Journal
FUZZY SETS AND SYSTEMS
Volume 157, Issue 7, Pages 952-963Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.fss.2005.09.011
Keywords
Zadeh's extension principle; fuzzy intervals; Dombi operator
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The extension principle defines the arithmetic operations on fuzzy intervals. In the extension principle one can use any t-norm, for modeling the conjunction operator. It is therefore important to know, which t-norms are consistent with a particular type of fuzzy intervals. We call a t-norm consistent, if the arithmetic operation is closed. In this paper we investigate the addition of sigmoid and two bell-shaped membership functions which appear in many natural processes and are used in machine learning applications. We prove that the addition is closed if the Dombi operator is used. The calculation of sum is quite simple and can be used in various applications such as fuzzy-neural networks. (C) 2005 Elsevier B.V. All rights reserved.
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