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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]

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]

Abstract: Extended possibilistic truth values are a flexible means to model the certainty or uncertainty about the truth value of a proposition. With respect to flexible database querying, they are suited to express the extent to which a database instance satisfies a query condition. Since a flexible query can impose several conditions, each with different importance, weighted aggregation is necessary. In this paper, weighted aggregation of extended possibilistic truth values is presented. The impact of the weights on extended possibilistic truth values in both conjunctive and disjunctive aggregation is handled. It is illustrated that the different aggregation types require a different approach. Special care is given to the case where both conjunctive and disjunctive aggregation are mixed together. It is shown that the weights will have to be propagated throughout the calculations, but that this can cause basic properties, like associativity, to get lost. The problems that can arise are illustrated and solutions are proposed. [Copyright &y& Elsevier]