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.
Only few ontology matching methods have considered that dealing with uncertainty in a matching process is a crucial issue. We are interested in this section to present some of them where the probability theory @cite_9 and the Dempster-Shafer theory ( @cite_12 , @cite_2 , @cite_5 ) are the main mathematical models used. In @cite_9 , the authors proposed an approach for matching ontologies based on bayesian networks which is an extension of the BayesOWL. The BayesOWL consists in translating an OWL ontology into a bayesian network (BN) through the application of a set of rules and procedures. In order to match two ontologies, first the source and target ontologies are translated into @math and @math respectively. The mapping is processed between the two ontologies as an evidential reasoning between @math and @math . The authors assume that the similarity information between a concept @math from a source ontology and a concept @math from a target ontology is measured by the joint probability distribution P( @math , @math ).
@cite_5 @cite_9 @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. This paper presents our ongoing effort on developing a principled methodology for automatic ontology mapping based on BayesOWL, a probabilistic framework we developed for modeling uncertainty in semantic web. In this approach, the source and target ontologies are first translated into Bayesian networks (BN); the concept mapping between the two ontologies are treated as evidential reasoning between the two translated BNs. Probabilities needed for constructing conditional probability tables (CPT) during translation and for measuring semantic similarity during mapping are learned using text classification techniques where each concept in an ontology is associated with a set of semantically relevant text documents, which are obtained by ontology guided web mining. The basic ideas of this approach are validated by positive results from computer experiments on two small real-world ontologies. Ontologies, at least in the form of taxonomies, have proved rather successful, and are employed in many fields, as far apart as biology and finance. Reaching an agreement over a single ontology has proved difficult, and to obtain actual interoperability it is necessary to map the different ontologies. Mapping one entity between a source ontology and one in a target ontology means to compare the first entity with all the entities in the second ontology: matchers analyse different aspects of the entities to identify the similarities. A single matcher can analyse only some aspects, and often has to rely on uncertain information. Therefore combining the outcomes of different matchers can yield better results. In this paper I present a framework that uses Dempster-Shafer as a model for interpreting and combining results computed by the matchers. The increasing number of ontologies of the semantic web poses new challenges for ontology mapping. Ontology mapping in the context of question answering can provide more correct results if the mapping process can deal with uncertainty effectively that is caused by the incomplete and inconsistent information used and produced by the mapping process. We present a novel approach of how Dempster-Shafer belief functions can be used to represent uncertain similarities created by both syntactic and semantic similarity algorithms. For ontology mapping in the context of question answering on the semantic web we propose a multi agent framework where agents create dynamic ontology mappings in order to integrate information and provide precise answers for the users query. We also discuss the problems which can be encountered if we have conflicting beliefs between agents in a particular mapping.