Considering the high heterogeneity of the ontologies published on the web, ontology matching is a crucial issue whose aim is to establish links between an entity of a source ontology and one or several entities from a target ontology. Perfectible similarity measures, considered as sources of information, are combined to establish these links. The theory of belief functions is a powerful mathematical tool for combining such uncertain information. In this paper, we introduce a decision process based on a distance measure to identify the best possible matching entities for a given source entity.
Although, the authors in @cite_2 handle uncertainty in the matching process, their proposal differ from that proposed in @cite_12 . In fact, they use the Dempster-Shafer theory in a specific context of question answering where including uncertainty may yield to better results. Not like in @cite_12 , they did not give in depth how the frame of discernment is constructed. In addition to that, uncertainty is handled only once the matching is processed. In fact, the similarity matrix is constructed for each matcher. Based on this matrix, the results are modeled using the theory of belief functions and then they are combined.
@cite_12 @cite_2
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An ontology matching method (or a matcher) aims at matching every entity (or concept) in one ontology to the most suitable entity (or entities) in another ontology. Usually it is almost impossible to find a perfect match in the second ontology for every entity in the first ontology, so a matcher generally returns a set of possible matches with some weights (uncertainty) attached to each pair of match. In order to improve a matching result, several matchers can be used and the matched results from these matchers are combined with suitable approaches. In this paper, we first propose two new matchers among three matchers we use. We then address the need of dealing with uncertainties in mapping by investigating how some uncertainty reasoning frameworks can be used to combine matching results. We apply both the Dempster Shafer theory of evidence (DS theory) and Possibility Theory to merge the results computed by different matchers. Our experimental results and comparisons with related work indicate that integrating these theories to deal with uncertain ontology matching is a promising way to improve the overall matching results. We propose an extended relational database model which can model both uncertainty and imprecision in data. This model is based on Dempster-Shafer theory which has become popular in AI as an uncertainty reasoning tool. The definitions of Be1 and Pls functions in Dempster-Shafer theory are extended to compute the beliefs of various comparisons (e.g., equality, less than, etc.) between two basic probability assignments. Based on these new definitions of Be1 and Pls functions and the Boolean combinations of Be1 and Pls values for two events, five relational operators such as Select, Cartesian Product, Join, Projection Intersect, and Union are defined. We analyze the Gale-Shapley matching problem within the context of Rawlsian justice. Defining a fair matching algorithm by a set of 4 axioms (Gender Indifference, Peer Indifference, Maximin Optimality, and Stability), we show that not all preference profiles admit a fair matching algorithm, the reason being that even this set of minimal axioms is too strong in a sense. Because of conflict between Stability and Maximin Optimality, even the algorithm which generates the mutual agreement match, paradoxically, has no chance to be fair. In this work, we present a novel approach to clustering Web site users into different groups and generating common user profiles. These profiles can be used to make recommendations, personalize Web sites, and for other uses such as targeting users for advertising. By using the concept of mass distribution in Dempster-Shafer's theory, the belief function similarity measure in our algorithm adds to the clustering task the ability to capture the uncertainty among Web user's navigation behavior. Our algorithm is relatively simple to use and gives comparable results to other approaches reported in the literature of web mining.