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Journal articles on the topic 'Reduct'

Author: Grafiati

Published: 4 June 2025

Last updated: 23 June 2025

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1

Quang, Nguyen Ba, Nguyen Long Giang, and Dang Thi Oanh. "A DISTANCE BASED INCREMENTAL FILTER-WRAPPER ALGORITHM FOR FINDING REDUCT IN INCOMPLETE DECISION TABLES." Vietnam Journal of Science and Technology 57, no. 4 (2019): 499. http://dx.doi.org/10.15625/2525-2518/57/4/13773.

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Tolerance rough set model is an effective tool for attribute reduction in incomplete decision tables. In recent years, some incremental algorithms have been proposed to find reduct of dynamic incomplete decision tables in order to reduce computation time. However, they are classical filter algorithms, in which the classification accuracy of decision tables is computed after obtaining reduct. Therefore, the obtained reducts of these algorithms are not optimal on cardinality of reduct and classification accuracy. In this paper, we propose the incremental filter-wrapper algorithm IDS_IFW_AO to find one reduct of an incomplete desision table in case of adding multiple objects. The experimental results on some sample datasets show that the proposed filter-wrapper algorithm IDS_IFW_AO is more effective than the filter algorithm IARM-I [17] on classification accuracy and cardinality of reduct

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2

Chen, Qing, Taihua Xu, and Jianjun Chen. "Attribute Reduction Based on Lift and Random Sampling." Symmetry 14, no. 9 (2022): 1828. http://dx.doi.org/10.3390/sym14091828.

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As one of the key topics in the development of neighborhood rough set, attribute reduction has attracted extensive attentions because of its practicability and interpretability for dimension reduction or feature selection. Although the random sampling strategy has been introduced in attribute reduction to avoid overfitting, uncontrollable sampling may still affect the efficiency of search reduct. By utilizing inherent characteristics of each label, Multi-label learning with Label specIfic FeaTures (Lift) algorithm can improve the performance of mathematical modeling. Therefore, here, it is attempted to use Lift algorithm to guide the sampling for reduce the uncontrollability of sampling. In this paper, an attribute reduction algorithm based on Lift and random sampling called ARLRS is proposed, which aims to improve the efficiency of searching reduct. Firstly, Lift algorithm is used to choose the samples from the dataset as the members of the first group, then the reduct of the first group is calculated. Secondly, random sampling strategy is used to divide the rest of samples into groups which have symmetry structure. Finally, the reducts are calculated group-by-group, which is guided by the maintenance of the reducts’ classification performance. Comparing with other 5 attribute reduction strategies based on rough set theory over 17 University of California Irvine(UCI) datasets, experimental results show that: (1) ARLRS algorithm can significantly reduce the time consumption of searching reduct; (2) the reduct derived from ARLRS algorithm can provide satisfying performance in classification tasks.

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3

Sil, Jaya, and Asit Kr Das. "Variable Length Reduct Vs. Minimum Length Reduct-A Comparative study." Procedia Technology 4 (2012): 58–68. http://dx.doi.org/10.1016/j.protcy.2012.05.007.

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4

Shao, Ming-Wen, and Yee Leung. "Relations between granular reduct and dominance reduct in formal contexts." Knowledge-Based Systems 65 (July 2014): 1–11. http://dx.doi.org/10.1016/j.knosys.2014.03.006.

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5

Demetrovics, János, Hoang Minh Quang, Vu Duc Thi, and Nguyen Viet Anh. "An Efficient Method to Reduce the Size of Consistent Decision Tables." Acta Cybernetica 23, no. 4 (2018): 1039–54. http://dx.doi.org/10.14232/actacyb.23.4.2018.4.

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Finding reductions from decision tables is one of the main objectives in information processing. Many studies focus on attribute reduct that reduces the number of columns in the decision table. The problem of finding all attribute reducts of consistent decision table is exponential in the number of attributes. In this paper, we aim at finding solutions for the problem of decision table reduction in polynomial time. More specifically, we deal with both the object reduct problem and the attribute reduct problem in consistent decision tables. We proved theoretically that our proposed methods for the two problems run in polynomial time. The proposed methods can be combined to significantly reduce the size of a consistent decision table both horizontally and vertically.

