Milan Mareš

Abstract:

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 to the multiplication. In this way the group axioms and some other useful algebraical properties of multiplication can be derived also for fuzzy quantities, at least for some of them and up to certain degree of similarity between them. The specific properties of the multiplication mean that the methods derived for the addition cannot be mechanically transmitted to the multiplicative case, and that rather different approach must be used. The main purpose of this paper is to show these differences and their consequences for the obtained results.

Classification:

04A72, 94D05, 26E50, 03E72