样本发散型含糊类的形式刻画

A Formal Characterization of Vague Classes with Divergent Exemplars

含糊类是基于样本和相似性得到的类。通过样本和与样本的相似性处理含糊对象是人们在面对含糊性时常用的方法。含糊类有样本收敛和样本发散两大类型,后者应该更为普遍。样本收敛的含糊类也是有核含糊类,可以通过核来处理边界情况。但是因为样本发散含糊类同时也是无核含糊类,所以这个方法不适用于样本发散含糊类。从人们对于含糊对象的实际处理看,除了用正面的样本外,还会用到反面的样本。将这个过程加以抽象,本文引入了负样本以及提出了由正样本和负样本共同处理边界情况的方案。在形式刻画方面,主要是在一阶语言的基础上通过增加正样本谓词、负样本谓词和论题词给出了语言L*及其语义。在L*中可以进一步定义正谓词、负谓词以及中间谓词,通过这些表达式可以对于含糊对象及其性质给出相应的刻画。

Vague classes are classes obtained through exemplars and similarity.The usual way we deal with vague objects is using exemplars and the similarity with exemplars.There are mainly two types of vague classes:vague classes with convergent exemplars and vague classes with divergent exemplars.The latter seems more common.For vague classes with convergent exemplars,which are also named as vague classes with core,the borderline cases can be handled by the definition of core.However,since the vague classes with divergent exemplars have no core,the method of core interpretation is unfit for divergent cases.In actual process of dealing with vague object,both the positive exemplars and the negative exemplars are employed by people.By abstracting the process,this paper introduces the concept of negative exemplars,and provides a method to deal with borderline cases by using both positive exemplars and negative exemplars.As for the formalized part,based on the first-order languages,this paper give language L and its semantics by adding positive exemplar predicate,negative exemplar predicate and topic term,In L,there could be further definition of positive predicate,negative predicate and middle predicate.Through these expressions,the vague objects and their features could be characterized.