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6

Giang, Nguyen Long, Demetrovics Janos, Vu Duc Thi, and Phan Dang Khoa. "Some Properties Related to Reduct of Consistent Decision Systems." Cybernetics and Information Technologies 21, no. 2 (2021): 3–9. http://dx.doi.org/10.2478/cait-2021-0015.

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Abstract Reduct of decision systems is the topic that has been attracting the interest of many researchers in data mining and machine learning for more than two decades. So far, many algorithms for finding reduct of decision systems by rough set theory have been proposed. However, most of the proposed algorithms are heuristic algorithms that find one reduct with the best classification quality. The complete study of properties of reduct of decision systems is limited. In this paper, we discover equivalence properties of reduct of consistent decision systems related to a Sperner-system. As the result, the study of the family of reducts in a consistent decision system is the study of Sperner-systems.

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7

Kudo, Yasuo, and Tetsuya Murai. "An Evaluation Method of Relative Reducts Based on Roughness of Partitions." International Journal of Cognitive Informatics and Natural Intelligence 4, no. 2 (2010): 50–62. http://dx.doi.org/10.4018/jcini.2010040104.

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This paper focuses on rough set theory which provides mathematical foundations of set-theoretical approximation for concepts, as well as reasoning about data. Also presented in this paper is the concept of relative reducts which is one of the most important notions for rule generation based on rough set theory. In this paper, from the viewpoint of approximation, the authors introduce an evaluation criterion for relative reducts using roughness of partitions that are constructed from relative reducts. The proposed criterion evaluates each relative reduct by the average of coverage of decision rules based on the relative reduct, which also corresponds to evaluate the roughness of partition constructed from the relative reduct,

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8

Han, Su-Qing, and Jue Wang. "Reduct and attribute order." Journal of Computer Science and Technology 19, no. 4 (2004): 429–49. http://dx.doi.org/10.1007/bf02944745.

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9

Thang, Nguyen Truong, Giang Long Nguyen, Hoang Viet Long, Nguyen Anh Tuan, Tuan Manh Tran, and Ngo Duy Tan. "Efficient Algorithms for Dynamic Incomplete Decision Systems." International Journal of Data Warehousing and Mining 17, no. 3 (2021): 44–67. http://dx.doi.org/10.4018/ijdwm.2021070103.

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Attribute reduction is a crucial problem in the process of data mining and knowledge discovery in big data. In incomplete decision systems, the model using tolerance rough set is fundamental to solve the problem by computing the redact to reduce the execution time. However, these proposals used the traditional filter approach so that the reduct was not optimal in the number of attributes and the accuracy of classification. The problem is critical in the dynamic incomplete decision systems which are more appropriate for real-world applications. Therefore, this paper proposes two novel incremental algorithms using the combination of filter and wrapper approach, namely IFWA_ADO and IFWA_DEO, respectively, for the dynamic incomplete decision systems. The IFWA_ADO computes reduct incrementally in cases of adding multiple objects while IFWA_DEO updates reduct when removing multiple objects. These algorithms are also verified on six data sets. Experimental results show that the filter-wrapper algorithms get higher performance than the other filter incremental algorithms.

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10

Caballero, Yailé, Delia Álvarez, Analay Baltá, Rafael Bello, and María García. "A new algorithm for feature selection based on rough sets theory." Revista Facultad de Ingeniería Universidad de Antioquia, no. 41 (March 31, 2014): 132–44. http://dx.doi.org/10.17533/udea.redin.19021.

