On the distributivity of T-power based implications

Due to the fact that Zadeh’s quantifiers constitute the usual method to modify fuzzy propositions, the so- called family of T-power based implications was proposed. In this paper,  the four basic distributive laws  related to T-power based fuzzy implications  and fuzzy logic operations (t-norms and t-conorms) are deeply studied. This study shows that two of the four distributive laws of the T-power based implications have a unique solution, while the other two have multiple solutions.