一种基于模糊信息的距离测度及应用

A Distance Measure Based on Fuzzy Information and Its Applications

通过借用Shannon信息理论中的相关概念,提出了基于模糊信息测度的模糊对称交互熵(FSCE)这一距离测度。接下来证明了它是度量空间中的度量,满足非负性、对称性、三角不等式三个条件。最后利用数值例子说明了在模糊模式识别中,FSCE与常见的模糊贴近度可以得到一致的识别结果,并有其优势和实际意义,为模糊模式识别提供了新的研究方法。

By borrowing some relative concepts in Shannon information theory, we present a new distance measure called fuzzy symmetric cross entropy（FSCE）, which is based on the fuzzy information measure theory. Next, we prove that FSCE is a metric which satisfies the conditions of non-negativity, symmetry and triangle inequality. At last, by using numerical examples in fuzzy pattern recognition, we illustrate that the recognition results are accordant with FSCE and other most common fuzzy nearness degree. It indicates that FSCE is practical significant with its advantage. And it can provide a new research approach for fuzzy pattern recognition.