In the real world, there may exist manifold data (e.g., Boolean, categorical, real-valued, set-valued, interval-valued, image, decision and missing data or attributes) in an information system which is referred to as ...
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In the real world, there may exist manifold data (e.g., Boolean, categorical, real-valued, set-valued, interval-valued, image, decision and missing data or attributes) in an information system which is referred to as a hybrid information system with images (HISI). Handling an HISI is conducive to generalize applications of rough set theory. This paper studies entropy measurement for a hybrid information system with images and considers an application for attribute reduction. We first give the distance between information values on each attribute in an HISI. Then, we present tolerance relations on the object set of an HISI based on this distance. Next, we define the rough approximations in an HISI by means of the presented tolerance relations. Furthermore, we study entropy measurement for an HISI by using theta-information entropy, theta-conditional information entropy and theta-joint information entropy. Based on Kryszkiewicz's ideal, we introduce the concepts of theta-generalized decision and theta-consistent in an HISI. Finally, we apply entropy measurement to perform attribute reduction in a theta-consistent HISI. It is worth mentioning that attribute reduction based on generalized decision and common attribute reduction in a theta-consistent HISI are the same.
Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in...
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Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E-g. The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre's obstruction for principally polarized abelian threefolds isogenous to E-3 and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields.
Attribute selection in an information system (IS) is an important issue when dealing with a large amount of data. An IS with incomplete interval-value data is called an incomplete interval-valued information system (I...
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Attribute selection in an information system (IS) is an important issue when dealing with a large amount of data. An IS with incomplete interval-value data is called an incomplete interval-valued information system (IIVIS). This paper proposes attribute selection approaches for an IIVIS. Firstly, the similarity degree between two information values of a given attribute in an IIVIS is proposed. Then, the tolerance relation on the object set with respect to a given attribute subset is obtained. Next, theta-reduction in an IIVIS is studied. What is more, connections between the proposed reduction and information entropy are revealed. Lastly, three reduction algorithms base on theta-discernibility matrix, theta-information entropy and theta-significance in an IIVIS are given.
A hole in a graph is a chordless cycle of length at least 4. A theta is a graph formed by three internally vertex-disjoint paths of length at least 2 between the same pair of distinct vertices. A wheel is a graph form...
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A hole in a graph is a chordless cycle of length at least 4. A theta is a graph formed by three internally vertex-disjoint paths of length at least 2 between the same pair of distinct vertices. A wheel is a graph formed by a hole and a node that has at least 3 neighbors in the hole. In this series of papers we study the class of graphs that do not contain as an induced subgraph a theta nor a wheel. In Part II of the series we prove a decomposition theorem for this class, that uses clique cutsets and 2-joins. In this paper we use this decomposition theorem to solve several problems related to finding induced paths and cycles in our class. (c) 2020 Elsevier Inc. All rights reserved.
A hole in a graph is a chordless cycle of length at least 4. A theta is a graph formed by three paths between the same pair of distinct vertices so that the union of any two of the paths induces a hole. A wheel is a g...
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A hole in a graph is a chordless cycle of length at least 4. A theta is a graph formed by three paths between the same pair of distinct vertices so that the union of any two of the paths induces a hole. A wheel is a graph formed by a hole and a vertex that has at least 3 neighbors in the hole. In this series of papers we study the class of graphs that do not contain as an induced subgraph a theta nor a wheel. In Part II of the series we prove a decomposition theorem for this class, that uses clique cutsets and 2-joins, and consequently obtain a polynomial time recognition algorithm for the class. In this paper we further use this decomposition theorem to obtain polynomial time algorithms for maximum weight clique, maximum weight stable set and coloring problems. We also show that for a graph G in the class, if its maximum clique size is omega, then its chromatic number is bounded by max {omega, 3}, and that the class is 3-clique-colorable. Crown Copyright (C) 2019 Published by Elsevier Inc. All rights reserved.
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