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1.
For decision-theoretic rough sets, a key issue is determining the thresholds for the probabilistic rough set model by setting appropriate cost functions. However, it is not easy to obtain correct cost functions because of a lack of prior knowledge and few previous studies have addressed the determination of learning thresholds and cost functions from datasets. In the present study, a multi-objective optimization model is proposed for threshold learning. In our model, we integrate an objective function that minimizes the decision cost with another that decreases the size of the boundary region. The ranges of the thresholds and two types of F_measure are used as constraints. In addition, a multi-objective genetic algorithm is employed to obtain the Pareto optimal set. We used 12 UCI datasets to validate the performance of our method, where the experimental results demonstrated the trade-off between the two objectives as well as showing that the thresholds obtained by our method were more intuitive than those obtained using other methods. The classification abilities of the solutions were improved by the F_measure constraints. 相似文献
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The probabilistic rough set (PRS) model ignores absolute quantitative information i.e., overlap between equivalence class and basic set. And graded rough set (GRS) model cannot reflect the distinctive degrees of information. In order to overcome these defects, this paper proposes the probabilistic graded rough set (PGRS), which is an extension of Pawlak's rough set and GRS. What is more, we propose double relative quantitative decision-theoretic rough set (Drq-DTRS) models, which essentially indicate the relative and absolute quantification. 相似文献
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Masahiro Inuiguchi Yukihiro Yoshioka Yoshifumi Kusunoki 《International Journal of Approximate Reasoning》2009,50(8):1199
In this paper, a variable-precision dominance-based rough set approach (VP-DRSA) is proposed together with several VP-DRSA-based approaches to attribute reduction. The properties of VP-DRSA are shown in comparison to previous dominance-based rough set approaches. An advantage of VP-DRSA over variable-consistency dominance-based rough set approach in decision rule induction is emphasized. Some relations among the VP-DRSA-based attribute reduction approaches are investigated. 相似文献
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Decui Liang Dun Liu Witold Pedrycz Pei Hu 《International Journal of Approximate Reasoning》2013,54(8):1087-1106
Based on decision-theoretic rough sets (DTRS), we augment the existing model by introducing into the granular values. More specifically, we generalize a concept of the precise value of loss function to triangular fuzzy decision-theoretic rough sets (TFDTRS). Firstly, ranking the expected loss with triangular fuzzy number is analyzed. In light of Bayesian decision procedure, we calculate three thresholds and derive decision rules. The relationship between the values of the thresholds and the risk attitude index of decision maker presented in the ranking function is analyzed. With the aid of multiple attribute group decision making, we design an algorithm to determine the values of losses used in TFDTRS. It is achieved with the use of particle swarm optimization. Our study provides a solution in the aspect of determining the value of loss function of DTRS and extends its range of applications. Finally, an example is presented to elaborate on the performance of the TFDTRS model. 相似文献
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Ying Yu Witold Pedrycz Duoqian Miao 《International Journal of Approximate Reasoning》2013,54(9):1373-1387
Automatic image annotation is concerned with the task of assigning one or more semantic concepts to a given image. It is a typical multi-label classification problem. This paper presents a novel multi-label classification framework MLNRS based on neighborhood rough sets for automatic image annotation which considers the uncertainty of the mapping from visual feature space to semantic concepts space. Given a new instances, its neighbors in the training set are firstly identified. After that, based on the concept of upper and lower approximations of neighborhood rough sets, all possible labels of the given instance are found. Then, based on the statistical information gained from the label sets of the neighbors, maximum a posteriori (MAP) principle is utilized to determine the label set for the given instance. Experiments completed for three different image datasets show that MLNRS achieves more promising performance in comparison with to some well-known multi-label learning algorithms. 相似文献
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PEI Dao-wu 《高校应用数学学报(英文版)》2014,29(3):253-264
In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the (fuzzy) relation in some generalized rough set model. Our results show that by using the axiomatic approach, the (fuzzy) relation determined by (fuzzy) approximation operators is unique in some (fuzzy) double-universe model. 相似文献
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Feature reduction based on rough set theory is an effective feature selection method in pattern recognition applications. Finding a minimal subset of the original features is inherent in rough set approach to feature selection. As feature reduction is a Nondeterministic Polynomial‐time‐hard problem, it is necessary to develop fast optimal or near‐optimal feature selection algorithms. This article aims to propose an exact feature selection algorithm in rough set that is efficient in terms of computation time. The proposed algorithm begins the examination of a solution tree by a breadth‐first strategy. The pruned nodes are held in a version of the trie data structure. Based on the monotonic property of dependency degree, all subsets of the pruned nodes cannot be optimal solutions. Thus, by detecting these subsets in trie, it is not necessary to calculate their dependency degree. The search on the tree continues until the optimal solution is found. This algorithm is improved by selecting an initial search level determined by the hill‐climbing method instead of searching the tree from the level below the root. The length of the minimal reduct and the size of data set can influence which starting search level is more efficient. The experimental results using some of the standard UCI data sets, demonstrate that the proposed algorithm is effective and efficient for data sets with more than 30 features. © 2014 Wiley Periodicals, Inc. Complexity 20: 50–62, 2015 相似文献
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《International Journal of Approximate Reasoning》2014,55(3):908-923
