中文摘要：

可拓集合从变换的角度描述事物具有某种性质的程度及其变化,并用关联函数定量化研究变化的分类和分类的变化以及矛盾问题的转化,因此关联函数是可拓集合的核心内容和可拓学的重要理论基础。基于现实生活中人们对客观事物特征的量值存在满意区间、可接受区间和不可接受区间等区别,在定义点与三区间套的位置值的概念基础上,构造了正域为有限区间的三区间套一维关联函数公式并探讨其性质,深化了一维关联函数的研究内容,拓展了可拓学描述现实矛盾问题的范围。

英文摘要：

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 general- dependent functions. The results can further deepen the contents of one-dimensional dependgnt functions and provide theoretical basics for the study on the muhi-dimensional ones.