A note on the finite T-sum of L − R fuzzy numbers and further considerations

In the first part of this paper we consider the α-cut of a sum of two fuzzy sets. We show that the α-cut of such a sum can be written as one closed interval determined by the minimum and maximum of some special functions, over a set uniquely determined by the considered t-norm. In the second part of...

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Bibliographic Details
Published in:Fuzzy sets and systems 2021-08, Vol.417, p.130-139
Main Authors: Urbański, Michał K., Wójcicka, Kinga M., Wójcicki, Paweł M.
Format: Article
Language:English
Subjects:
alpha-cut
Fuzzy number
t-Norm
t-Norm-based addition
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Summary:In the first part of this paper we consider the α-cut of a sum of two fuzzy sets. We show that the α-cut of such a sum can be written as one closed interval determined by the minimum and maximum of some special functions, over a set uniquely determined by the considered t-norm. In the second part of the paper we show that not only α-cut of a sum of two fuzzy intervals has this property, but also α-cut of a continuous function of two variables, strictly increasing in each argument as well. Two examples of the presented theory are considered.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2020.12.023