On Interval Perturbation of the ɑ-Symmetric Implicational Algorithm

Yiming Tang, Jianghui Han, Guangqing Bao, Rui Chen

Abstract: Perturbation is an important property of fuzzy reasoning algorithms. It is an important task to estimate the upper and lower bounds of the output after a perturbation (such as an interval perturbation) is given to the input. In this study, the interval perturbation problem of a fuzzy reasoning algorithm, i.e., the ɑ-symmetric implicational algorithm, is researched systematically. For FMP (Fuzzy Modus Ponens) and FMT (Fuzzy Modus Tollens) problems of fuzzy reasoning, aiming at the case of a single rule, the estimation for the upper and lower bounds are obtained for the input interval disturbance, in which R-implications and (S, N)-implications are mainly employed. Then the stability is verified on account of the upper and lower bounds. Following that, for the multi-rule case, the upper and lower bounds of the output are also given, and the corresponding stability is validated. In conclusion, it is found that the ɑ-symmetric implicational algorithm has good stability.