On the symmetric quintuple implicational method of fuzzy reasoning

Document Type : Research Paper


1 School of Computer and Information, Hefei University of Technology, Hefei, 230009, P.R.China

2 Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6R 2V4, Canada



A novel fuzzy reasoning method called the SQI (symmetric quintuple implicational) method
is put forward, which is a generalization of the QIP (quintuple implication principle) method. First of all, the symmetric quintuple implicational principles are presented, which are distinct from the ones of the QIP method. Then unified optimal solutions of the SQI method are obtained for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens), meanwhile corresponding reversible properties are verified. Furthermore, focusing on the case of multiple rules, optimal solutions of the SQI method are achieved, which involves two general approaches, i.e., FITA (first-infer-then-aggregate) and FATI (first-aggregate-then-infer). Equivalence relation of continuity and interpolation is analyzed for both FITA and FATI under the environment of the SQI method. Finally, one computing example arising in the field of affective computing is given for the SQI method with FATI. It is found that the SQI method preserves the same properties as the QIP method.