In this paper, it is noticed that the definition of fuzzy equality of Sasaki (1993) is not concordant with that of Es and Coker (1995) and Sostak (1985, 1988). Furthermore, the construction of fuzzy equality and fuzzy function is far from the way of natural fuzzification. For this purpose, the fuzzy equality of two points of a crisp set which is more convenient than that in Es and Coker (1995) and Sostak (1985, 1988) and the fuzzy function having weaker conditions than that is given in Sasaki (1993) are redefined in much more natural way. Then various types of fuzzy functions are introduced and their fundamental properties are established. (C) 1999 Elsevier Science B.V. All rights reserved.
