Fuzzy uniqueness of fuzzy mappings

For fuzzy mappings between fuzzy sets of higher level we study a notion of fuzzy uniqueness. i.e. of fuzzy functions, which formalizes the intuition that ‘almost identical’ images under f.Characterizations are given for such fuzzy mappings which are really (i.e. with truth value 1) fuzzy unique or fuzzy biunique, and for those fuzzy sets which can be domains of really fuzzy unique fuzzy mappings.Finally, as an application fuzzy cardinals, their ordering, sum, and product are introduced, and some properties proved.