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Additions of Completely Correlated Fuzzy Numbers

Christer Carlsson, Robert Fullér, Péter Majlender, Additions of Completely Correlated Fuzzy Numbers. In: FUZZY IEEE 2004 CD-ROM Conference Proceedings, 2004.

Abstract:

In this paper we will consider additions
of
interactive fuzzy numbers. The interactivity relation
between fuzzy numbers
will be defined by their joint possibility
distribution. We
will show that Nguyen's theorem remains valid in this
environment. We will give explicit formulas
for the $\gamma$-level sets of the extended
sum of two completely correlated
fuzzy numbers.
We will show that the interactive and the
non-interactive sums have the same membership function
for any pair of completely
positively correlated fuzzy numbers.
Finally, we will prove that (i) the interactive sum
of two completely negatively
correlated fuzzy numbers $A$ and $B$ with $A(x) = B(-x)$ for
all $x \in {\mathbb R}$, will be (crisp) zero;
(ii) the interactive difference of two completely positively
correlated fuzzy numbers $A$ and $B$ with
identical membership function, that is, $A(x) = B(x)$ for all
$x \in {\mathbb R}$, will be (crisp) zero.

BibTeX entry:

@INPROCEEDINGS{inpCaFuMa04b,
  title = {Additions of Completely Correlated Fuzzy Numbers},
  booktitle = {FUZZY IEEE 2004 CD-ROM Conference Proceedings},
  author = {Carlsson, Christer and Fullér, Robert and Majlender, Péter},
  year = {2004},
}

Belongs to TUCS Research Unit(s): Other

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