the operations in the set of fuzzy numbers are usually obtained bythe zadeh extension principle. but these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. in fact the zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...

The operations in the set of fuzzy numbers are usually obtained bythe Zadeh extension principle. But these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. In fact the Zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...

In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...

The purpose of this paper is to propose a ranking method for solving fuzzy multiple criteria decision making (FMCDM) problems. The representation of multiplication operation on fuzzy numbers is useful for the decision makers to rank all alternatives and choose the best one under the fuzzy multiple criteria decision making environment. The representation of multiplication operation on three fuzz...

The addition operation over the class of fuzzy numbers or fuzzy quantities was investigated and discussed e.g. in [1], [8] or [7]. It is easy to define in an analogous way also the operation of multiplication (cf. [1] or in certain sense also [3] and [4]). Moreover, some of the methods and concepts suggested for the addition case in [5] and further used in [6] and [7] can be evidently adapted t...

For fuzzy mathematical models using general fuzzy sets rather than fuzzy numbers or fuzzy vectors, operations (addition and scalar multiplication) and orderings of fuzzy sets are needed, and the concept of fuzzy set-valued convex mappings is important. In the present paper, fundamental properties of operations, orderings, and fuzzy set-valued convex mappings for general fuzzy sets are investiga...