A similarity measure for fuzzy rulebases based on linguistic gradients

Fuzzy rulebases are an approximate representation of some interesting system. As such, they could potentially be used for indexing and searching candidate solutions in case-based reasoning (CBR) systems in a variety of application areas. However, there is currently no method for directly and efficiently determining the similarity between two rulebases, which is a necessary element of their use in any CBR system. We propose a method for measuring similarity between two linguistic fuzzy rulebases, based on the granular computing technique of linguistic gradients. The proposed similarity measure is based on comparing the linguistic structure of two rulebases, using the linguistic gradient operator to reveal that structure. Our algorithm operates at the level of linguistic rulebases, rather than a defuzzified reasoning surface, and thus belongs to the Computing-with-Words paradigm. In a validation experiment, we compare our new method with the root-mean-square difference between reasoning surfaces for 603 pairs of fuzzy rulebases drawn from the literature. A Spearman correlation analysis shows that our new linguistic method is consistent with the numerical RMS results, while being theoretically and empirically faster than computing an accurate RMS difference.