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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. © 2009 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The comparison of sets of objects is a research topic with applications in diverse fields such as computer science, biology and psychology. Since the introduction of the Jaccard index, many techniques have been proposed. This paper aims at extending an existing framework of comparison indices for sets. Firstly, the novel indices account for similarities between elements, rather than identity of elements as is the case for existing techniques. As a result, a richer framework of comparison indices is obtained. The use of fuzzy quantifiers in this framework is shown. Secondly, the machinery for sets is extended to the case of multisets, which results in two classes of comparison indices. The first class considers each element instance as a separate element, while the second class considers groups of elements instances as an atomic entity. The number of instances is then a property of this group, that is taken into account when calculating similarity between element groups. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. © 2008 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]