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Rough Sets Theory has opened new trends for the development of data analysis techniques. In this theory, the notion of reduct is very significant, but obtaining a reduct in a decision system is an expensive computing process although very important in data analysis and new discoveries. Because of this, it has been necessary to develop different variants to calculate reducts. The present work looks into the utility that offers Rough Sets in feature selection and a new method is presented with the purpose of calculate a good reduct. This new method consists of a greedy algorithm that uses heuristics to work out a good reduct in acceptable times. Experimental results obtained by using different data sets are presented.

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11

Yan, Wangwang, Yan Chen, Jinlong Shi, Hualong Yu, and Xibei Yang. "Ensemble and Quick Strategy for Searching Reduct: A Hybrid Mechanism." Information 12, no. 1 (2021): 25. http://dx.doi.org/10.3390/info12010025.

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Attribute reduction is commonly referred to as the key topic in researching rough set. Concerning the strategies for searching reduct, though various heuristics based forward greedy searchings have been developed, most of them were designed for pursuing one and only one characteristic which is closely related to the performance of reduct. Nevertheless, it is frequently expected that a justifiable searching should explicitly involves three main characteristics: (1) the process of obtaining reduct with low time consumption; (2) generate reduct with high stability; (3) acquire reduct with competent classification ability. To fill such gap, a hybrid based searching mechanism is designed, which takes the above characteristics into account. Such a mechanism not only adopts multiple fitness functions to evaluate the candidate attributes, but also queries the distance between attributes for determining whether two or more attributes can be added into the reduct simultaneously. The former may be useful in deriving reduct with higher stability and competent classification ability, and the latter may contribute to the lower time consumption of deriving reduct. By comparing with 5 state-of-the-art algorithms for searching reduct, the experimental results over 20 UCI data sets demonstrate the effectiveness of our new mechanism. This study suggests a new trend of attribute reduction for achieving a balance among various characteristics.

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Yan, Wangwang, Yan Chen, Jinlong Shi, Hualong Yu, and Xibei Yang. "Ensemble and Quick Strategy for Searching Reduct: A Hybrid Mechanism." Information 12, no. 1 (2021): 25. http://dx.doi.org/10.3390/info12010025.

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Attribute reduction is commonly referred to as the key topic in researching rough set. Concerning the strategies for searching reduct, though various heuristics based forward greedy searchings have been developed, most of them were designed for pursuing one and only one characteristic which is closely related to the performance of reduct. Nevertheless, it is frequently expected that a justifiable searching should explicitly involves three main characteristics: (1) the process of obtaining reduct with low time consumption; (2) generate reduct with high stability; (3) acquire reduct with competent classification ability. To fill such gap, a hybrid based searching mechanism is designed, which takes the above characteristics into account. Such a mechanism not only adopts multiple fitness functions to evaluate the candidate attributes, but also queries the distance between attributes for determining whether two or more attributes can be added into the reduct simultaneously. The former may be useful in deriving reduct with higher stability and competent classification ability, and the latter may contribute to the lower time consumption of deriving reduct. By comparing with 5 state-of-the-art algorithms for searching reduct, the experimental results over 20 UCI data sets demonstrate the effectiveness of our new mechanism. This study suggests a new trend of attribute reduction for achieving a balance among various characteristics.

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13

Min, Won Keun. "Attribute Reduction in Soft Contexts Based on Soft Sets and Its Application to Formal Contexts." Mathematics 8, no. 5 (2020): 689. http://dx.doi.org/10.3390/math8050689.

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We introduce the notion of the reduct of soft contexts, which is a special notion of a consistent set for soft contexts. Then, we study its properties and show that this notion is well explained by the two classes, 1 0 and 2 0 , of independent attributes. In particular, we describe in detail how to extract a reduct from a given consistent set. Then, based on this extraction process, we propose a six-step method for constructing a reduct from a given consistent set. Additionally, to apply this method to formal contexts, we examine the relationship between the reducts of a given formal context and the reducts of the associated soft context. We finally illustrate the process of obtaining reducts in a formal context using this relationship and the six-step method using an example.

