Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study |
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| Institution: | 1. School of International Audit, Nanjing Audit University, Nanjing 2111815, China;2. School of Business, Central South University, Changsha 410083, China;3. School of Accounting, Hunan University of Commerce, Changsha 410205, China;1. School of Management, Hefei University of Technology, Hefei, Anhui 230009, China;2. Key Laboratory of Process Optimization and Intelligent Decision-Making, Ministry of Education, Hefei, Anhui 230009, China;3. School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China;1. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, 33071 Oviedo, Spain;2. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, 9000 Gent, Belgium;3. Department of Mathematics, KU Leuven, 3001 Leuven, Belgium;1. School of International Audit, Nanjing Audit University, Nanjing 211815, China;2. School of Business, Central South University, Changsha 410083, China;1. School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China;2. School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China |
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| Abstract: | To examine the multiplicative consistency of interval fuzzy preference relations (IFPRs), this paper first analyzes the limitations associated with the previous consistency concepts. Accordingly, a new consistency concept is defined that is an extension of the crisp case and overcomes limitations in the previous concepts. Next, a linear programming model to judge the consistency of IFPRs is constructed, and an approach to derive multiplicative consistent IFPRs is introduced. Furthermore, goal-programming models to determine missing values in an incomplete IFPR are constructed that have the highest consistent level with respect to known values. Moreover, a multiplicative consistency and consensus based method for group decision making with IFPRs is developed that can address incomplete and inconsistent cases. Finally, two practical decision-making problems are offered to demonstrate the feasibility and efficiency of the new method, and an analysis of a numerical and theoretical comparison with several related methods is performed. |
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| Keywords: | Decision analysis Interval fuzzy preference relation Multiplicative consistency Programming model Consensus |
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