Extension set studies the degree and its change of some characteristic that one thing owns from the point of transformation, and describes them by using dependent functions. So, the dependent function is the core of the extension set and an important theoretic foundation of extenics. We summarize the current results of one-dimensional functions and unify the simple and elementary dependent functions. On the basis of the definitions of both distance and side-distance between the point and all kinds of intervals and position value between the point and various types of nested intervals, we propose the basic formulas and properties of generaldependent functions. The results can further deepen the contents of one-dimensional dependent functions and provide theoretical basics for the study on the multi-dimensional ones.

extension set  /  dependent function  /  three nested intervals  /  position value