Symmetric implicational method of fuzzy reasoning

•New fuzzy reasoning method combining logic system with reasoning model is proposed.•The new method contains the full implication inference method as its particular case.•The previous principles for the full implication inference method are improved.•Unified forms of the new method are obtained.•Excellent reversibility properties of the new method are verified.

Fuzzy reasoning should take into account the factors of both the logic system and the reasoning model, thus a new fuzzy reasoning method called the symmetric implicational method is proposed, which contains the full implication inference method as its particular case. The previous full implication inference principles are improved, and unified forms of the new method are respectively established for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) to let different fuzzy implications be used under the same way. Furthermore, reversibility properties of the new method are analyzed from some conditions that many fuzzy implications satisfy, and it is found that its reversibility properties seem fine. Lastly, the more general α-symmetric implicational method is put forward, and its unified forms are achieved.