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14

Chen, Yan, Jingjing Song, Keyu Liu, Yaojin Lin, and Xibei Yang. "Combined Accelerator for Attribute Reduction: A Sample Perspective." Mathematical Problems in Engineering 2020 (February 19, 2020): 1–13. http://dx.doi.org/10.1155/2020/2350627.

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In the field of neighborhood rough set, attribute reduction is considered as a key topic. Neighborhood relation and rough approximation play crucial roles in the process of obtaining the reduct. Presently, many strategies have been proposed to accelerate such process from the viewpoint of samples. However, these methods speed up the process of obtaining the reduct only from binary relation or rough approximation, and then the obtained results in time consumption may not be fully improved. To fill such a gap, a combined acceleration strategy based on compressing the scanning space of both neighborhood and lower approximation is proposed, which aims to further reduce the time consumption of obtaining the reduct. In addition, 15 UCI data sets have been selected, and the experimental results show us the following: (1) our proposed approach significantly reduces the elapsed time of obtaining the reduct; (2) compared with previous approaches, our combined acceleration strategy will not change the result of the reduct. This research suggests a new trend of attribute reduction using the multiple views.

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15

Kudo, Yasuo, and Tetsuya Murai. "Heuristic Algorithm for Attribute Reduction Based on Classification Ability by Condition Attributes." Journal of Advanced Computational Intelligence and Intelligent Informatics 15, no. 1 (2011): 102–9. http://dx.doi.org/10.20965/jaciii.2011.p0102.

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The heuristic algorithm we propose to compute a relative reduct candidate is based on evaluating classification ability of condition attributes. Considering the discernibility and equivalence of objects for condition attributes in relative reducts, we introduce evaluation criteria for condition attributes and relative reducts. The computational complexity of the proposed algorithm isO(|U|2|C|2). Experimental results indicate that our algorithm often generates a relative reduct producing a good evaluation result.

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16

Hoang, Quang Minh, Vu Duc Thi, and Nguyen Ngoc San. "Some algorithms related to consistent decision table." Journal of Computer Science and Cybernetics 33, no. 2 (2017): 131–42. http://dx.doi.org/10.15625/1813-9663/33/2/9281.

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Rough set theory is useful mathematical tool developed to deal with vagueness and uncertainty. As an important concept of rough set theory, an attribute reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of the given information table. Rough set theory is also the most popular for generating decision rules from decision table. In this paper, we propose an algorithm finding object reduct of consistent decsion table. On the other hand, we also show an algorithm to find some attribute reducts and the correctness of our algorithms is proof-theoretically. These our algorithms have polynomial time complexity. Our finding object reduct helps other algorithms of finding attribute reducts become more effectively, especially as working with huge consistent decision table.

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17

Li, Hua, Deyu Li, Yanhui Zhai, Suge Wang, and Jing Zhang. "A Variable Precision Attribute Reduction Approach in Multilabel Decision Tables." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/359626.

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Owing to the high dimensionality of multilabel data, feature selection in multilabel learning will be necessary in order to reduce the redundant features and improve the performance of multilabel classification. Rough set theory, as a valid mathematical tool for data analysis, has been widely applied to feature selection (also called attribute reduction). In this study, we propose a variable precision attribute reduct for multilabel data based on rough set theory, calledδ-confidence reduct, which can correctly capture the uncertainty implied among labels. Furthermore, judgement theory and discernibility matrix associated withδ-confidence reduct are also introduced, from which we can obtain the approach to knowledge reduction in multilabel decision tables.

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18

Boonjing, Veera, and Pisit Chanvarasuth. "Efficient Breadth-First Reduct Search." Mathematics 8, no. 5 (2020): 833. http://dx.doi.org/10.3390/math8050833.

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This paper formulates the problem of determining all reducts of an information system as a graph search problem. The search space is represented in the form of a rooted graph. The proposed algorithm uses a breadth-first search strategy to search for all reducts starting from the graph root. It expands nodes in breadth-first order and uses a pruning rule to decrease the search space. It is mathematically shown that the proposed algorithm is both time and space efficient.

