Generalized T-norm and Fractional “AND” Operation Model

In the process of uncertainties reasoning with universal logic, T-norm is the mathematical model of “AND” operation. T-norm and T-generator were defined on interval [0,1] in previous work. In the recent relational work, authors put forward fractional logic based on continuous radix [a, b]. This paper studied the T-norm and T-generator on any interval [a, b], discussed the two kinds of generalized T-generators: “Automorphic increase T-generator” and “Infinite decrease T-generator”. Authors found and proved the useful and important theorem: “generating theorem of generalized T-norm”. Using the integrated clusters of generalized T-norm and T-generator, authors gave the mathematical generating method for “AND” operation model of fractional logic based on any interval [a, b]. The operation model is already used to uncertainties reasoning and flexible control now.