Geodesic
A New Definition of the Fuzzy Set
International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 1, pp. 125-140.

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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.
Keywords: fuzzy set theory, fuzzy arithmetic, possibility
Mots-clés : zbiór rozmyty, prawdopodobieństwo, arytmetyka rozmyta 
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Piegat, A. A New Definition of the Fuzzy Set. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 1, pp. 125-140. http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_1_a9/

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