A possibilistic view on set and multiset comparison

Comparative evaluation operators for sets and multisets are proposed from a possibilistic point of view. In general, an evaluator estimates the possibility of (non) co-reference of two arbitrary (sub)-objects. Such operators can be used in a hierarchical possibilistic framework for finding co-referent objects with a complex structure. This paper first discusses properties of evaluators in general and continues with studying operators for sets and multisets, thereby making a clear distinction between hard and soft evaluators. Hard evaluators are based on evaluation of derived (multi)sets, while soft evaluators use a low level evaluator to incorporate co-reference at element level. The two important parts of such a soft evaluator are an injective element mapping and an aggregation function. An algorithm to provide the injective mapping is presented and discussed. For the aggregation step, ordered weighted conjunction is studied by introducing parameterized fuzzy quantifiers to calculate weight vectors. An advanced learning strategy is introduced to train the optimal parameter matrix.