粗糙度量和模糊信息颗粒化

Coarse measurement and fuzzy information granulation

信息是由对象、属性、值组成的三元组 ,当对属性值用较粗的标度去度量时就得到了其论域上的粗糙度量 .据此构造了模糊集合理论的基础概念 ,即模糊集合是不确定标度下的粗糙度量 ,隶属函数则是粗糙程度不同的度量间的转换函数 ,模糊集合将信息模糊颗粒化 ,这些信息颗粒之间的相互关系就是模糊映射或模糊计算 .基于这些概念的模糊系统具有可理解性 .

This paper takes information as an element consisting of object, attribute and value. When we measure the attribute in a larger of uncertain scale, we will obtain a coarse value in its universe. We refer to the measurement as a coarse measurement by means of which the basic concepts of fuzzy sets theory are explained in a different way. Firstly, fuzzy sets are the values of coarse measurement with uncertain scales. Secondly, membership functions are transfer functions between the values resulting from different coarse measurements. Lastly, the fuzzy mapping of fuzzy calculation reflects the relationship between the fuzzy information granules. Base on these concepts, the fuzzy systems are interpretable.