The Further Studies On Triangular Norm And Their Decision Operators

This paper mainly disscusses the t-norm and decision operator based on the the-ory of its application in multi-criteria decision-making.Firstly,based on the concept of a trigonometric function type generating function,we propose a triangle function of t-norms,t-conorms and uninorm operator,further give a general method of this kind of triangle function type triangular norm operator for multi-attribute decision making under the intuitionistic fuzzy environment,and verify the correctness of the method through an instance of an investment bank’s investing in enterprises.Sec-ondly,according to the research method of triangle norms,we generalize the concept of nullnorms and get the concepts of the dual nullnorms and the conjugate nullnorms and provide a new method of generating a new dual(complementary)nullnorms from a known dual(complementary)nullnorms based on a strictly monotonically increas-ing continuous function.Finally,according to the nullnorms and conjugate nullnorms operator,we make a generalization of intuitionistic fuzzy and uncertain language variables and obtain a series of generalized intuitionistic fuzzy uncertain linguistic variables based on nullnorms.and conjugate nullnorms and their operation rules,and the intuitionistic fuzzy uncertain linguistic weighted geometric operators based on nullnorms and conjugate nullnorms.Moreover,a method of multi-criteria group de-cision making using intuitionistic fuzzy uncertain linguistic variables is also given.Finally,the correctness of the method is verified through an investment decision mak-ing example.