The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
William Zhu - One of the best experts on this subject based on the ideXlab platform.
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Closed-set lattice of regular sets based on a serial and Transitive Relation through matroids
International Journal of Machine Learning and Cybernetics, 2013Co-Authors: William ZhuAbstract:Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a serial and Transitive Relation on a universe, the collection of all the regular sets of the generalized rough set is a lattice. In this paper, we use the lattice to construct a matroid and then study Relationships between the lattice and the closed-set lattice of the matroid. First, the collection of all the regular sets based on a serial and Transitive Relation is proved to be a semimodular lattice. Then, a matroid is constructed through the height function of the semimodular lattice. Finally, we propose an approach to obtain all the closed sets of the matroid from the semimodular lattice. Borrowing from matroids, results show that lattice theory provides an interesting view to investigate rough sets.
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CCECE - Matroidal structure of generalized rough sets based on symmetric and Transitive Relations
2013 26th IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), 2013Co-Authors: Bin Yang, William ZhuAbstract:Rough set theory is an effective tool for dealing with vagueness or uncertainty in information systems. It is efficient for data pre-process and widely used in attribute reduction in data mining. Matroid theory is a branch of combinatorial mathematics and borrows extensively from linear algebra and graph theory, so it is an important mathematical structure with high applicability. Moreover, matroids have been applied to diverse fields such as algorithm design, combinatorial optimization and integer programming. Therefore, the establishment of matroidal structures of general rough sets may be much helpful for some problems such as attribute reduction in information systems. This paper studies generalized rough sets based on symmetric and Transitive Relations from the operator-oriented view by matroidal approaches. We firstly construct a matroidal structure of generalized rough sets based on symmetric and Transitive Relations, and provide an approach to study the matroid induced by a symmetric and Transitive Relation. Secondly, this paper establishes a close Relationship between matroids and generalized rough sets. Approximation quality and roughness of generalized rough sets can be computed by the circuit of matroid theory. At last, a symmetric and Transitive Relation can be constructed by a matroid with some special properties.
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Matroidal structure of generalized rough sets based on symmetric and Transitive Relations
arXiv: Artificial Intelligence, 2012Co-Authors: Bin Yang, William ZhuAbstract:Rough sets are efficient for data pre-process in data mining. Lower and upper approximations are two core concepts of rough sets. This paper studies generalized rough sets based on symmetric and Transitive Relations from the operator-oriented view by matroidal approaches. We firstly construct a matroidal structure of generalized rough sets based on symmetric and Transitive Relations, and provide an approach to study the matroid induced by a symmetric and Transitive Relation. Secondly, this paper establishes a close Relationship between matroids and generalized rough sets. Approximation quality and roughness of generalized rough sets can be computed by the circuit of matroid theory. At last, a symmetric and Transitive Relation can be constructed by a matroid with some special properties.
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Matroidal structure based on serial and Transitive Relation
arXiv: Artificial Intelligence, 2012Co-Authors: Yanfang Liu, William ZhuAbstract:Rough set is mainly concerned with the approximations of objects through a binary Relation on a universe. It has been applied to machine learning, knowledge discovery and data mining. Matroid is a combinatorial generalization of linear independence in vector spaces. It has been used in combinatorial optimization and algorithm design. In order to take advantages of both rough sets and matroids, we propose a matroidal structure based on a serial and Transitive Relation on a universe. We define the minimal neighborhood of a Relation on a universe. The minimal neighborhood satisfies the circuit axiom of matroids when the Relation is serial and Transitive, then a matroid is generated. Similarly, we induce an equivalence Relation through the circuits of a matroid. The connections between the upper approximation operators of Relations and the closure operators of matroids are studied, respectively. Moreover, we investigate the Relationships between the above two inductions.
Derek J. S. Robinson - One of the best experts on this subject based on the ideXlab platform.
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Sylow permutability in soluble minimax groups
Ricerche di Matematica, 2017Co-Authors: Derek J. S. RobinsonAbstract:A PST-group is a group in which Sylow permutability is a Transitive Relation. A classification is given of the soluble minimax groups whose finite quotients are PST-groups.
