THE CONSTRUCTION OF POSSIBILITY MEASURES FROM SAMPLES ON T-SEMI-PARTITIONS

We address the (generalized) extension problem for possibility measure s: given a map defined on a family of(fuzzy) sets, is it possible to e xtend it to a (generalized) possibility measure? The extension problem for possibility measures is known to be equivalent to a system of sup -T equations, with T a t-norm. A key role is played by the greatest so lution (of type inf-J, with J a border implicator). When the family of sets considered is a semi-partition, another important solution (of t ype sup-T, with T a t-norm) can be identified. In the treatment of the generalized possibilistic extension problem, we show that a fuzzifica tion of the greatest solution also plays a central role. On the other hand, an immediate fuzzification of the sup-T type solution is investi gated. General necessary and sufficient conditions for this fuzzificat ion to be a solution are established. This fuzzification is then furth er discussed in the case of a T-semi-partition or a T-partition. Final ly, we investigate possible criteria for extendability, inspired by Wa ng's classical criterion of P-consistency. (C) 1998 Elsevier Science I nc. All rights reserved.