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19

Zielosko, Beata, and Urszula Stańczyk. "Reduct-based ranking of attributes." Procedia Computer Science 176 (2020): 2576–85. http://dx.doi.org/10.1016/j.procs.2020.09.315.

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20

Jiang, Zehua, Keyu Liu, Jingjing Song, Xibei Yang, Jinhai Li, and Yuhua Qian. "Accelerator for crosswise computing reduct." Applied Soft Computing 98 (January 2021): 106740. http://dx.doi.org/10.1016/j.asoc.2020.106740.

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21

Inbarani, Hannah H., Ahmad Taher Azar, and Bagyamathi Mathiyazhagan. "Hybrid Rough Set With Black Hole Optimization-Based Feature Selection Algorithm for Protein Structure Prediction." International Journal of Sociotechnology and Knowledge Development 14, no. 1 (2022): 1–45. http://dx.doi.org/10.4018/ijskd.290657.

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In this paper, a new approach for hybridizing Rough Set Quick Reduct and Relative Reduct approaches with Black Hole optimization algorithm is proposed. This algorithm is inspired of black holes. A black hole is a region of spacetime where the gravitational field is so strong that nothing— not even light— that enters this region can ever escape from it. Every black hole has a mass and charge. In this Algorithm, each solution of problem is considered as a black hole and gravity force is used for global search and the electrical force is used for local search. The proposed algorithm is compared with leading algorithms such as, Rough Set Quick Reduct, Rough Set Relative Reduct, Rough Set particle swarm optimization based Quick Reduct, Rough Set based PSO Relative Reduct, Rough Set Harmony Search based Quick Reduct, and Rough Set Harmony Search based Relative Reduct.

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22

Phuong, Ho Thi, and Nguyen Long Giang. "Fuzzy distance-based filter-wrapper incremental algorithms for attribute reduction when adding or deleting attribute set." Vietnam Journal of Science and Technology 59, no. 2 (2021): 261–74. http://dx.doi.org/10.15625/2525-2518/59/2/15698.

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Attribute reduction is a critical problem in the data preprocessing step with the aim of minimizing redundant attributes to improve the efficiency of data mining models. The fuzzy rough set theory is considered an effective tool to solve the attribute reduction problem directly on the original decision system, without data preprocessing. With the current digital transformation trend, decision systems are larger in size and updated. To solve the attribute reduction problem directly on change decision systems, a number of recent studies have proposed incremental algorithms to find reducts according to fuzzy rough set approach to reduce execution time. However, the proposed algorithms follow the traditional filter approach. Therefore, the obtained reduct is not optimal in both criteria: the number of attribute of the reducts and the accuracy of classification model. In this paper, we propose incremental algorithms that find reducts following filter-wrapper approach using fuzzy distance measure in the case of adding and deleting attribute set. The experimental results on the sample datasets show that the proposed algorithms significantly reduce the number of attributes in reduct and improve the classification accuracy compared to other algorithms using filter approach

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23

KOWALSKI, PIOTR, and SERGE RANDRIAMBOLOLONA. "STRONGLY MINIMAL REDUCTS OF VALUED FIELDS." Journal of Symbolic Logic 81, no. 2 (2016): 510–23. http://dx.doi.org/10.1017/jsl.2015.61.

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AbstractWe prove that if a strongly minimal nonlocally modular reduct of an algebraically closed valued field of characteristic 0 contains +, then this reduct is bi-interpretable with the underlying field.

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24

Li, Zhanqi, Pan Cheng, Linzi Yin, and Yuyin Guan. "A Recursive Attribute Reduction Algorithm and Its Application in Predicting the Hot Metal Silicon Content in Blast Furnaces." Big Data and Cognitive Computing 9, no. 1 (2025): 6. https://doi.org/10.3390/bdcc9010006.

