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The symbolic level of a dynamic scene interpretation system is presented. This symbolic level is based on plan prototypes represented by Petri nets whose interpretation is expressed thanks to 1st order cubes, and on a reasoning aiming at instantiating the plan prototypes with objects delivered by the numerical processing of sensor data. A purely symbolic meta-structure, grounded on the lattice theory, is then proposed to deal with the symbolic uncertainty issues. Examples on real world data are given.

The algebra of truth values for fuzzy sets of type-2 consists of all mappings from the unit interval into itself, with operations certain convolutions of these mappings with respect to pointwise max and min. This algebra generalizes the truth-value algebras of both type-1 and of interval-valued fuzzy sets, and has been studied rather extensively both from a theoretical and applied point of view. This paper addresses the situation when the unit interval is replaced by two finite chains. Most of the basic theory goes through, but there are several special circumstances of interest. These algebras are of interest on two counts, both as special cases of bases for fuzzy theories, and as mathematical entities per se.