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On continuity of the entropy-based differently implicational algorithm

Yiming Tang;  Witold Pedrycz — 2019

Kybernetika

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...

Symmetric implicational restriction method of fuzzy inference

Yiming Tang;  Wenbin Wu;  Youcheng Zhang;  Witold Pedrycz;  Fuji Ren;  Jun Liu — 2021

Kybernetika

The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy...

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