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Sylow permutability in generalized soluble groups
Journal of Group Theory, 2017Co-Authors: Derek J. S. RobinsonAbstract:AbstractA PST-group is a group in which Sylow permutability is a Transitive Relation in the group. A classification is given of finitely generated hyperabelian groups all of whose finite quotients are PST-groups.
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Sylow permutability in locally finite groups
Ricerche di Matematica, 2010Co-Authors: Derek J. S. RobinsonAbstract:A theorem is established which describes the structure of locally finite groups in whose finite subgroups Sylow permutability is a Transitive Relation.
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THE STRUCTURE OF FINITE GROUPS IN WHICH PERMUTABILITY IS A Transitive Relation
Journal of The Australian Mathematical Society, 2001Co-Authors: Derek J. S. RobinsonAbstract:(Received 30 October 1999; revised 28 June 2000)Communicated by R. B. HowlettAbstractThe structure of finite groups in which permutability is Transitive (PT-groups) is studied in detail.In particular a finite /T-group has simple chief factors and the p -chief factors fall into at most twoisomorphism classes. Th e structure of finite T-groups, that is, groups in which normality is Transitive, isalso discussed, as is that of groups generated by subnormal or normal P 7-subgroups.2000 Mathematics subject classification: primary 20D35.
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The structure of finite groups in which permutability is a Transitive Relation
Journal of the Australian Mathematical Society, 2001Co-Authors: Derek J. S. RobinsonAbstract:AbstractThe structure of finite groups in which permutability is Transitive (PT-groups) is studied in detail. In particular a finite PT-group has simple chief factors and the p-chief factors fall into at most two isomorphism classes. The structure of finite T-groups, that is, groups in which normality is Transitive, is also discussed, as is that of groups generated by subnormal or normal PT-subgroups.
Wu Zhang - One of the best experts on this subject based on the ideXlab platform.
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on completing sparse knowledge base with Transitive Relation embedding
National Conference on Artificial Intelligence, 2019Co-Authors: Zili Zhou, Shaowu Liu, Wu ZhangAbstract:Multi-Relation embedding is a popular approach to knowledge base completion that learns embedding representations of entities and Relations to compute the plausibility of missing triplet. The effectiveness of embedding approach depends on the sparsity of KB and falls for infrequent entities that only appeared a few times. This paper addresses this issue by proposing a new model exploiting the entity-independent Transitive Relation patterns, namely Transitive Relation Embedding (TRE). The TRE model alleviates the sparsity problem for predicting on infrequent entities while enjoys the generalisation power of embedding. Experiments on three public datasets against seven baselines showed the merits of TRE in terms of knowledge base completion accuracy as well as computational complexity.
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AAAI - On Completing Sparse Knowledge Base with Transitive Relation Embedding
Proceedings of the AAAI Conference on Artificial Intelligence, 2019Co-Authors: Zili Zhou, Shaowu Liu, Wu ZhangAbstract:Multi-Relation embedding is a popular approach to knowledge base completion that learns embedding representations of entities and Relations to compute the plausibility of missing triplet. The effectiveness of embedding approach depends on the sparsity of KB and falls for infrequent entities that only appeared a few times. This paper addresses this issue by proposing a new model exploiting the entity-independent Transitive Relation patterns, namely Transitive Relation Embedding (TRE). The TRE model alleviates the sparsity problem for predicting on infrequent entities while enjoys the generalisation power of embedding. Experiments on three public datasets against seven baselines showed the merits of TRE in terms of knowledge base completion accuracy as well as computational complexity.
Lidia Tendera - One of the best experts on this subject based on the ideXlab platform.
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The Fluted Fragment with Transitive Relations.
arXiv: Logic in Computer Science, 2020Co-Authors: Ian Pratt-hartmann, Lidia TenderaAbstract:We study the satisfiability problem for the fluted fragment extended with Transitive Relations. The logic enjoys the finite model property when only one Transitive Relation is available and the finite model property is lost when additionally either equality or a second Transitive Relation is allowed. We show that the satisfiability problem for the fluted fragment with one Transitive Relation and equality remains decidable. On the other hand we show that the satisfiability problem is undecidable already for the two-variable fragment of the logic in the presence of three Transitive Relations (or two Transitive Relations and equality).
