Abstract: The research aim of flexible logics is to explore the general law of logic, it indicates that propositional truth value error is described by the continuously changeable generalized self-correlation coefficient k∈[0,∞].N-norm is the mathematic model of 1-level operation in uncertain reasoning. In the real world, many logic reasoning controls must be accomplished in the original true value domain. This paper used triangular norm theory as an important mathematical tool to study the flexible logics on interval[0,∞].N-norm and N-generator on[0,∞] were defined, and the relative main properties were studied. Generation theorem of N-norm was proven. Method for calculating generalized self-correlation coefficient k was given. The paper proved that exponential N-generator is N-generator integrity cluster on[0,∞].These researches provided the important theoretical base for 1-level operation model on[0,∞] interval in flexible logics.

Key words: Flexible logics, Norm, Generator, Generalized self-correlation coefficient, Generator integrity cluster