Universal triple I method with maximum fuzzy entropy employing R-implications

The universal triple I method with maximum fuzzy entropy (the entropy-universal triple I method for short) is proposed and investigated, which takes the fuzzy entropy triple I method as its particular case. To begin with, the entropy-universal triple I principles for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) are put forward, which improve the previous fuzzy entropy triple I principles. Furthermore, the existence condition of solution of entropy-universal triple I method is analyzed, and then its unified forms are achieved for FMP and FMT aiming at the case of R-implication. Finally, the reversibility property of the entropy-universal triple I method is researched for the R-implication.