Vague集之间的相似度量及其在模式识别中的应用

Similarity measures between vague sets and their applications to pattern recognition

讨论Vague集之间的相似度量问题 .首先 ,基于Vague集定义本身的动态趋势 ,分别给出元素相对于Vague集的隶属度与非隶属度的合理表示 ,进而提出一种新的度量Vague集之间相似程度的方法 ,并讨论其性质 .然后 ,将元素在Vague集中所呈现的三部分 :隶属度、非隶属度和不确定程度的相对重要性以及每个元素的相对重要性考虑进去 ,提出并讨论一种新的加权相似度量方法 .进一步 ,将上述Vague集之间的相似度量和加权相似度量推广到连续论域 ,得到相应度量的积分表示 ,同时指出Hong和Kim给出的度量方法是结论的特例 .最后 。

Similarity measures between vague sets are di scussed. Firstly, based on the dynamic tendency of vague sets, the degree of membership and the degree of n on-membership of an element to a vague set are appropriately expressed, respect ivel y. Then, a new kind of method for measuring the degree of similarity between vague sets is proposed, and its properties are discussed. Then a new weighted si milarity measure between vague sets is presented and discussed by taking into ac count the relative importance of the three parts: membership degree, non-member s hip degree and uncertainty degree of an element to vague sets and the relative i mportance of each element in the discoursed universe. Furthermore, a set of corr esponding integral representations of similarity measures is obtained by general izing above similarity measure and weighted similarity measure to a continuous u niverse. Hong and Kim's similarity measures are special case of the measures pro posed in this paper. Finally, the similarity measures between vague sets are app lied to pattern recognition.