Fuzzy Sets and Systems 160 (2009) 2141 – 2158 www.elsevier.com/locate/fss Impact of weights on conjunctive and disjunctive aggregation of extended possibilistic truth values Tom Matthé ∗ , Guy De Tré, Axel Hallez Ghent University, Department of Telecommunications and Information Processing, Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium Available online 26 February 2009 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. © 2009 Elsevier B.V. All rights reserved. Keywords: Fuzzy connectives and aggregation operators; Flexible querying; Extended possibilistic truth values 1. Introduction Databases are continuously growing in size, and, using traditional querying techniques, users are confronted with difficulties to find the information they are looking for. So, more and more, users are realizing the benefits of using flexible querying systems [1,4,5,7,14,15,17,23,24]. The main goal of flexible querying is to allow the user to express his/her query in a more flexible way. Preferences can be used to indicate the users wishes. Introducing these preferences can be done at two levels: inside elementary query conditions, allowing for the user to impose flexible search criteria which express to what degree particular attribute values are adequate for the result, and between query conditions, allowing for the user to attach weights, expressing importance, to the individual query conditions. This paper will not deal with the preferences inside the elementary query conditions, and hence will not discuss the evaluation of selection criteria. The focus of this paper lies on one aspect of flexible querying, namely on the aggregation of the results of the evaluation of the individual selection criteria (which can be flexible or not), taking into account that weights can be attached to the individual selection criteria. Primarily, these are mathematical concepts, above which there is a layer of practical decision making. However, discussing this decision making is not the goal of this paper. ∗ Corresponding author. E-mail addresses: Tom.MATTHE@UGent.be (T. Matthé), Guy.DETRE@UGent.be (G. De Tré), Axel.HALLEZ@UGent.be (A. Hallez). 0165-0114/$-see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.fss.2009.02.011