A Novel Three-Phase LINMAP Method for Hybrid Multi-Criteria Group Decision Making With Dual Hesitant Fuzzy Truth Degrees
Based on the idea of linear programming technique for multidimensional analysis of preference (LINMAP), a novel three-phase LINMAP method is presented for solving hybrid multi-criteria group decision making (MCGDM) with dual hesitant fuzzy (DHF) truth degrees and incomplete criteria weights informat...
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| Published in: | IEEE access Vol. 8; pp. 112462 - 112483 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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2020
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| ISSN: | 2169-3536, 2169-3536 |
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| Abstract | Based on the idea of linear programming technique for multidimensional analysis of preference (LINMAP), a novel three-phase LINMAP method is presented for solving hybrid multi-criteria group decision making (MCGDM) with dual hesitant fuzzy (DHF) truth degrees and incomplete criteria weights information. Firstly, by simultaneously taking into account the difference between each alternative and all the others for the decision maker (DM), the difference of each alternative between the individual DM and the decision group, and the difference of each alternative between the individual DM and all the others, a tri-objective nonlinear programming model is created to determine the DMs' weights. Secondly, to derive the criteria weights, the objective positive ideal solution (OPIS), and the objective negative ideal solution (ONIS), a new four-objective DHF mathematical programming model is established by minimizing inconsistency and maximizing consistency based on OPIS and ONIS, and a pair of parametric nonlinear programming models are technically established by unequal weighted summation approach for solving the four-objective DHF mathematical programming model, which can provide DMs with more agility and flexible space to change their preference. Thirdly, by considering the distances of each alternative from the OPIS and ONIS for individual DM and the decision group, a minimizing deviation optimal model is established to derive the group ranking order of alternatives. Finally, a new method is put forward for solving hybrid MCGDM with DHF truth degrees, and the validity and practicability of the proposed method is analyzed through a case of water quality monitoring system (WQMS) selection. |
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| AbstractList | Based on the idea of linear programming technique for multidimensional analysis of preference (LINMAP), a novel three-phase LINMAP method is presented here for solving hybrid multi-criteria group decision making (MCGDM) with dual hesitant fuzzy (DHF) truth degrees and incomplete criteria weights information. Firstly, by simultaneously taking into account the difference between each alternative and all the others for the decision maker (DM), the difference of each alternative between the individual DM and the decision group, and the difference of each alternative between the individual DM and all the others, a tri-objective nonlinear programming model is created to determine the DMs’ weights. Secondly, to derive the criteria weights, objective positive ideal solution (OPIS), and the objective negative ideal solution (ONIS), a new four-objective DHF mathematical programming model is established by minimizing inconsistency and maximizing consistency based on OPIS and ONIS, and a pair of parametric nonlinear programming models are technically established by unequal weighted summation approach for solving the four-objective DHF mathematical programming model, which can provide DMs with more agility and flexible space to change their preference. Thirdly, by considering the distances of each alternative from the OPIS and ONIS for individual DM and the decision group, a minimizing deviation optimal model is established to derive the group ranking order of alternatives. Finally, a new method is put forward for solving hybrid MCGDM with DHF truth degrees, and the validity and practicability of the proposed method is analyzed through a case of water quality monitoring system (WQMS) selection. Based on the idea of linear programming technique for multidimensional analysis of preference (LINMAP), a novel three-phase LINMAP method is presented for solving hybrid multi-criteria group decision making (MCGDM) with dual hesitant fuzzy (DHF) truth degrees and incomplete criteria weights information. Firstly, by simultaneously taking into account the difference between each alternative and all the others for the decision maker (DM), the difference of each alternative between the individual DM and the decision group, and the difference of each alternative between the individual DM and all the others, a tri-objective nonlinear programming model is created to determine the DMs' weights. Secondly, to derive the criteria weights, the objective positive ideal solution (OPIS), and the objective negative ideal solution (ONIS), a new four-objective DHF mathematical programming model is established by minimizing inconsistency and maximizing consistency based on OPIS and ONIS, and a pair of parametric nonlinear programming models are technically established by unequal weighted summation approach for solving the four-objective DHF mathematical programming model, which can provide DMs with more agility and flexible space to change their preference. Thirdly, by considering the distances of each alternative from the OPIS and ONIS for individual DM and the decision group, a minimizing deviation optimal model is established to derive the group ranking order of alternatives. Finally, a new method is put forward for solving hybrid MCGDM with DHF truth degrees, and the validity and practicability of the proposed method is analyzed through a case of water quality monitoring system (WQMS) selection. |
| Author | Lu, Xiaoyun Dong, Jiuying Wan, Shuping |
| Author_xml | – sequence: 1 givenname: Xiaoyun orcidid: 0000-0003-3632-8027 surname: Lu fullname: Lu, Xiaoyun organization: School of Computer, Qinghai Normal University, Xining, China – sequence: 2 givenname: Jiuying orcidid: 0000-0003-2859-5264 surname: Dong fullname: Dong, Jiuying email: jiuyingdong@126.com organization: School of Statistics, Jiangxi University of Finance and Economics, Nanchang, China – sequence: 3 givenname: Shuping orcidid: 0000-0001-6504-9700 surname: Wan fullname: Wan, Shuping email: shupingwan@163.com organization: School of Information Technology, Jiangxi University of Finance and Economics, Nanchang, China |
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| SubjectTerms | Decision making dual hesitant fuzzy mathematical programming model dual hesitant fuzzy set Environmental monitoring fuzzy true degree Hafnium Indexes Linear programming linear programming technique for multidimensional analysis of preference Mathematical analysis Mathematical model Mathematical models Mathematical programming Multi-criteria group decision making Multiple criterion Nonlinear programming Optimization Programming Water quality |
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| Title | A Novel Three-Phase LINMAP Method for Hybrid Multi-Criteria Group Decision Making With Dual Hesitant Fuzzy Truth Degrees |
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