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Fuzzy Reasoning Based on Truth-Value Progression: A Control-Theoretic Design Approach

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Abstract

Fuzzy logic, especially fuzzy reasoning, has been widely used in many real-world applications for its tremendous practical value. This paper mainly focuses on a new theoretical principle of fuzzy logic, fuzzy reasoning, and its applications. It starts with enunciating a novel foundation: the Fundamental Axiom of Reasoning. We then propose a practical framework, which enables the Fundamental Axiom of Reasoning to be applied to various applications. This framework is divided into discrete case and continuous case. In the discrete case, we first solve the sorites paradox. We then proceed to a pattern recognition problem. So far, these are all passive approach in that the Fundamental Axiom of Reasoning is used as is to measure if the reasoning is valid. In the continuous case, we proceed to actively designing the reasoning so that the Fundamental Axiom of Reasoning is always guaranteed through Lyapunov stability approaches. This is formulated as a control-theoretic task. The problem of reasoning is converted to a control design one. This is then applied to a vehicle following problem. Through theoretical analysis and practical demonstrations, we show how the Fundamental Axiom of Reasoning can be conceptualized, articulated, and formalized in fuzzy reasoning.

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Acknowledgements

This research is sponsored in part by the NSFC Program (Nos. 61872217, U20A20285, 52122217, U1801263), and the research is also sponsored in part by the key R &D projects of the ministry of science and technology (No. 2020YFB1710901).

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Authors and Affiliations

  1. School of Vehicle and Mobility, Tsinghua University, Beijing, 100084, China

    Tianchuang Meng, Wei Zhang, Jin Huang, Diange Yang & Zhihua Zhong

  2. The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Ye-Hwa Chen

  3. Department of Mechanical Engineering, National University of Singapore, Singapore, 117575, Singapore

    Chee-Meng Chew

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  1. Tianchuang Meng
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  2. Wei Zhang
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  3. Jin Huang
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Correspondence to Wei Zhang or Jin Huang.

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Meng, T., Zhang, W., Huang, J. et al. Fuzzy Reasoning Based on Truth-Value Progression: A Control-Theoretic Design Approach. Int. J. Fuzzy Syst. 25, 1559–1578 (2023). https://doi.org/10.1007/s40815-023-01459-4

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