Robustness of fuzzy reasoning via logically equivalence measure. (English) Zbl 1126.68082
Summary: We discuss robustness of fuzzy reasoning. After proposing the definition of perturbation of fuzzy sets based on some logic-oriented equivalence measure, we present robustness results for various fuzzy logic connectives, fuzzy implication operators, inference rules and fuzzy reasoning machines, and discuss the relations between the robustness of fuzzy reasoning and that of fuzzy conjunction and implication operators. The robustness results are presented in terms of \(\delta \)-equalities of fuzzy sets based on some logic-oriented equivalence measure, and the maximum of \(\delta \) (which ensures the corresponding \(\delta \)-equality holds) is derived.
MSC:
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
Keywords:
fuzzy sets; fuzzy reasoning; robustness of fuzzy reasoning; logically equivalence; \(\delta \)-equalityReferences:
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