Covering rough sets generalize traditional rough sets by considering coverings of the universe instead of partitions, and neighborhood-covering rough sets have been demonstrated to be a reasonable selection for attribute reduction with covering rough sets. In this paper, numerical algorithms of attribute reduction with neighborhood-covering rough sets are developed by using evidence theory. We firstly employ belief and plausibility functions to measure lower and upper approximations in neighborhood-covering rough sets, and then, the attribute reductions of covering information systems and decision systems are characterized by these respective functions. The concepts of the significance and the relative significance of coverings are also developed to design algorithms for finding reducts. Based on these discussions, connections between neighborhood-covering rough sets and evidence theory are set up to establish a basic framework of numerical characterizations of attribute reduction with these sets. 相似文献
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用模糊集合与模糊等价关系对单向奇异粗集进行了研究,并给出了单向奇异粗糙模糊集合的数学结构及其并、交、补运算和性质.同时证明了单向奇异粗糙模糊集合对并、交、补运算构成完全可无限分配的软代数. 相似文献
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《Optimization》2012,61(5):603-611
Classical mathematics is usually crisp while most real-life problems are not; therefore, classical mathematics is usually not suitable for dealing with real-life problems. In this article, we present a systematic and focused study of the application of rough sets (Z. Pawlak, Rough sets, In. J. Comput. Informa. Sci. 11 (1982), pp. 341–356.) to a basic area of decision theory, namely ‘mathematical programming’. This new framework concerns mathematical programming in a rough environment and is called ‘rough programming’ (L. Baoding, Theory and Practice of Uncertain Programming, 1st ed., Physica-Verlag, Heidelberg, 2002; E.A. Youness, Characterizing solutions of rough programming problems, Eut. J. Oper. Res. 168 (2006), pp. 1019–1029). It implies the existence of the roughness in any part of the problem as a result of the leakage, uncertainty and vagueness in the available information. We classify rough programming problems into three classes according to the place of the roughness. In rough programming, wherever roughness exists, new concepts like rough feasibility and rough optimality come to the front of our interest. The study of convexity for rough programming problems plays a key role in understanding global optimality in a rough environment. For this, a theoretical framework of convexity in rough programming and conceptualization of the solution is created on the lines of their crisp counterparts. 相似文献
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This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology. 相似文献
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Classical rough set theory is based on the conventional indiscernibility relation. It is not suitable for analyzing incomplete information. Some successful extended rough set models based on different non-equivalence relations have been proposed. The data-driven valued tolerance relation is such a non-equivalence relation. However, the calculation method of tolerance degree has some limitations. In this paper, known same probability dominant valued tolerance relation is proposed to solve this problem. On this basis, an extended rough set model based on known same probability dominant valued tolerance relation is presented. Some properties of the new model are analyzed. In order to compare the classification performance of different generalized indiscernibility relations, based on the category utility function in cluster analysis, an incomplete category utility function is proposed, which can measure the classification performance of different generalized indiscernibility relations effectively. Experimental results show that the known same probability dominant valued tolerance relation can get better classification results than other generalized indiscernibility relations. 相似文献
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Ping Zhu 《International Journal of Approximate Reasoning》2011,52(3):461-472
Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the coverings themselves, we introduce unary and composition operations on coverings. A notion of homomorphism is provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively. 相似文献
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In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a valued dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of a data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases. 相似文献
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《International Journal of Approximate Reasoning》2014,55(3):867-884
In rough set theory, attribute reduction is a challenging problem in the applications in which data with numbers of attributes available. Moreover, due to dynamic characteristics of data collection in decision systems, attribute reduction will change dynamically as attribute set in decision systems varies over time. How to carry out updating attribute reduction by utilizing previous information is an important task that can help to improve the efficiency of knowledge discovery. In view of that attribute reduction algorithms in incomplete decision systems with the variation of attribute set have not yet been discussed so far. This paper focuses on positive region-based attribute reduction algorithm to solve the attribute reduction problem efficiently in the incomplete decision systems with dynamically varying attribute set. We first introduce an incremental manner to calculate the new positive region and tolerance classes. Consequently, based on the calculated positive region and tolerance classes, the corresponding attribute reduction algorithms on how to compute new attribute reduct are put forward respectively when an attribute set is added into and deleted from the incomplete decision systems. Finally, numerical experiments conducted on different data sets from UCI validate the effectiveness and efficiency of the proposed algorithms in incomplete decision systems with the variation of attribute set. 相似文献
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In this paper, we investigate whether consistent mappings can be used as homomorphism mappings between a covering based approximation space and its image with respect to twenty-two pairs of covering upper and lower approximation operators. We also consider the problem of constructing such mappings and minimizing them. In addition, we investigate the problem of reducing the data volume using consistent mappings as well as the maximum amount of their compressibility. We also apply our algorithms against several datasets. 相似文献
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Laurence Kirby 《Mathematical Logic Quarterly》2010,56(6):631-642
A survey of the isomorphic submodels of Vω, the set of hereditarily finite sets. In the usual language of set theory, Vω has 2?0 isomorphic submodels. But other set‐theoretic languages give different systems of submodels. For example, the language of adjunction allows only countably many isomorphic submodels of Vω (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献