ON IMPLICATION AND INDISTINGUISHABILITY IN THE SETTING OF FUZZY LOGIC

Many implication connectives used in the Fuzzy Set Theory are obtained from DeMorgan triples by using the formalism of either the Boolean Logic, the Intuitionistic Logic or the Quantum Logic. This paper aims to give a comprehensive survey of the characteristics and main properties of such implications by paying special attention to the two properties which are considered as the most essential to an implication connective, i.e. a) by means of the implication an order relation is obtained, and b) the basic rule of inference, the Modus Ponens, is satisfied. The properties of the material equivalence obtained from each of these implications are also checked.