Fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers and interval-valued fuzzy number arithmetic operators |
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| Authors: | Shyi-Ming Chen Jim-Ho Chen |
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| Affiliation: | 1. Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, R. O. C;2. Department of Computer Science and Information Engineering, Jinwen University of Science and Technology, Taipei County, Taiwan, R. O. C;1. School of Information Science and Engineering, Shaoguan University, Shaoguan 512005, China;2. School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, India;1. Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran;2. Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Power System Excellence, Tehran 15914, Iran;3. School of Electrical, Electronic, and Comms. Engineering, University College Dublin, Dublin D04V1W8, Ireland;1. Key Laboratory of Medical Virology and Virus Disease, National Health and Family Planning Commission of the People''s Republic of China; National Institute for Viral Disease Control and Prevention, Chinese Center for Disease Control and Prevention, Beijing 102206, China;2. Guangdong Provincial Center for Disease Control and Prevention, Guangzhou 511430, Guangdong, China;1. Department of Physics, Chemistry and Mathematics, Federal University of São Carlos, Sorocaba, SP, Brazil;2. Department of Applied Mathematics, IMECC, University of Campinas, Campinas, SP, Brazil |
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| Abstract: | In this paper, we present a new method for fuzzy risk analysis based on a new similarity measure between interval-valued fuzzy numbers and new interval-valued fuzzy number arithmetic operators. First, we present a new similarity measure between interval-valued fuzzy numbers. The proposed similarity measure considers the similarity of the gravities on the X-axis between upper fuzzy numbers, the difference of the spreads between upper fuzzy numbers, the heights of the upper fuzzy numbers, the degree of similarity on the X-axis between interval-valued fuzzy numbers, and the gravities on the Y-axis between interval-valued fuzzy numbers. We also present three properties of the proposed similarity measure between interval-valued fuzzy numbers. Then, we present new interval-valued fuzzy number arithmetic operators. Finally, we apply the proposed similarity measure between interval-valued fuzzy numbers and the proposed interval-valued fuzzy number arithmetic operators to propose a fuzzy risk analysis algorithm to deal with fuzzy risk analysis problems. The proposed method provides a useful way for handling fuzzy risk analysis problems based on interval-valued fuzzy numbers. |
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