对文献中与全区间序结构有着密切联系的几个条件进行了深入的研究,得出全区间序结构的几个充要条件。通过讨论可以看出:一个偏好结构为全区间序结构当且仅当大偏好关系矩阵的行元素按Tl排列(从高到低),列按Tc排列时,可以表为一种特殊形式的矩阵,从而,通过大偏好关系矩阵的形式,很容易判断一个结构是否为全区间序结构。
Some conditions associated with total interval order structures in the literature is discussed. Several necessary and sufficient conditions are obtained. It can be seen from investigation that a preference structure is a total interval order structure if the matrix of the large preference relation can be represented in a very special way when the elements of the universe are ranked from higher to lower based on T1 in the row and Tc in the column resp. ,and thus it is easy to determine whether a structure is a total interval order structure or not by means of the matrix representation of the large preference relation.