On robustness of the full implication triple I inference method with respect to finer measurements. (English) Zbl 1316.68196
Summary: This paper mainly discusses three points. First of all, different types of equalities and similarity degrees between two fuzzy sets on a given universe of discourse are compared and analyzed. In particular, the concept of \((T,\delta)\) equality is revised as a measure to evaluate robustness of fuzzy reasoning. Besides, several induced metrics with respect to left-continuous T-norms are investigated, and properties of the related metric spaces are discussed. Finally, based on discussions above, the continuity of the triple I method with respect to the revised measures is proved, which reflects the good behavior of robustness of the triple I method.
MSC:
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
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