FUZZY NUMBERS ARE THE ONLY FUZZY-SETS THAT KEEP INVERTIBLE OPERATIONSINVERTIBLE

In standard arithmetic, if we, e.g., accidentally add a wrong number y to the preliminary result x, we can undo this operation by subtractin g y from the result x + y. In this paper, we prove the following two r esults: First, a similar possibility to invert (undo) addition holds f ar fuzzy numbers (although in case of fuzzy numbers, we cannot simply undo addition by subtracting y from the sum). Second, if we add a sing le fuzzy set that is not a fuzzy number, we lose invertibility. Thus, invertibility requirement leads to a new characterization of the class of ail fuzzy numbers. (C) 1997 Elsevier Science B.V.