The Axiomatic Characterization of the Grey Shapley Value
One of the most significant solution concepts in cooperative grey game theory is the grey Shapley value. This value is a fascinating one among the models and methods of operations research, and has been the subject of extensive study by other researchers. The objective of this study is to characteri...
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2025-01-01
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| author | Mehmet Gençtürk Mahmut Sami Öztürk Osman Palancı |
| author_facet | Mehmet Gençtürk Mahmut Sami Öztürk Osman Palancı |
| author_sort | Mehmet Gençtürk |
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| description | One of the most significant solution concepts in cooperative grey game theory is the grey Shapley value. This value is a fascinating one among the models and methods of operations research, and has been the subject of extensive study by other researchers. The objective of this study is to characterize and redefine this value in cooperative games where coalition values are grey numbers. In this study, the grey Shapley value is characterized by the following axioms: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-gain loss, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-null player, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-differential marginality. Finally, this study concludes with an investigation of some applications involving production costs. This study is based on an investigation of the costs incurred when milk producers collaborate. |
| format | Article |
| id | doaj-art-4c5112cfa31d409fa70df836a280dccb |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-4c5112cfa31d409fa70df836a280dccb2025-01-24T13:22:16ZengMDPI AGAxioms2075-16802025-01-011415110.3390/axioms14010051The Axiomatic Characterization of the Grey Shapley ValueMehmet Gençtürk0Mahmut Sami Öztürk1Osman Palancı2Department of Business Administration, Faculty of Economics and Administrative Sciences, Suleyman Demirel University, 32260 Isparta, TurkeyDepartment of Business Administration, Faculty of Economics and Administrative Sciences, Suleyman Demirel University, 32260 Isparta, TurkeyDepartment of Business Administration, Faculty of Economics and Administrative Sciences, Suleyman Demirel University, 32260 Isparta, TurkeyOne of the most significant solution concepts in cooperative grey game theory is the grey Shapley value. This value is a fascinating one among the models and methods of operations research, and has been the subject of extensive study by other researchers. The objective of this study is to characterize and redefine this value in cooperative games where coalition values are grey numbers. In this study, the grey Shapley value is characterized by the following axioms: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-gain loss, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-null player, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-differential marginality. Finally, this study concludes with an investigation of some applications involving production costs. This study is based on an investigation of the costs incurred when milk producers collaborate.https://www.mdpi.com/2075-1680/14/1/51grey system theorycooperative grey gamesgrey Shapley valuecharacterizationcost management |
| spellingShingle | Mehmet Gençtürk Mahmut Sami Öztürk Osman Palancı The Axiomatic Characterization of the Grey Shapley Value Axioms grey system theory cooperative grey games grey Shapley value characterization cost management |
| title | The Axiomatic Characterization of the Grey Shapley Value |
| title_full | The Axiomatic Characterization of the Grey Shapley Value |
| title_fullStr | The Axiomatic Characterization of the Grey Shapley Value |
| title_full_unstemmed | The Axiomatic Characterization of the Grey Shapley Value |
| title_short | The Axiomatic Characterization of the Grey Shapley Value |
| title_sort | axiomatic characterization of the grey shapley value |
| topic | grey system theory cooperative grey games grey Shapley value characterization cost management |
| url | https://www.mdpi.com/2075-1680/14/1/51 |
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