Fuzzy arithmetic based on boundary weak t-norms

Authors:
Michal K. Urbański;Janusz Wasowski
Affiliations:
Faculty of Physics, Warsaw University of Technology, Poland;Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Poland
Venue:
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Year:
2005

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Abstract

In this paper we propose the new extended class of t-norm operators called the boundary weak. The aim of the extension of this operator is that the sum of the fuzzy numbers in the arithmetic based on such t-norm gives the more narrow fuzzy number if compared to arithmetic based on standard t-norm. This extension is based on the replacement of the condition T(x, 1) = x by the weaker one: T(x, 1) ≤ x, for x ∈ [0,1].