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MFCS - The Fluted Fragment with Transitivity
2019Co-Authors: Ian Pratt-hartmann, Lidia TenderaAbstract:We study the satisfiability problem for the fluted fragment extended with Transitive Relations. We show that the logic enjoys the finite model property when only one Transitive Relation is available. On the other hand we show that the satisfiability problem is undecidable already for the two-variable fragment of the logic in the presence of three Transitive Relations.
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On the satisfiability problem for fragments of two-variable logic with one Transitive Relation
Journal of Logic and Computation, 2019Co-Authors: Wiesław Szwast, Lidia TenderaAbstract:Abstract We study the satisfiability problem for two-variable first-order logic over structures with one Transitive Relation. We show that the problem is decidable in 2-NExpTime for the fragment consisting of formulas where existential quantifiers are guarded by Transitive atoms. As this fragment enjoys neither the finite model property nor the tree model property, to show decidability we introduce a novel model construction technique based on the infinite Ramsey theorem. We also point out why the technique is not sufficient to obtain decidability for the full two-variable logic with one Transitive Relation; hence, contrary to our previous claim, [FO$^2$ with one Transitive Relation is decidable, STACS 2013: 317-328], the status of the latter problem remains open.
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The Fluted Fragment with Transitivity
arXiv: Logic in Computer Science, 2019Co-Authors: Ian Pratt-hartmann, Lidia TenderaAbstract:We study the satisfiability problem for the fluted fragment extended with Transitive Relations. We show that the logic enjoys the finite model property when only one Transitive Relation is available. On the other hand we show that the satisfiability problem is undecidable already for the two-variable fragment of the logic in the presence of three Transitive Relations.
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On the satisfiability problem for fragments of the two-variable logic with one Transitive Relation
arXiv: Logic in Computer Science, 2018Co-Authors: Wiesław Szwast, Lidia TenderaAbstract:We study the satisfiability problem for the two-variable first-order logic over structures with one Transitive Relation. % We show that the problem is decidable in 2-NExpTime for the fragment consisting of formulas where existential quantifiers are guarded by Transitive atoms. As this fragment enjoys neither the finite model nor the tree model property, to show decidability we introduce novel model construction technique based on the infinite Ramsey theorem. We also point out why the technique is not sufficient to obtain decidability for the full two-variable logic with one Transitive Relation, hence contrary to our previous claim, [31], the status of the latter problem remains open.
Zili Zhou - One of the best experts on this subject based on the ideXlab platform.
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on completing sparse knowledge base with Transitive Relation embedding
National Conference on Artificial Intelligence, 2019Co-Authors: Zili Zhou, Shaowu Liu, Wu ZhangAbstract:Multi-Relation embedding is a popular approach to knowledge base completion that learns embedding representations of entities and Relations to compute the plausibility of missing triplet. The effectiveness of embedding approach depends on the sparsity of KB and falls for infrequent entities that only appeared a few times. This paper addresses this issue by proposing a new model exploiting the entity-independent Transitive Relation patterns, namely Transitive Relation Embedding (TRE). The TRE model alleviates the sparsity problem for predicting on infrequent entities while enjoys the generalisation power of embedding. Experiments on three public datasets against seven baselines showed the merits of TRE in terms of knowledge base completion accuracy as well as computational complexity.
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AAAI - On Completing Sparse Knowledge Base with Transitive Relation Embedding
Proceedings of the AAAI Conference on Artificial Intelligence, 2019Co-Authors: Zili Zhou, Shaowu Liu, Wu ZhangAbstract:Multi-Relation embedding is a popular approach to knowledge base completion that learns embedding representations of entities and Relations to compute the plausibility of missing triplet. The effectiveness of embedding approach depends on the sparsity of KB and falls for infrequent entities that only appeared a few times. This paper addresses this issue by proposing a new model exploiting the entity-independent Transitive Relation patterns, namely Transitive Relation Embedding (TRE). The TRE model alleviates the sparsity problem for predicting on infrequent entities while enjoys the generalisation power of embedding. Experiments on three public datasets against seven baselines showed the merits of TRE in terms of knowledge base completion accuracy as well as computational complexity.
