Possibility theory: an integral theoretic approach
Fuzzy Sets and Systems
Possibility and necessity integrals
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Fuzzy sets as a basis for a theory of possibility
Fuzzy Sets and Systems
Fuzzy Measure Theory
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Constructing possibility measures
ISUMA '95 Proceedings of the 3rd International Symposium on Uncertainty Modelling and Analysis
Algorithms for possibility assessments: Coherence and extension
Fuzzy Sets and Systems
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We address the (generalized) extension problem for possibility measures: given a map defined on a family of (fuzzy) sets, is it possible to extend it to a (generalized) possibility measure? The extension problem for possibility measures is known to be equivalent to a system of sup-%plane1D;4AF; equations, with %plane1D;4AF; a t-norm. A key role is played by the greatest solution (of type inf-, with a border implicator). When the family of sets considered is a semi-partition, another important solution (of type sup-%plane1D;4AF;, with %plane1D;4AF; a t-norm) can be identified. In the treatment of the generalized possibilistic extension problem, we show that a fuzzification of the greatest solution also plays a central role. On the other hand, an immediate fuzzification of the sup-%plane1D;4AF; type solution is investigated. General necessary and sufficient conditions for this fuzzification to be a solution are established. This fuzzification is then further discussed in the case of a %plane1D;4AF;-semi-partition or a %plane1D;4AF;-partition. Finally, we investigate possible criteria for extendability, inspired by Wang's classical criterion of P-consistency.