Uncertainty in Ontology Matching: A Decision Rule-Based Approach

Considering the high heterogeneity of the ontologies pub-lished 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, consid-ered 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 pro-cess based on a distance measure to identify the best possible matching entities for a given source entity.

💡 Research Summary

The paper addresses the problem of ontology matching under uncertainty, a critical issue given the proliferation of heterogeneous ontologies on the Web. Traditional ontology matching relies on similarity measures (e.g., lexical, structural) that produce a single confidence score for each candidate correspondence. However, no single measure can capture all aspects of similarity, and combining several measures inevitably leads to conflicting information. To handle this, the authors adopt the Theory of Belief Functions (also known as Dempster‑Shafer theory) as a formal framework for representing and aggregating uncertain evidence from multiple matchers.

First, three string‑based similarity techniques—Levenshtein distance, Jaro distance, and Hamming distance—are applied to a pair of ontologies concerning conference organization. For each source entity (e.g., “ConferenceMember”) the similarity scores obtained from the three matchers are interpreted as basic belief assignments (bbas). Each matcher contributes a mass to the specific target entity it suggests (e.g., “ConferenceFees”) and the remaining mass is allocated to the total ignorance set Θ, ensuring that each bba sums to one.

Next, the three bbas are combined using Dempster’s rule of combination, which assumes that the sources are reliable and normalizes away conflicting mass. The resulting combined bba reflects a consensus view of the evidence: it assigns belief not only to individual target entities but also to the ignorance set, thereby preserving residual uncertainty.

The core contribution of the paper is a novel decision rule that selects the most plausible correspondence by measuring the Jousselme distance between the combined bba and a set of categorical bbas. A categorical bba is a degenerate belief function that places all its mass on a single hypothesis X (or on a simple union of two hypotheses). The Jousselme distance, defined as

 d(m₁,m₂)=√{½ (m₁−m₂)ᵀ D (m₁−m₂)}

where D is a matrix derived from the Jaccard similarity of focal elements, captures both the overlap and the cardinality of the hypotheses. The decision rule is formalized as

 X* = arg min_{X∈2^Θ, |X|≤2} d(m_comb, m_X)

where the search is limited to hypotheses of cardinality one or two to keep the computational cost manageable. The hypothesis X* with the smallest distance is taken as the final matching decision.

Applying this rule to the conference ontology example, the authors find that the union hypothesis “ConferenceFees ∪ Conference” yields the smallest distance (≈0.52) and is therefore selected as the best correspondence for “ConferenceMember”. This demonstrates that the distance‑based rule can naturally handle 1:n (or n:1) mappings, something that traditional singleton‑focused decision criteria (maximum belief, maximum plausibility, or maximum pignistic probability) cannot do directly.

The paper also discusses related work, noting that few existing ontology matching approaches incorporate uncertainty handling. Prior studies have used Bayesian networks, probabilistic models, or Dempster‑Shafer theory, but they typically resolve to a single best match rather than evaluating composite hypotheses. The proposed distance‑based decision rule fills this gap by providing a principled way to compare and select composite hypotheses.

Limitations are acknowledged: restricting the search to hypotheses of size ≤2 may exclude more complex correspondences in large ontologies, and the approach has only been evaluated on a modest example. Future work is suggested to explore dynamic hypothesis selection, alternative distance measures, and scalability to ontologies with thousands of classes.

In summary, the authors present a coherent framework that (1) models individual matcher outputs as belief functions, (2) aggregates them using Dempster’s rule, and (3) selects the most plausible correspondence via a Jousselme‑distance minimization. The experimental illustration confirms that the method can capture uncertain and composite matches, offering a promising direction for robust ontology alignment in the Semantic Web.