The Method to Construct Elementary Dependent Function on Single Interval

Abstract

Extension theory are widely used in many fields such as automation, manufacturing process, operations management and artificial intelligence. Dependent function is the core of extension set. In this paper, we construct the elementary dependent function on the single interval, i.e., the discussion field is the same as the positive one, and it includes finite and infinite ones, respectively. Some properties are also discussed. The proposed functions allow extension theory with a broader scope.

An Extenics-Based Criteria Clustering Method

“…In order to describe the difference of points in the same interval, we difine the distance between point x and interval X=<a,b> is specified [6,7]: Definition 1. Suppose x is any point in real axis, and X =<a,b> is any interval in real field, we define …”

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

“…∈ is called as location value for the variable x corresponding to the nested interval 0 X and X . Obviously, Definition 6 is similar to Definition 1 of paper [8].…”

“…In real-world applications, elementary dependent function has been widely used. Papers [8][9][10][11] obtained some types of elementary dependent function whose both discussion and positive fields are limited or infinite at the same time. In reality, there still be another situation that the positive field is limited and the discussion field is infinite.…”