The Method to Construct Elementary Dependent Function Whose Discussion Field is an Infinite Interval and Positive Field Finite

Abstract

Extension theory are widely used in many fields such as machinery, manufacturing, meterials and automation. Dependent function is the core of extension set. On the basis of extension distance between the point and the infinite interval, we construct the formulas of location value and the corresponding elementary dependent function whose discussion field is an infinite interval and positive field finite, and get some properties. The proposed function allows extension theory in the areas of materials science and engineering science with a broader scope.

The Method to Construct Elementary Dependent Function on Single Interval

“…The elementary one discuss the situation of nested interval, i.e., the positive interval is within the discussion one. However, the simple one do not notice the extensible and unextensible fields, and the intervals of elementary dependent function are different ones [7][8][9][10]. In this paper, we propose two formulas of dependent function on single finite and infinite intervals.…”