一种改进的直觉模糊集相似度测量及应用

Applications of a Modified Similarity Measure Between Intuitionistic Fuzzy Sets

两直觉模糊集之间的相似度测量作为直觉模糊集的重要专题,已经引起了许多学者的重视与研究,提出很多度量公式,但部分公式中存在反直觉缺陷.土耳其学者Boran和Akay提出一种新的基于双参数的相似度测量公式,然而,在他们引入的一个与成员隶属度和非成员隶属度取值对应的等腰直角三角形区域中,所提出的公式的取值只能涉及最特殊的一条直线即斜边中线,本文将对这个公式做出一个改进,将公式所涉及的范围延伸到整个三角形区域中,提出一个应用更为广泛的测量公式,并给出实例证明其在模式识别中应用的有效性.

In nowadays,similarity measure between IFSs has become one of the most significant issues in the field of IFS,several studies on similarity measures have been proposed in the literatures,including a newbiparametric similarity measure on intuitionistic fuzzy sets proposed by Boran and Akay from Turkey. The findings indicate that some of the proposed similarity measures exist counter-intuitive cases. Furthermore,on the basis of these findings,Boran and Akay imported an isosceles right triangle area,which is corresponding to the values of the membership degree and the non-membership degree. However the distance measure function only applies to the most special condition-the midline of the hypotenuse. In this paper,a newgeneral type of similarity measure for IFSs is proposed along with its proofs,the formula involves the whole area of the triangle. In the last,two examples are used to showthe method is effective in pattern recognition.