The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.
@article{bwmeta1.element.bwnjournal-article-amcv15i1p125bwm,
author = {Piegat, Andrzej},
title = {A new definition of the fuzzy set},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {15},
year = {2005},
pages = {125-140},
zbl = {1070.68137},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv15i1p125bwm}
}
Piegat, Andrzej. A new definition of the fuzzy set. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) pp. 125-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv15i1p125bwm/
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