限制等价函数与模糊相似度

Restricted Equivalence Functions and Fuzzy Similarity Measures

模糊相似度作为度量模糊集之间相似程度的重要工具,已经在理论研究与应用领域发挥了十分重要的作用,而限制等价函数与模糊相似度具有紧密的联系。本文对于限制等价函数的性质与构造方法展开进一步讨论,研究限制等价函数与自同构,t-模,以及t-余模之间的关系,进而研究由限制等价函数构造的模糊相似度的性质。我们的结果表明,这种由限制等价函数构造的模糊相似度具有相当好的性质。

Fuzzy similarity measures as an important tool for measuring similarity degree between fuzzy sets, have played a very important role in theoretical researches and applied fields,and restricted equivalence functions are closely related to fuzzy similarity measures. In this paper, we further discuss the main properties and construction methods of restricted equivalence functions, the relationship between the restricted equivalence functions and automorphisms, t-norms and t-conorms. Then basic properties of fuzzy similarity measures constructed by restricted equivalence functions are investiga- ted. Our results show that this kind of fuzzy similarity measures are good ones.