The distance of probabilistic fuzzy sets for classification |
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| Authors: | Wen-Jing Huang Geng Zhang Han-Xiong Li |
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| Affiliation: | 1. School of Mechanical and Electrical Engineering, Central South University, Changsha, China;2. Department of SEEM, City University of Hong Kong, Hong Kong, China;1. Department of Mechanical Engineering, Utkal University, Bhubaneswar-751004, Odisha, India;2. Department of Mechanical Engineering, Indira Gandhi Institute of Technology, Sarang - 759146, Odisha, India;1. Federal Rural University of Semi-Árido, Campus Angicos, Angicos, RN, Brazil;2. Federal University of Rio Grande do Norte, Department of Computer Engineering and Automation, Natal, Brazil |
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| Abstract: | The probabilistic fuzzy set (PFS) is designed for handling the uncertainties with both stochastic and fuzzy nature. In this paper, the concept of the distance between probabilistic fuzzy sets is introduced and its metric definition is conducted, which may be finite or continuous. And some related distances are discussed. The proposed distance considers the random perturbation in progress by introducing the distance of probability distribution, thus it improves the ability to handle random uncertainties, and some inadequacy of the distance of probability distribution is remedied. Finally, a PFS-based distance classifier is proposed to discuss the classification problem, the numerical experiment shows the superiority of this proposed distance in fuzzy and stochastic circumstance. |
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| Keywords: | Probabilistic fuzzy set The distance between probabilistic fuzzy sets PFS-based distance FS-based distance |
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