Unified full implication algorithms of fuzzy reasoning

This paper discusses the full implication inference of fuzzy reasoning. For all residuated implications induced by left continuous t-norms, unified α-triple I algorithms are constructed to generalize the known results. As the corollaries of the main results of this paper, some special algorithms can be easily derived based on four important residuated implications. These algorithms would be beneficial to applications of fuzzy reasoning. Based on properties of residuated implications, the proofs of the many conclusions are greatly simplified.