Document Type : Research Paper


Department of Social Sciences, University of Chieti-Pescara, via dei Vestini, 66013, Chieti, Italia


The operations in the set of fuzzy numbers are usually obtained by
the Zadeh extension principle. But these definitions can have some disadvantages
for the applications both by an algebraic point of view and by practical
aspects. In fact the Zadeh multiplication is not distributive with respect to
the addition, the shape of fuzzy numbers is not preserved by multiplication,
the indeterminateness of the sum is too increasing. Then, for the applications
in the Natural and Social Sciences it is important to individuate some suitable
variants of the classical addition and multiplication of fuzzy numbers that have
not the previous disadvantage. Here, some possible alternatives to the Zadeh
operations are studied.


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