A preservation theorem for fuzzy number theory (Q1112797)

In this paper the question of an unambiguous application of Zadeh's extension principle is examined. Moreover one proves that if a property for real numbers is expressed by an equation \(p=q\) and in both p and q the variables are distinct, then such a property can be extended to fuzzy numbers. As an example, associativity and commutativity properties hold for fuzzy numbers while distributivity or existence of an inverse do not hold for fuzzy numbers. \{After the publication of this paper the author has become aware that this result was previously proved by \textit{E. G. Manes} in J. Math. Anal. Appl. 85, 409-451 (1982; Zbl 0497.18011).\}