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For many complex industrial applications, traditional attribute reduction algorithms are often inefficient in obtaining optimal reducts that align with mechanistic analyses and practical production requirements. To solve this problem, we propose a recursive attribute reduction algorithm that calculates the optimal reduct. First, we present the notion of priority sequence to describe the background meaning of attributes and evaluate the optimal reduct. Next, we define a necessary element set to identify the “individually necessary” characteristics of the attributes. On this basis, a recursive algorithm is proposed to calculate the optimal reduct. Its boundary logic is guided by the conflict between the necessary element set and the core attribute set. The experiments demonstrate the proposed algorithm’s uniqueness and its ability to enhance the prediction accuracy of the hot metal silicon content in blast furnaces.

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Ge, Hao, Chuanjian Yang, and Longshu Li. "Positive Region Reduct Based on Relative Discernibility and Acceleration Strategy." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 26, no. 04 (2018): 521–51. http://dx.doi.org/10.1142/s0218488518500253.

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Attribute reduction is one of key issues in rough set theory, and positive region reduct is a classical type of reducts. However, a lot of reduction algorithms have more high time expenses when dealing with high-volume and high-dimensional data sets. To overcome this shortcoming, in this paper, a relative discernibility reduction method based on the simplified decision table of the original decision table is researched for obtaining positive region reduct. Moreover, to further improve performance of reduction algorithm, we develop an accelerator for attribute reduction, which reduces the radix sort times of the reduction process to raise algorithm efficiency. By the accelerator, two positive region reduction algorithms, i.e., FARA-RS and BARA-RS, based on the relative discernibility are designed. FARA-RS simultaneously reduce the size of the universe and the number of radix sort to achieve speedup and BARA-RS only reduce the number of radix sort to achieve acceleration. The experimental results show that the proposed reduction algorithms are effective and feasible for high dimensional and large data sets.

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Huang, Jianxin, Peiqiu Yu та Weikang Li. "Updating the Reduct in Fuzzy β-Covering via Matrix Approaches While Adding and Deleting Some Objects of the Universe". Information 11, № 1 (2019): 3. http://dx.doi.org/10.3390/info11010003.

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Since fuzzy β -covering was proposed, few papers have focused on how to calculate the reduct in fuzzy β -covering and how to update the reduct while adding and deleting some objects of the universe. Here, we propose a matrix-based approach for computing the reduct in a fuzzy β -covering and updating it dynamically using a matrix. First, matrix forms for computing the reduct in a fuzzy β -covering are proposed. Second, properties of the matrix-based approaches are studied while adding and deleting objects. Then, matrix-based algorithms for updating the reduct in a fuzzy β -covering are proposed. Finally, the efficiency and validity of the designed algorithms are verified by experiments.

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butalia, Ayesha, Divya Shah, and Dr R. V. Dharaskar. "Mushroom plant analysis through Reduct Technique." International Journal of Computer Applications 1, no. 5 (2010): 68–73. http://dx.doi.org/10.5120/123-239.

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Upadhyaya, Shuchita, Alka Arora, and Rajni Jain. "Reduct Driven Pattern Extraction from Clusters." International Journal of Computational Intelligence Systems 2, no. 1 (2009): 10. http://dx.doi.org/10.2991/jnmp.2009.2.1.2.

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29

Deng, Tingquan, Chengdong Yang, and Xiaofei Wang. "A reduct derived from feature selection." Pattern Recognition Letters 33, no. 12 (2012): 1638–46. http://dx.doi.org/10.1016/j.patrec.2012.03.028.

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Upadhyaya, Shuchita, Alka Arora, and Rajni Jain. "Reduct Driven Pattern Extraction from Clusters." International Journal of Computational Intelligence Systems 2, no. 1 (2009): 10–16. http://dx.doi.org/10.1080/18756891.2009.9727635.

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31

Wang, Jiayang. "The Feature Core of Dynamic Reduct." Applied Mathematics 03, no. 05 (2012): 484–88. http://dx.doi.org/10.4236/am.2012.35073.

