Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment
The best–worst method (BWM) has recently demonstrated its applicability in addressing various decision-making problems in a practical setting. The traditional BWM method is based on deterministic information gathered from experts as pairwise comparisons of several criteria. The advantage of BWM is t...
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MDPI AG
2022-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/11/659 |
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| author | Qazi Shoeb Ahmad Mohammad Faisal Khan Naeem Ahmad |
| author_facet | Qazi Shoeb Ahmad Mohammad Faisal Khan Naeem Ahmad |
| author_sort | Qazi Shoeb Ahmad |
| collection | DOAJ |
| description | The best–worst method (BWM) has recently demonstrated its applicability in addressing various decision-making problems in a practical setting. The traditional BWM method is based on deterministic information gathered from experts as pairwise comparisons of several criteria. The advantage of BWM is that it uses fewer calculations and analyses while maintaining good, acceptable consistency ratio values. A multi-choice best–worst method (MCBWM), which considers several options for pairwise comparison of preferences between the criteria, has recently been developed. The experts are given the option to select values from several comparison scales. The MCBWM technique has been shown to be better. Presenting the options for which an optimal solution has been found simplifies the calculation and establishes the ideal weight values. This study proposes two different mathematical programming models for solving multi-criteria decision-making problems having multiple decision-makers. The two methods are proposed considering the multi-choice uncertainty assumption in pairwise criteria comparisons. Additionally, it considers the best–worst method as the base model. The multi-choice uncertainty is applied to determine the best choice out of multiple choices. It gives a real-life scenario to the decision-making problems. Although there are many other forms of uncertainty, such as fuzzy, intuitionistic fuzzy, neutrosophic, probabilistic, etc., it focuses on choices instead of ambiguity in terms of the probabilistic or fuzzy nature of parameters. The parameter considered as multi-choice is the pairwise comparison. These parameters are handled by applying the Lagrange interpolating polynomial method. The proposed models are novel in terms of their mathematical structure and group decision-making approach. The models are formulated and further validated by solving numerical examples. It provides a framework for solving mcdm problems where the weightage to the decision-makers is also incorporated. The CR values for all the models of example 1 and 2, and the case study has been found acceptable. |
| first_indexed | 2024-03-09T18:28:01Z |
| format | Article |
| id | doaj.art-0e1a0af36ccd49e49ee94919a16881b3 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T18:28:01Z |
| publishDate | 2022-11-01 |
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| record_format | Article |
| series | Axioms |
| spelling | doaj.art-0e1a0af36ccd49e49ee94919a16881b32023-11-24T07:43:39ZengMDPI AGAxioms2075-16802022-11-01111165910.3390/axioms11110659Multi-Criteria Group Decision-Making Models in a Multi-Choice EnvironmentQazi Shoeb Ahmad0Mohammad Faisal Khan1Naeem Ahmad2Department of Statistics, Deanship of Educational Services, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Basic Science, College of Science & Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi ArabiaDepartment of Civil Engineering, College of Engineering, Qassim University, Unaizah 56452, Saudi ArabiaThe best–worst method (BWM) has recently demonstrated its applicability in addressing various decision-making problems in a practical setting. The traditional BWM method is based on deterministic information gathered from experts as pairwise comparisons of several criteria. The advantage of BWM is that it uses fewer calculations and analyses while maintaining good, acceptable consistency ratio values. A multi-choice best–worst method (MCBWM), which considers several options for pairwise comparison of preferences between the criteria, has recently been developed. The experts are given the option to select values from several comparison scales. The MCBWM technique has been shown to be better. Presenting the options for which an optimal solution has been found simplifies the calculation and establishes the ideal weight values. This study proposes two different mathematical programming models for solving multi-criteria decision-making problems having multiple decision-makers. The two methods are proposed considering the multi-choice uncertainty assumption in pairwise criteria comparisons. Additionally, it considers the best–worst method as the base model. The multi-choice uncertainty is applied to determine the best choice out of multiple choices. It gives a real-life scenario to the decision-making problems. Although there are many other forms of uncertainty, such as fuzzy, intuitionistic fuzzy, neutrosophic, probabilistic, etc., it focuses on choices instead of ambiguity in terms of the probabilistic or fuzzy nature of parameters. The parameter considered as multi-choice is the pairwise comparison. These parameters are handled by applying the Lagrange interpolating polynomial method. The proposed models are novel in terms of their mathematical structure and group decision-making approach. The models are formulated and further validated by solving numerical examples. It provides a framework for solving mcdm problems where the weightage to the decision-makers is also incorporated. The CR values for all the models of example 1 and 2, and the case study has been found acceptable.https://www.mdpi.com/2075-1680/11/11/659best–worst methodmulti-choice best–worst methodmulti-criteria decision-makinggroup decision-makingmathematical programming |
| spellingShingle | Qazi Shoeb Ahmad Mohammad Faisal Khan Naeem Ahmad Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment Axioms best–worst method multi-choice best–worst method multi-criteria decision-making group decision-making mathematical programming |
| title | Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment |
| title_full | Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment |
| title_fullStr | Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment |
| title_full_unstemmed | Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment |
| title_short | Multi-Criteria Group Decision-Making Models in a Multi-Choice Environment |
| title_sort | multi criteria group decision making models in a multi choice environment |
| topic | best–worst method multi-choice best–worst method multi-criteria decision-making group decision-making mathematical programming |
| url | https://www.mdpi.com/2075-1680/11/11/659 |
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