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A possibilistic view on set and multiset comparison

Bronselaer A., Hallez A., Tre G. de

Control and Cybernetics

2009

Vol. 38, no 2

341-366

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.

Bitmap based structures for the modeling of fuzzy entities

Verstraete J., Tre G. de, Hallez A.

Control and Cybernetics

2006

Vol. 35, no 1

147-164

Bitmap models are a known technique to model field based geographic information. Commonly, geographic information is modelled in a crisp sense, even though in reality it most likely is an approximation. In this article, we present the use of bitmap based structures to model imprecise or uncertain locations and ditto regions: these structures should be considered to be extensions of respectively a point and a polygon. The imprecission or uncertainty is modelled using fuzzy set theory. Apart from presenting the structures, appropriate operators are denned and explained.