Fuzzy Domination Graphs in Decision Support Tasks
In decision support tasks, one often has to deal with uncertainty due to fuzzy judgments of the decision maker or the expert. This paper proposes methods that allow you to rank the alternatives based on fuzzy evaluations. This is achieved by using fuzzy weighted summation, fuzzy implication, a compu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/2837 |
| _version_ | 1797591304700428288 |
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| author | Vladimir Sudakov Alexander Zhukov |
| author_facet | Vladimir Sudakov Alexander Zhukov |
| author_sort | Vladimir Sudakov |
| collection | DOAJ |
| description | In decision support tasks, one often has to deal with uncertainty due to fuzzy judgments of the decision maker or the expert. This paper proposes methods that allow you to rank the alternatives based on fuzzy evaluations. This is achieved by using fuzzy weighted summation, fuzzy implication, a computation graph showing the criteria, and a fuzzy dominance graph showing the alternatives. If the criteria have equal importance, then fuzzy graphs corresponding to the dominance of each of the criteria are used. An algorithm that is used for both the transition from fuzzy dominance graphs and the ranking of alternatives is proposed. This algorithm is based on the idea of constructing Kemeny medians or other concordant rankings at a given confidence level in the existence of corresponding arcs. Computational experiments have shown the performance of these approaches. It is reasonable to apply them in problems that require complex expert evaluations with a large number of alternatives and criteria. |
| first_indexed | 2024-03-11T01:35:31Z |
| format | Article |
| id | doaj.art-bdc192a7655942dd8eb142eb930b7a85 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:35:31Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bdc192a7655942dd8eb142eb930b7a852023-11-18T17:02:03ZengMDPI AGMathematics2227-73902023-06-011113283710.3390/math11132837Fuzzy Domination Graphs in Decision Support TasksVladimir Sudakov0Alexander Zhukov1Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, 125167 Moscow, RussiaFGBSI The Federal Center of Analysis, 109316 Moscow, RussiaIn decision support tasks, one often has to deal with uncertainty due to fuzzy judgments of the decision maker or the expert. This paper proposes methods that allow you to rank the alternatives based on fuzzy evaluations. This is achieved by using fuzzy weighted summation, fuzzy implication, a computation graph showing the criteria, and a fuzzy dominance graph showing the alternatives. If the criteria have equal importance, then fuzzy graphs corresponding to the dominance of each of the criteria are used. An algorithm that is used for both the transition from fuzzy dominance graphs and the ranking of alternatives is proposed. This algorithm is based on the idea of constructing Kemeny medians or other concordant rankings at a given confidence level in the existence of corresponding arcs. Computational experiments have shown the performance of these approaches. It is reasonable to apply them in problems that require complex expert evaluations with a large number of alternatives and criteria.https://www.mdpi.com/2227-7390/11/13/2837fuzzy numbermulticriteria decision analysisfuzzy graphweighted sum modelranking |
| spellingShingle | Vladimir Sudakov Alexander Zhukov Fuzzy Domination Graphs in Decision Support Tasks Mathematics fuzzy number multicriteria decision analysis fuzzy graph weighted sum model ranking |
| title | Fuzzy Domination Graphs in Decision Support Tasks |
| title_full | Fuzzy Domination Graphs in Decision Support Tasks |
| title_fullStr | Fuzzy Domination Graphs in Decision Support Tasks |
| title_full_unstemmed | Fuzzy Domination Graphs in Decision Support Tasks |
| title_short | Fuzzy Domination Graphs in Decision Support Tasks |
| title_sort | fuzzy domination graphs in decision support tasks |
| topic | fuzzy number multicriteria decision analysis fuzzy graph weighted sum model ranking |
| url | https://www.mdpi.com/2227-7390/11/13/2837 |
| work_keys_str_mv | AT vladimirsudakov fuzzydominationgraphsindecisionsupporttasks AT alexanderzhukov fuzzydominationgraphsindecisionsupporttasks |