Aggregating information and ranking alternatives in decision making with intuitionistic multiplicative preference relations |
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| Affiliation: | 1. College of Communications Engineering, PLA University of Science and Technology, Nanjing, Jiangsu 210007, China;2. Business School, Sichuan University, Chengdu 610064, Sichuan, China;1. Data Mining and Optimisation Research Group, Centre for Artificial Intelligence Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia;2. Faculty of Information & Communication Technologies, Swinburne University of Technology, Victoria 3122, Australia;1. KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, B-9000 Gent, Belgium;2. Laboratory of Hydrology and Water Management, Ghent University, Coupure links 653, B-9000 Gent, Belgium;1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, China;2. School of Electronics and Computer Science, University of Southampton Malaysia Campus, Nusajaya, Johor, Malaysia;3. Department of Electrical and Computer Engineering, Curtin University, WA, Australia;1. School of Electrical and Electronic Engineering, Yonsei University, Sinchon-dong, Seodaemun-gu, Seoul 120-749, Republic of Korea;2. Department of Electrical Electronic and Control Engineering, Hankyong National University, Sukjong-dong, Ansung-si, Gyunggi-do 456-749, Republic of Korea |
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| Abstract: | The intuitionistic multiplicative preference relation (IMPR), whose all elements are measured by an unsymmetrical scale (Saaty's 1–9 scale) instead of the symmetrical scale in the intuitionistic fuzzy preference relation (IFPR), is suitable for describing the asymmetric preference information. In decision making process, one of the most crucial issues is how to rank alternatives from the given preference relation constructed by the decision maker. In this paper, two approaches are proposed for deriving the ranking orders of the alternatives from two different angles. To do it, a transformation mechanism is developed to transform an IMPR to a corresponding IFPR, and then all alternatives depicted by the given IMPR can be ranked via solving a familiar IFPR. In addition, the generalized intuitionistic multiplicative ordered weighted averaging (GIMOWA) and the geometric (GIMOWG) operators are given by taking fully account of the different weights associated with the particular ordered positions and their desirable properties are also discussed. After that, through a practical example, the proposed approaches are compared with the previous work and a numerical analysis of the results is also given. |
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| Keywords: | Decision making Intuitionistic multiplicative preference relation Aggregation operators Transformation function |
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