A discrete method based on distance measure in linguistic space and its application for CMADM problem |
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Authors: | Rong Zhao Peng Ge Peiyu Ren Manuel Fernández-Martínez |
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Institution: | 1. Business School, Sichuan University, Chengdu, China;2. The Department of Civil &3. Environmental Engineering, University of Washington(Seattle), Seattle, WA, USA;4. University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, Murcia, Spain |
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Abstract: | ABSTRACTOwing to the complexity of decision environment, not all the attributes in multiple attribute decision making are quantitative. There are also some qualitative attributes, which are related to the integration of multiple attribute decision making (MADM) and linguistic multiple attribute decision making (LMADM). The specific method for composite multiple attribute decision making (CMADM) problems is crucial for decision maker (DM) to make scientific decision. In this paper, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is extended to a Composite Technique for Order Preference by Similarity to an Ideal Solution (CTOPSIS) method to solve the CMADM problems. As the basis of the CTOPSIS method, the distance measure model in linguistic space and in n-dimension linguistic space is generated based on the non-linear mapping. Based on the distance measure in linguistic space, a standard deviation method is taken to get the attribute weight. At the same time, the distance measure models are proposed based on the distance measure in n-dimension linguistic space, which are used to calculate the distance between the alternatives and the positive and negative idea points separately. Furthermore, a CTOPSIS method is generated to solve the CMADM problems. Finally, a numerical example is illustrated to explain the process. And the result shows that the CTOPSIS method is quite practical and more approximate to the real decision making situation. |
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Keywords: | Composite multiple attribute decision making distance measure linguistic variable ideal point attribute weight |
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