Generalized fuzzy sets and representation of incomplete knowledge

Abstract In this paper, we focus our attention on a kind of generalized fuzzy sets. For such sets, the grade of membership of an element in a subset should completely be described from the viewpoint of the obverse as well as the reverse side. More precisely, this kind of generalized fuzzy subset is defined by a pair of membership functions which are not required to satisfy any additional conditions. Set operations are given and some examples are briefly discussed.