Distance measure of picture fuzzy sets and its application in multi-criteria decision making problem
Distance measurement is an important technique for determining the similarity of two Picture Fuzzy Sets (PFSs). The article presents a novel idea of distance measure for PFSs, which is then applied to solve Multi-Criteria Decision-Making (MCDM) problems. By using the distance measure of the PFSs, th...
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| Format: | Article |
| Language: | English |
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Ayandegan Institute of Higher Education,
2024-12-01
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| Series: | Journal of Fuzzy Extension and Applications |
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| Online Access: | https://www.journal-fea.com/article_199554_6a8ba1b358321876393b0c9c8f064078.pdf |
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| _version_ | 1832577790924292096 |
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| author | Amal Adak Manish Gunjan Aliakbar Haghighi |
| author_facet | Amal Adak Manish Gunjan Aliakbar Haghighi |
| author_sort | Amal Adak |
| collection | DOAJ |
| description | Distance measurement is an important technique for determining the similarity of two Picture Fuzzy Sets (PFSs). The article presents a novel idea of distance measure for PFSs, which is then applied to solve Multi-Criteria Decision-Making (MCDM) problems. By using the distance measure of the PFSs, the TOPSIS approach is applied to solve MCDM problems. The score function is employed to determine the best alternatives for both Picture Fuzzy Positive Ideal Solution (PFPIS) and Picture Fuzzy Negative Ideal Solutions (PFNIS). The options are ranked using the revised index technique and the relative closeness coefficient method. An illustrative numerical example is provided to demonstrate the feasibility and practicality of the proposed distance measure for PFSs. |
| format | Article |
| id | doaj-art-163d73a8ba774327af1e1858e340bc18 |
| institution | Kabale University |
| issn | 2783-1442 2717-3453 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Ayandegan Institute of Higher Education, |
| record_format | Article |
| series | Journal of Fuzzy Extension and Applications |
| spelling | doaj-art-163d73a8ba774327af1e1858e340bc182025-01-30T15:07:17ZengAyandegan Institute of Higher Education,Journal of Fuzzy Extension and Applications2783-14422717-34532024-12-015459460410.22105/jfea.2024.449236.1420199554Distance measure of picture fuzzy sets and its application in multi-criteria decision making problemAmal Adak0Manish Gunjan1Aliakbar Haghighi2Department of Mathematics, Ganesh Dutt College, Begusarai, India, 851101.Department of Mathematics, Lalit Narayan Mithila University, Darbhanga, India.Department of Mathematics, Prairie View A&M University, Prairie View, Texas 77446, USA.Distance measurement is an important technique for determining the similarity of two Picture Fuzzy Sets (PFSs). The article presents a novel idea of distance measure for PFSs, which is then applied to solve Multi-Criteria Decision-Making (MCDM) problems. By using the distance measure of the PFSs, the TOPSIS approach is applied to solve MCDM problems. The score function is employed to determine the best alternatives for both Picture Fuzzy Positive Ideal Solution (PFPIS) and Picture Fuzzy Negative Ideal Solutions (PFNIS). The options are ranked using the revised index technique and the relative closeness coefficient method. An illustrative numerical example is provided to demonstrate the feasibility and practicality of the proposed distance measure for PFSs.https://www.journal-fea.com/article_199554_6a8ba1b358321876393b0c9c8f064078.pdfintuitionistic fuzzy setspicture fuzzy setssimilarity measurescore functionrevised index method |
| spellingShingle | Amal Adak Manish Gunjan Aliakbar Haghighi Distance measure of picture fuzzy sets and its application in multi-criteria decision making problem Journal of Fuzzy Extension and Applications intuitionistic fuzzy sets picture fuzzy sets similarity measure score function revised index method |
| title | Distance measure of picture fuzzy sets and its application in multi-criteria decision making problem |
| title_full | Distance measure of picture fuzzy sets and its application in multi-criteria decision making problem |
| title_fullStr | Distance measure of picture fuzzy sets and its application in multi-criteria decision making problem |
| title_full_unstemmed | Distance measure of picture fuzzy sets and its application in multi-criteria decision making problem |
| title_short | Distance measure of picture fuzzy sets and its application in multi-criteria decision making problem |
| title_sort | distance measure of picture fuzzy sets and its application in multi criteria decision making problem |
| topic | intuitionistic fuzzy sets picture fuzzy sets similarity measure score function revised index method |
| url | https://www.journal-fea.com/article_199554_6a8ba1b358321876393b0c9c8f064078.pdf |
| work_keys_str_mv | AT amaladak distancemeasureofpicturefuzzysetsanditsapplicationinmulticriteriadecisionmakingproblem AT manishgunjan distancemeasureofpicturefuzzysetsanditsapplicationinmulticriteriadecisionmakingproblem AT aliakbarhaghighi distancemeasureofpicturefuzzysetsanditsapplicationinmulticriteriadecisionmakingproblem |