Summary: Arithmetic operations over fuzzy quantities of fuzzy numbers do not generally fulfil some of the important group properties, namely those concerning the opposite (or inverse) elements. This seriously complicates the solution of equations in which some fuzzy elements appear – either as coefficients, or as variables and right-hand-sides. This lack of group properties can be overcome if some kind of equivalence between fuzzy quantities is considered instead of the strong equality. This fact can be used for solving equations with fuzzy elements. The equality can be substituted by an equivalence, which turns the equation into an equivalention, and some of the arithmetic operations can be effectively applied.
There exist several types of equivalences adequate to different operations [see the author, Kybernetika 29, No. 2, 121-132 (1993; Zbl 0788.04006)]. In this brief paper we consider only one of them, applicable to one – in fact the simplest one – type of equivalentions. As mentioned in the conclusive remarks there exist theoretical tools which make our expectation concerning other types of equivalentions rather optimistic.