The Distributivity Of An Extended Residual Implication On Fuzzy Truth Values

In this thesis,we study the distributivity of an extended residual implication and coimplication on fuzzy truth values of type-2 fuzzy sets.We first discuss the distributive laws of the extended residual implications and coimplications about operators max and min,respectively.We then obtain some related properties of the extended residual implications and coimplications.We further get the distributivity of the extended residual implications and coimplications about the extended max and min opertors,respectively.Finally,we give the distributive laws of the extended residual implications and coimplications about the extended t-norms and t-conorms,respectively,which generalize the distributivity laws of the extended residual implications and coimplications about the max and min operators,respectively.