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The Sugeno integral has been identified and used as an aggregation operator many times in the past. In this paper, an extension of the Sugeno integral for the framework of possibilistic truth values is presented, resulting in a powerful domain-specific aggregation operator. Next, it is shown how the presented integral can be plugged into a reasoning framework for identification of coreferent objects, which are entity descriptions that refer to the same entity in a different way. The concept of hierarchical fuzzy measures, linked to an object structure is introduced, offering a new conditional possibilistic reasoning framework for object matching. C 2008 Wiley Periodicals, Inc.

Traditional databases can manage only crisp information, a limitation that also holds for geographic information systems and spatial databases. In this paper, we present a technique based on triangulated irregular networks (or TINs for short) and fuzzy set theory to model imprecise or uncertain regions. A fuzzy region is represented by a Extended TIN, which allows for an associated value for each point of the region in the presented approach to be considered; this associated value will be a membership grade. As is common in fuzzy set theory, membership grades can indicate a degree of "belonging to the set"; in our approach these are the degree to which every crisp location belongs to the fuzzy region (membership grades in fuzzy set theory can have other interpretations7 as well, but these are not needed for the modelling of fuzzy regions). While modelling a fuzzy region as described provides a more accurate model of a real world situation, it does require many operators from the geographic realm to be extended and also new operators (mainly from the fuzzy realm) to be added at the object level. In this paper, from the GIS realm, the calculation of the surface area and the minimum bounding rectangle for fuzzy regions are considered; from the fuzzy realm the calculation of the α-cut is considered. Other operations (i.e. convex hull of a fuzzy region, distance between two fuzzy regions, …) are still under development.

Comparing objects can be considered as a hierarchical process. Separate aspects of objects are compared to each other, and the results of these comparisons are combined into a single result in one or more steps by aggregation operators. The set of operators used to compare the objects and the way these operators are related with each other is called the comparison scheme. If a threshold is applied to the final result of the object comparison, the mathematical properties of the operators in the comparison scheme can be used to derive thresholds on the intermediate results.These derived threshold can be used to break of a comparison early, thus offering a reduction of the comparison cost. Using this information, we show that the order in which the operators are evaluated has an influence on the average cost of comparing two objects. Next, we proceed with a study of the properties that allow us to find an optimal order, such that this average cost is minimized. Finally, we provide an algorithm that calculates an optimal order efficiently. Although specifically developed for object comparison, the algorithm can be applied to all kinds of selection processes that involve the combination of several test results. C 2009 Wiley Periodicals, Inc.