Consider random hypergraphs on n vertices, where each k-element subset of vertices is selected with probability p independently and randomly as a hyperedge. By sparse we mean that the total number of hyperedges is O(n...
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ISBN:
(纸本)9781577355120
Consider random hypergraphs on n vertices, where each k-element subset of vertices is selected with probability p independently and randomly as a hyperedge. By sparse we mean that the total number of hyperedges is O(n) or O(n ln n). When k = 2, these are exactly the classical Erdös-Rényi random graphs G(n, p). We prove that with high probability, hinge width on these sparse random hypergraphs can grow linearly with the expected number of hyperedges. Some random constraint satisfaction problems such as Model RB and Model RD have satisfiability thresholds on these sparse constraint hypergraphs, thus the large hinge width results provide some theoretical evidence for random instances around satisfiability thresholds to be hard for a standard hinge-decomposition based algorithm. We also conduct experiments on these and other kinds of random graphs with several hundreds vertices, including regular random graphs and power law random graphs. The experimental results also show that hinge width can grow linearly with the number of edges on these different random graphs. These results may be of further interests.
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Formal concept analysis and rough set analysis are two complementary approaches for analyzing data. This paper studies approaches to constructing fuzzy concept lattices based on generalized fuzzy rough approximation operators. For a residual implicator θ satisfying θ (a, b) = θ(1-b, 1-a) and its dual σ, a pair of (θ, σ)-fuzzy rough approximation operators is defined. We then propose three kinds of fuzzy operators, and examine some of their basic properties. Thus, three complete fuzzy concept lattices can be produced, for which the properties are analogous to those of the classical concept lattices.
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