Variable Differently Implicational Inference for R- and S-Implications

Abstract

As a generalization of the compositional rule of inference (CRI) algorithm and the fully implicational algorithm, the differently implicational algorithm of fuzzy inference not only inherit the advantages of the fully implicational algorithm, but also has stronger practicability. Then, the variable differently implicational algorithm was proposed to make the current differently implicational algorithms compose a united whole. In this paper, the variable differently implicational algorithm is further researched focusing on the fuzzy modus tollens (FMT) problem. The differently implicational principle for FMT is improved. Moreover, the unified solutions of the variable differently implicational algorithm for FMT are accomplished for R- and S-implications. Following that, as an important index of fuzzy inference, the continuity of this algorithm is analyzed for main R- and S-implications, in which excellent performance is obtained. Finally, its optimal solutions as well as inference examples are provided for several specific R- and S-implications.