New similarity index based on the aggregation of membership functions through OWA operator

Abstract

In the field of data analysis, the use of metrics is a classical way to assess pairwise similarity. Unfortunately the popular distances are often inoperative because of the noise, the multidimensionality and the heterogeneous nature of data. These drawbacks lead us to propose a similarity index based on fuzzy set theory. Each object of the dataset is described with the vector of its fuzzy attributes. Thanks to aggregation operators, the object is fuzzified by using the fuzzy attributes. Thus each object becomes a fuzzy subset within the dataset. The similarity of a reference object compared to another one is assessed through the membership function of the fuzzified reference object and an aggregation method using OWA operator.