The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties |
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| Institution: | 1. High-Tech Institute of Xi''an, Xi''an, Shaanxi 710025, PR China;2. Decision Sciences Institute, Fuzhou University, Fuzhou University, Fuzhou 350116, PR China;3. Department of Radiation Oncology, The University of Texas Southwestern Medical Center, Dallas, TX 75235, USA\n;1. High-Tech Institute of Xi''an, Xi''an, Shaanxi 710025, PR China;2. Harbin Institute of Technology, Harbin, Heilongjiang 150001, PR China;3. Xi''an University of Technology, Xi''an, Shaanxi 710048, PR China;4. Hainan Normal University, Haikou, Hainan 570100, PR China;1. Decision Sciences Institute, Fuzhou University, Fuzhou, Fujian, PR China;2. Department of Computer Science, University of Jaén, Jaén, Spain;3. School of Computing and Mathematics, Ulster University, Northern Ireland, UK;1. School of Management, Hefei University of Technology, Hefei, Box 270, Hefei 230009, Anhui, PR China;2. Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei 230009, Anhui, PR China;1. Decision Sciences Institute, Fuzhou University, Fuzhou 350002, PR China;2. School of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, PR China;3. Department of Management, Xi''an High-tech Institute, Xi''an 710025, PR China;4. Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon Tong, Hong Kong |
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| Abstract: | Many multiple attribute decision analysis (MADA) problems are characterised by both quantitative and qualitative attributes with various types of uncertainties. Incompleteness (or ignorance) and vagueness (or fuzziness) are among the most common uncertainties in decision analysis. The evidential reasoning (ER) approach has been developed in the 1990s and in the recent years to support the solution of MADA problems with ignorance, a kind of probabilistic uncertainty. In this paper, the ER approach is further developed to deal with MADA problems with both probabilistic and fuzzy uncertainties.In this newly developed ER approach, precise data, ignorance and fuzziness are all modelled under the unified framework of a distributed fuzzy belief structure, leading to a fuzzy belief decision matrix. A utility-based grade match method is proposed to transform both numerical data and qualitative (fuzzy) assessment information of various formats into the fuzzy belief structure. A new fuzzy ER algorithm is developed to aggregate multiple attributes using the information contained in the fuzzy belief matrix, resulting in an aggregated fuzzy distributed assessment for each alternative. Different from the existing ER algorithm that is of a recursive nature, the new fuzzy ER algorithm provides an analytical means for combining all attributes without iteration, thus providing scope and flexibility for sensitivity analysis and optimisation. A numerical example is provided to illustrate the detailed implementation process of the new ER approach and its validity and wide applicability. |
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