Abstract: By examplification,it is shown that  L. A. Zadeh  improperly defined fuzzy sets with mapping and furthermore,he also incorrectly defined the join and intersection operations by selecting the maximal and minimal values.In fact,the fuzzy school knew the problem of selecting the values and they provide many arithmetic operators,especially the notions of t-and s-bound norms which are proven wrong.Therefore,it can be concluded that fuzzy-set theorists have not yet provided a reasonable definition for the join and intersection operations.

Key words: fuzzy sets, mapping, law of excluded middle