Kilicman, Adem Khameneh, Hamed Zahedi Alcantud, José Carlos R. Fuzzy orders, especially T-preorders, can express the vague priority over a list of alternatives. The cardinal consistency of such relations is achieved through the T-transitivity condition, while the ordinal consistency of the final decision at a given threshold α ϵ (0,1) is not guaranteed by the T-consistency. This paper investigates the problem of ordinal consistency, as the minimum requirement for a reliable judgment, of a partial preference induced by a fuzzy relation at a given level α ϵ (0,1), so-called α-preference relation. We first define new concepts of T - L-cyclic and T-consistency at a given level α for fuzzy relations. Based on digraph theory, a new methodology is designed for finding the locations of all consistent and inconsistent L-cycles of an α -preference. An algorithm is proposed to eliminate the ordinal inconsistency through the TM-transitivity. Meanwhile, a new T-consistency index is introduced to measure the acceptable consistency level of fuzzy relations. Furthermore, some results concerning the ordinal consistency of T-preorders are applied to design another algorithm for creating a consistent collective judgment based on initial fuzzy assessments of alternatives in a group ranking problem. The proposed method constructs the consistent fuzzy order matrix for each case (expert), then calculates the group consensus by aggregating these matrices. The collective fuzzy order is then checked for consistency level. Finally, a numerical example with a real dataset is given to illustrate the application of the proposed method in a ranking problem. Elsevier 2022-12-15 Article PeerReviewed Khameneh, Azadeh Zahedi and Kilicman, Adem and Khameneh, Hamed Zahedi and Alcantud, José Carlos R. (2022) Consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments. Expert Systems with Applications, 209. art. no. 118234. pp. 1-18. ISSN 0957-4174 https://www.sciencedirect.com/science/article/pii/S0957417422013823 10.1016/j.eswa.2022.118234 |
| spellingShingle | Khameneh, Azadeh Zahedi Kilicman, Adem Khameneh, Hamed Zahedi Alcantud, José Carlos R. Consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments |
| title | Consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments |
| title_full | Consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments |
| title_fullStr | Consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments |
| title_full_unstemmed | Consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments |
| title_short | Consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments |
| title_sort | consistency of total fuzzy relations: new algorithms to detect and repair inconsistent judgments |
| url | http://psasir.upm.edu.my/id/eprint/100787/ http://psasir.upm.edu.my/id/eprint/100787/ http://psasir.upm.edu.my/id/eprint/100787/ |