Boolean fuzzy sets and possibility measures

B-possibility and B-necessity measures are defined as the qualitative analo gues of the well known [0, 1]-measures. Their connection to B-fuzzy sets (B oolean fuzzy sets) is established. It is also proved that B-fuzzy sets defi ne B-possibility and B-necessity measures by their membership function. We also introduce the possibility of a B-fuzzy set and prove that it is the ex tension of the possibility measure defined on crisp sets. This extension ca n be defined in two ways which are proved to be equivalent. (C) 2000 Elsevi er Science B.V. All rights reserved.