On some structures of fuzzy numbers
Antonio Maturo2009, Iranian Journal of Fuzzy Systems
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Abstract
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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