Group decision making in the analytic hierarchy process by hesitant fuzzy numbers
Abstract Due to the increasing complexity of decision problems, many managers employ multiple experts to reach a good decision in a group decision making. Now, if there is ambiguity in the evaluation of experts, the use of fuzzy numbers can be useful for each expert. In these situations, the use of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2023-12-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-49076-3 |
| _version_ | 1797398020235460608 |
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| author | Mahdi Ranjbar Sohrab Effati |
| author_facet | Mahdi Ranjbar Sohrab Effati |
| author_sort | Mahdi Ranjbar |
| collection | DOAJ |
| description | Abstract Due to the increasing complexity of decision problems, many managers employ multiple experts to reach a good decision in a group decision making. Now, if there is ambiguity in the evaluation of experts, the use of fuzzy numbers can be useful for each expert. In these situations, the use of hesitant fuzzy numbers (HFNs) which consists of several fuzzy numbers with special conditions can be suggested. HFNs are as an extension of the fuzzy numbers to take a better determining the membership functions of the parameters by several experts. Because of simple and fast calculations, in this paper, we use triangular HFNs in the pairwise comparison matrix of analytic hierarchy process by opinions of a group of decision makers in a hesitant fuzzy environment. We define consistency of the hesitant fuzzy pairwise comparison matrix and use the arithmetic operations on the HFNs and a new method of comparing HFNs to get the hesitant fuzzy performance score. By using score function to hesitant fuzzy score we can get a final score for alternatives. Finally, a practical example is provided to show the the effectiveness of this study. The obtained results from this paper show that new method can get a better answer by keeping the experts’ opinions in the process of solving the problem. |
| first_indexed | 2024-03-09T01:19:38Z |
| format | Article |
| id | doaj.art-897b5095c3e144869e6345f3a84a044f |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-09T01:19:38Z |
| publishDate | 2023-12-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-897b5095c3e144869e6345f3a84a044f2023-12-10T12:15:40ZengNature PortfolioScientific Reports2045-23222023-12-0113111410.1038/s41598-023-49076-3Group decision making in the analytic hierarchy process by hesitant fuzzy numbersMahdi Ranjbar0Sohrab Effati1Applied Mathematics, Ferdowsi University of MashhadApplied Mathematics, Ferdowsi University of MashhadAbstract Due to the increasing complexity of decision problems, many managers employ multiple experts to reach a good decision in a group decision making. Now, if there is ambiguity in the evaluation of experts, the use of fuzzy numbers can be useful for each expert. In these situations, the use of hesitant fuzzy numbers (HFNs) which consists of several fuzzy numbers with special conditions can be suggested. HFNs are as an extension of the fuzzy numbers to take a better determining the membership functions of the parameters by several experts. Because of simple and fast calculations, in this paper, we use triangular HFNs in the pairwise comparison matrix of analytic hierarchy process by opinions of a group of decision makers in a hesitant fuzzy environment. We define consistency of the hesitant fuzzy pairwise comparison matrix and use the arithmetic operations on the HFNs and a new method of comparing HFNs to get the hesitant fuzzy performance score. By using score function to hesitant fuzzy score we can get a final score for alternatives. Finally, a practical example is provided to show the the effectiveness of this study. The obtained results from this paper show that new method can get a better answer by keeping the experts’ opinions in the process of solving the problem.https://doi.org/10.1038/s41598-023-49076-3 |
| spellingShingle | Mahdi Ranjbar Sohrab Effati Group decision making in the analytic hierarchy process by hesitant fuzzy numbers Scientific Reports |
| title | Group decision making in the analytic hierarchy process by hesitant fuzzy numbers |
| title_full | Group decision making in the analytic hierarchy process by hesitant fuzzy numbers |
| title_fullStr | Group decision making in the analytic hierarchy process by hesitant fuzzy numbers |
| title_full_unstemmed | Group decision making in the analytic hierarchy process by hesitant fuzzy numbers |
| title_short | Group decision making in the analytic hierarchy process by hesitant fuzzy numbers |
| title_sort | group decision making in the analytic hierarchy process by hesitant fuzzy numbers |
| url | https://doi.org/10.1038/s41598-023-49076-3 |
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