A novel approach to guarantee good robustness of fuzzy reasoning

• Lipschitz aggregation property and copula characteristic of t-norms and implications are discussed and the robustness of rule-based fuzzy reasoning is investigated.
• According to Lipschitz aggregation property and copula characteristic of t-norms and implications, suitable t-norm and implication can be chosen to satisfy the need of robustness of fuzzy reasoning.
• The approach provides guidance for choosing suitable fuzzy connective operators and decision making application in rule-based fuzzy reasoning.
• The experiments which illustrate the ideas are the applications of intelligent information processing.

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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