MADM method based on prospect theory and evidential reasoning approach with unknown attribute weights under intuitionistic fuzzy environment |
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| Affiliation: | 1. Transportation Management College, Dalian Maritime University, Dalian 116026, China;2. Guizhou Highway Survey and Design Academy Co., Ltd., Guizhou 550081, China;1. Department of Electronics and Communication Engineering, National Institute of Technology Goa, Farmagudi, Ponda, Goa, 403401, India;2. Department of Instrumentation and Control Engineering, PSG College of Technology, Coimbatore, 641004, India;3. Department of Electronics and Communication Engineering, Institute of Aeronautical Engineering, Dundigal, Hyderabad, 500 043, India;1. Luxembourg Institute of Socio-Economic Research (LISER), Maison des Sciences Humaines, 11, Porte des Sciences L- 4366 Esch-sur-Alzette, Luxembourg\n;2. University of Salerno, Via Giovanni Paolo II, 132 84084 Fisciano (SA), Italy;1. Department of Computer Systems, Polytechnic University of Madrid, Madrid 28031, Spain;2. Department of Biochemistry and Molecular Biology I, Complutense University, Madrid 28040, Spain\n;1. Technical Staff Member, IBM India Research Labs, New Delhi, India;2. Manager and Senior Technical Staff Member, IBM India Research Labs, New Delhi, India;3. Senior Manager and Senior Technical Staff Member, IBM India Research Labs, New Delhi, India;1. Department of Information and Communication Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea;2. School of Electronics and Information Engineering, Korea Aerospace University, 76 Hanggongdaehak-ro, Deogyang-gu, Goyang-si, Gyeonggi-do 10540, Republic of Korea |
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| Abstract: | This paper proposes an intuitionistic fuzzy decision method based on prospect theory and the evidential reasoning approach, aiming at analyzing multi-attribute decision making problems in which the criteria values are intuitionistic fuzzy numbers and the information of attributes weights is unknown. Firstly, the measures of entropy and cross entropy are defined for intuitionistic fuzzy sets by taking into consideration the preference of decision maker towards hesitancy degree. Secondly, combined with bounded rationality, the prospect decision matrix is calculated in the light of prospect theory and intuitionistic fuzzy distance. Thirdly, the correlational analyses are conducted between the attribute weights and three indicators which are entropy, cross entropy and prospect value, and optimization models for identifying attribute weights are built under the circumstances that the weights are incomplete and unknown. Finally, in order to avoid the loss of decision making information, the evidential reasoning approach is applied to the calculation of comprehensive prospective values for all alternatives. Following the value calculation, the ranking and the optimal alternative are determined based on the comprehensive prospective values. Illustrating examples demonstrate that the proposed method is reasonable and feasible. |
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