Transitive closures of fuzzy thesauri for information-retrieval systems
International Journal of Man-Machine Studies
Science of Computer Programming - Special issue on mathematics of program construction
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Abstract derivation of transitive closure algorithms
Information Processing Letters
Journal of the ACM (JACM)
A limit theorem in dynamic fuzzy systems with transitive fuzzy relations
Fuzzy Sets and Systems
A representation theorem for min-transitive fuzzy relations
Fuzzy Sets and Systems
A modification of Warshall's algorithm for the transitive closure of binary relations
Communications of the ACM
A note on multiplying Boolean matrices
Communications of the ACM
Fuzzy Sets and Systems
Transitive closure and betweenness relations
Fuzzy Sets and Systems
Convergence of products of fuzzy matrices
Fuzzy Sets and Systems
On compositions of lattice matrices
Fuzzy Sets and Systems
Numerical representation of transitive fuzzy relations
Fuzzy Sets and Systems
Proceedings of the Second International Conference on Mathematics of Program Construction
On the existence and construction of T-transitive closures
Information Sciences: an International Journal
Context-Sensitive Semantic Query Expansion
ICAIS '02 Proceedings of the 2002 IEEE International Conference on Artificial Intelligence Systems (ICAIS'02)
The complete linkage clustering algorithm revisited
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
Algorithms for the computation of T-transitive closures
IEEE Transactions on Fuzzy Systems
A top-down algorithm for generating the Hasse tree of a fuzzy preorder closure
IEEE Transactions on Fuzzy Systems
Semantic representation of multimedia content: Knowledge representation and semantic indexing
Multimedia Tools and Applications
Computing a T-transitive lower approximation or opening of a proximity relation
Fuzzy Sets and Systems
Semantics Enabled Problem Based Brokering of Organizational Knowledge
Proceedings of the 2007 conference on Emerging Artificial Intelligence Applications in Computer Engineering: Real Word AI Systems with Applications in eHealth, HCI, Information Retrieval and Pervasive Technologies
New approaches to fuzzy-rough feature selection
IEEE Transactions on Fuzzy Systems
A novel hierarchical-clustering-combination scheme based on fuzzy-similarity relations
IEEE Transactions on Fuzzy Systems
Minimizing uncertainty in semantic identification when computing resources are limited
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
Formal concept analysis based on fuzzy granularity base for different granulations
Fuzzy Sets and Systems
Fuzzy relation equations and subsystems of fuzzy transition systems
Knowledge-Based Systems
Finding rough and fuzzy-rough set reducts with SAT
Information Sciences: an International Journal
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The property of transitivity is one of the most important for fuzzy binary relations, especially in the cases when they are used for the representation of real-life similarity or ordering information. As far as the algorithmic part of the actual calculation of the transitive closure of such relations is concerned, works in the literature mainly focus on crisp symmetric relations, paying little attention to the case of general fuzzy binary relations. Most works that deal with the algorithmic part of the transitive closure of fuzzy relations focus only on the case of max-min transitivity, disregarding other types of transitivity. In this paper, after formalizing the notion of sparseness and providing a representation model for sparse relations that displays both computational and storage merits, we propose an algorithm for the incremental update of fuzzy sup-t transitive relations. The incremental transitive update (ITU) algorithm achieves the re-establishment of transitivity when an already transitive relation is only locally disturbed. Based on this algorithm, we propose an extension to handle the sup-t transitive closure of any fuzzy binary relation, through a novel incremental transitive closure (ITC) algorithm. The ITU and ITC algorithms can be applied on any fuzzy binary relation and t-norm; properties such as reflexivity, symmetricity and idempotency are not a requirement. Under the specified assumptions for the average sparse relation, both of the proposed algorithms have considerably smaller computational complexity than the conventional approach; this is established both theoretically and verified via appropriate computing experiments.