A novel risk attitudinal ranking method for intuitionistic fuzzy values and application to MADM |
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| Affiliation: | 1. College 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;3. Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China;1. Federal University of Technology (UTFPR), Elect. Eng. Dept., Av. Alberto Carazzai, 1640, 86300-000 Cornélio Procópio, PR, Brazil;2. Federal University of São Carlos (UFSCAR), Rodovia Washington Luís, km 235 – SP 310, 13565-905 São Carlos, SP, Brazil;1. School of Software Engineering, Chongqing University, Chongqing 400044, PR China;2. School of Computing, National University of Singapore, Singapore 117417, Singapore;3. School of Information Science and Engineering, Lanzhou University, Gansu 730000, PR China;4. Faculty of Computer and Information Science, Southwest University, Chongqing 400715, PR China;5. Faculty of Engineering, The University of Sydney, Sydney 2006, Australia;1. School of Computer and Software Engineering, Xihua University, Chengdu 610039, China;2. School of Digital Media, Jiangnan University, Wuxi 214122, China;1. State Key Laboratory of Ocean Engineering, Shanghai 200240, China;2. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China;3. Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University (KAU), Jeddah, Saudi Arabia;1. School of Automation and Electrical Engineering, Beijing University of Science & Technology, Beijing 100083, PR China;2. College of Automotive Engineering, Shanghai University of Engineering Science, Shanghai, PR China;3. Department of Computer and Information Science, University of Michigan-Dearborn, Dearborn, MI 48128, USA;1. University of Thessaly Department of Computer Science and Biomedical Informatics, Lamia, Greece;2. University of Piraeus, Department of Digital Systems, Piraeus, Greece |
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| Abstract: | The ranking of intuitionistic fuzzy sets (IFSs) is very important for the intuitionistic fuzzy decision making. The aim of this paper is to propose a new risk attitudinal ranking method of IFSs and apply to multi-attribute decision making (MADM) with incomplete weight information. Motivated by technique for order preference by similarity to ideal solution (TOPSIS), we utilize the closeness degree to characterize the amount of information according to the geometrical representation of an IFS. The area of triangle is calculated to measure the reliability of information. It is proved that the closeness degree and the triangle area just form an interval. Thereby, a new lexicographical method is proposed based on the intervals for ranking the intuitionistic fuzzy values (IFVs). Furthermore, considered the risk attitude of decision maker sufficiently, a novel risk attitudinal ranking measure is developed to rank the IFVs on the basis of the continuous ordered weighted average (C-OWA) operator and this interval. Through maximizing the closeness degrees of alternatives, we construct a multi-objective fractional programming model which is transformed into a linear program. Thus, the attribute weights are derived objectively by solving this linear program. Then, a new method is put forward for MADM with IFVs and incomplete weight information. Finally, an example analysis of a teacher selection is given to verify the effectiveness and practicability of the proposed method. |
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| Keywords: | Intuitionistic fuzzy sets Multi-attribute decision making Technique for order preference by similarity to ideal solution Fractional programming Risk attitude |
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