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

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2 Author(s)
Saastamoinen, K. ; Lab. of Appl. Math., Lappeenranta Univ. of Technol., Finland ; Luukka, P.

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 SHN 1, x2>≥SGN 1, x2>≥SAN 1, x2>. Secondly, we show that the use of different means is highly recommendable in some cases.

Published in:

Fuzzy Systems, 2003. FUZZ '03. The 12th IEEE International Conference on  (Volume:2 )

Date of Conference:

25-28 May 2003