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Robustness of fuzzy connectives and fuzzy reasoning with respect to general divergence measures. (English) Zbl 1374.03045

Summary: This paper discusses the robustness of fuzzy connectives and fuzzy reasoning with respect to general divergence measures. First of all, the concept of DF-metric is proposed. Secondly, several DF-metrics are introduced as well as their properties and some inequalities about them. Then a formula of divergence measure composed by DF-metric is presented. Finally, based on the proposed divergence measures, the concept of perturbations of fuzzy sets is extended. According to the extended concept, the perturbation parameters raised by various fuzzy connectives are studied and the perturbations of fuzzy reasoning are also investigated.

MSC:

03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence
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