A novel approach to guarantee good robustness of fuzzy reasoning |
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| Affiliation: | 1. School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;2. School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China;3. School of Computer Science and Technology, Huaiyin Normal University, Huai’an 223300, China;4. School of Mathematical Science, Huaiyin Normal University, Huai’an 223300, China;1. Université de Toulouse, INSA, UPS, INP, LISBP, 135 Avenue de Rangueil, F-31077 Toulouse, France;2. INRA, UMR792, Laboratoire d’Ingénierie des Systèmes Biologiques et des Procédés, F-31400 Toulouse, France;3. CNRS, UMR5504, F-31400 Toulouse, France;1. The University of Queensland, UQ Centre for Clinical Research, Herston, QLD 4029, Australia;2. College of Engineering, Qatar University, Qatar;1. Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, PR China;2. School of Mechatronic Engineering and Automation, Shanghai University, 200072, PR China;1. Department of Mathematics, Institute for Systems Genomics, Center for Health, Intervention, and Prevention (CHIP), University of Connecticut, 196 Auditorium Rd U-3009, Storrs, CT 06269, USA;2. Department of Statistics, Institute for Systems Genomics, Center for Health, Intervention, and Prevention (CHIP), Center for Quantitative Medicine, University of Connecticut, 215 Glenbrook Road, U-4098, Storrs, CT 06269, USA;3. Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4098, Storrs, CT 06269, USA |
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| Abstract: | The analysis of internal connective operators of fuzzy reasoning is very significant and the robustness of fuzzy reasoning has been calling for study. An interesting and important question is that, how to choose suitable internal connective operators to guarantee good robustness of rule-based fuzzy reasoning? This paper is intended to answer it. In this paper, Lipschitz aggregation property and copula characteristic of t-norms and implications are discussed. The robustness of rule-based fuzzy reasoning is investigated and the relationships among input perturbation, rule perturbation and output perturbation are presented. The suitable t-norm and implication can be chosen to satisfy the need of robustness of fuzzy reasoning. In 1-Lipschitz operators, if both t-norm and implication are copulas, the rule-based fuzzy reasoning is much more stable and more reliable. In copulas, if both t-norm and implication are 1-l∞-Lipschitz, they can guarantee good robustness of fuzzy reasoning. The experiments not only illustrate the ideas proposed in the paper but also can be regarded as applications of soft computing. The approach in the paper also provides guidance for choosing suitable fuzzy connective operators and decision making application in rule-based fuzzy reasoning. |
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| Keywords: | Fuzzy reasoning Robustness Triangular norm Implication Lipschitz Copula |
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