Testing continuous t-norm called Lukasiewicz algebra with different means in classification

In this paper, we have done new similarity measures from a continuous t-norm by implementing it in different mean measures. For the implementation, we use a Minkowsky metric based on Lukasiewicz algebra. We test these new similarities in both the generalised and normal form of Lukasiewicz algebra with weight optimisation. The mean measures examined here are arithmetic, geometric and harmonic means. We show that the magnitude order of the similarities are S_H^N 1, x₂>≥S_G^N 1, x₂>≥S_A^N 1, x₂>. Secondly, we show that the use of different means is highly recommendable in some cases.