Fuzzy continuous function and its application to fuzzy neural nets (I)

There are close connections between fuzzy continuous function and fuzzy neural nets.. In this paper, based on our earlier work that fuzzy continuous function must exist the supremum and infimum, we give a necessary and sufficient condition under which the fuzzy continuous function on a closed interval can attain its supremum and infimum. Furthermore, we obtain that the set of all fuzzy continuous functions become a complete translation invariant metrizable commutative semigroup with unit element with respect to addition and uniform metric.