Comparison of the use of different similarities based on T-norms in the classification tasks

In this paper we have derived four different fuzzy similarities from three extensions of t-norms mentioned in [1] pages 195200. We have derived these similarities in the same spirit like they would have been used in Łukasiewicz algebra. We will present four different similarities based on the extensions of t-norms these are known as Tinf-extension, P-extension, E-extension and Hn extension. Similarity based on Hn extension is made by implementing different parameters into Eextension based similarity. We will use these similarities in classification tasks and show some classification results of these similarities when they are used as classifiers. We will show that actually similarity relation based on Tinf-extension is based on Łukasiewicz algebra and that it gives the best classification results from similarities derived and tested here. We will also show that weighting will make classification results better. This study will be a short preliminary work as we aim to move on to study some other algebraic structures than Łukasiewicz. In our extended version of this paper we will investigate the use of some other means than arithmetic with these equivalence relations presented here.