| An improved α-cut approach to transforming fuzzy membership function into basic belief assignment |
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| 作者姓名： | Yang Yi X.Rong Li Han Deqiang |
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| 作者单位： | SKLSVMS, School of Aerospace, Xi’an Jiaotong University;Department of Electrical Engineering, University of New Orleans;Center for Information Engineering Science Research, Xi’an Jiaotong University |
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| 基金项目： | supported by the Grant for State Key Program for Basic Research of China (No. 2013CB329405);National Natural Science Foundation of China (No. 61573275);Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 61221063);Science and Technology Project of Shaanxi Province (No. 2013KJXX-46);Postdoctoral Science Foundation of China (No. 2016M592790);Fundamental Research Funds for the Central Universities of China (No. xjj2014122) |
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| 摘 要： | In practical applications, pieces of evidence originated from different sources might be modeled by different uncertainty theories. To implement the evidence combination under the Dempster–Shafer evidence theory(DST) framework, transformations from the other type of uncertainty representation into the basic belief assignment are needed. a-Cut is an important approach to transforming a fuzzy membership function into a basic belief assignment, which provides a bridge between the fuzzy set theory and the DST. Some drawbacks of the traditional a-cut approach caused by its normalization step are pointed out in this paper. An improved a-cut approach is proposed, which can counteract the drawbacks of the traditional a-cut approach and has good properties. Illustrative examples, experiments and related analyses are provided to show the rationality of the improved a-cut approach.
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| 关 键 词： | Belief functions Evidence theory Fuzzy sets Membership functions Uncertainty |
An improved α-cut approach to transforming fuzzy membership function into basic belief assignment |
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| Yang Yi,X.Rong Li,Han Deqiang.An improved α-cut approach to transforming fuzzy membership function into basic belief assignment[J].Chinese Journal of Aeronautics,2016(4):1042-1051. |
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| Institution: | 1. SKLSVMS, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China;2. Department of Electrical Engineering, University of New 0rleans, New 0rleans, LA70148, USA;3. Center for Information Engineering Science Research, Xi’an Jiaotong University, Xi’an 710049, China |
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| Abstract: | In practical applications, pieces of evidence originated from different sources might be modeled by different uncertainty theories. To implement the evidence combination under the Dempster–Shafer evidence theory (DST) framework, transformations from the other type of uncer-tainty representation into the basic belief assignment are needed. a-Cut is an important approach to transforming a fuzzy membership function into a basic belief assignment, which provides a bridge between the fuzzy set theory and the DST. Some drawbacks of the traditional a-cut approach caused by its normalization step are pointed out in this paper. An improved a-cut approach is pro-posed, which can counteract the drawbacks of the traditional a-cut approach and has good prop-erties. Illustrative examples, experiments and related analyses are provided to show the rationality of the improved a-cut approach. |
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| Keywords: | Belief functions Evidence theory Fuzzy sets Membership functions Uncertainty |
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