Kybernetika 55 no. 2, 307-336, 2019

On continuity of the entropy-based differently implicational algorithm

Yiming Tang and Witold PedryczDOI: 10.14736/kyb-2019-2-0307

Abstract:

Aiming at the previously-proposed entropy-based differently implicational algorithm of fuzzy inference, this study analyzes its continuity. To begin with, for the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, the continuous as well as uniformly continuous properties of the entropy-based differently implicational algorithm are demonstrated for the Tchebyshev and Hamming metrics, in which the R-implications derived from left-continuous t-norms are employed. Furthermore, four numerical fuzzy inference examples are provided, and it is found that the entropy-based differently implicational algorithm can obtain more reasonable solution in contrast with the fuzzy entropy full implication algorithm. Finally, in the entropy-based differently implicational algorithm, we point out that the first fuzzy implication reflects the effect of rule base, and that the second fuzzy implication embodies the inference mechanism.

Keywords:

continuity, fuzzy entropy, fuzzy inference, compositional rule of inference

Classification:

03B52, 94D05

paper.pdf

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