Some new logarithmic aggregation operators and their application to group decision making problem based on t-norm and t-conorm

In this paper, a logarithmic operational law for intuitionistic fuzzy numbers is defined, in which the based $$\ell$$ real number such that $$\ell \in \left( {0,1} \right)$$ with condition \ne 1$$ . Some properties of laws have been studied and on these, several Einstein averaging geometric operators, namely weighted (LIFEWA) operator, ordered (LIFEOWA) hybrid (LIFEHA) (LIFEWG) (LIFEOWG) (LIFEHG) operator introduced, can overcome weaknesses algebraic operators. Furthermore, proposed operators multi-attribute group decision-making problem established under laws. Finally, an illustrative example used to illustrate applicability validity approach compare results existing methods show effectiveness it.