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Uma, Shankar Rao Erothi, and Rodda Sireesha. "Reduct ECOC Framework for Network Intrusion Detection System." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 3 (2020): 258–66. https://doi.org/10.35940/ijeat.B4238.029320.

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Now a day’s network security is major concern for e-government and e-commerce applications. A wide range of malicious activities are increasing with the usage of internet and network technologies. Identifying novel threats and finding modern solutions for network to prevent from these threats are important. Designing an effective intrusion detection system is significant to continuously look out the network activities to efficiently thwart malicious attacks or to identify the intruders. To tackle multi class imbalance classification problem in networks, a reduct based ECOC ensemble framework for NIDS is proposed to efficiently identify attacks in a multi class scenario. The Reduct-ECOC classifier is validated on highly imbalanced benchmark NSL-KDD intrusion datasets as well as other UCI-ML datasets. The experimental results on eight highly imbalanced datasets show that Reduct-ECOC classifier performs better than many other state-of-art multi-class classification ECOC learning methods.

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Khoa, Phan Dang, Janos Demetrovics, Vu Duc Thi, and Pham Viet Anh. "Some NP-Complete Problems for Attribute Reduction in Consistent Decision Tables." Serdica Journal of Computing 14, no. 1-2 (2021): 27–41. http://dx.doi.org/10.55630/sjc.2020.14.27-41.

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Over recent years, the research of attribute reduction for general decision systems and, in particular, for consistent decision tables has attracted great attention from the computer science community due to the emerge of big data. It has been known that, for a consistent decision table, we can derive a polynomial time complexity algorithm for finding a reduct. In addition, finding redundant properties can also be done in polynomial time. However, finding all reduct sets in a consistent decision table is a problem with exponential time complexity. In this paper, we study complexity of the problem for finding a certain class of reduct sets. In particular, we make use of a new concept of relative reduct in the consistent decision table. We present two NP-complete problems related to the proposed concept. These problems are related to the cardinality constraint and the relative reduct set. On the basis of this result, we show that finding a reduct with the smallest cardinality cannot be done by an algorithm with polynomial time complexity.

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Truong, Do Si, Lam Thanh Hien, and Nguyen Thanh Tung. "AN EFFECTIVE ALGORITHM FOR COMPUTING REDUCTS IN DECISION TABLES." Journal of Computer Science and Cybernetics 38, no. 3 (2022): 277–92. http://dx.doi.org/10.15625/1813-9663/38/3/17450.

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Attribute reduction is one important part researched in rough set theory. A reduct from a decision table is a minimal subset of the conditional attributes which provide the same information for classification purposes as the entire set of available attributes. The classification task for the high dimensional decision table could be solved faster if a reduct, instead of the original whole set of attributes, is used. In this paper, we propose a reduct computing algorithm using attribute clustering. The proposed algorithm works in three main stages. In the first stage, irrelevant attributes are eliminated. In the second stage relevant attributes are divided into appropriately selected number of clusters by Partitioning Around Medoids (PAM) clustering method integrated with a special metric in attribute space which is the normalized variation of information. In the third stage, the representative attribute from each cluster is selected that is the most class-related. The selected attributes form the approximate reduct. The proposed algorithm is implemented and experimented. The experimental results show that the proposed algorithm is capable of computing approximate reduct with small size and high classification accuracy, when the number of clusters used to group the attributes is appropriately selected.

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Chen, Yen-Liang, and Fang-Chi Chi. "Summarization of information systems based on rough set theory." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 1001–15. http://dx.doi.org/10.3233/jifs-201160.

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In the rough set theory proposed by Pawlak, the concept of reduct is very important. The reduct is the minimum attribute set that preserves the partition of the universe. A great deal of research in the past has attempted to reduce the representation of the original table. The advantage of using a reduced representation table is that it can summarize the original table so that it retains the original knowledge without distortion. However, using reduct to summarize tables may encounter the problem of the table still being too large, so users will be overwhelmed by too much information. To solve this problem, this article considers how to further reduce the size of the table without causing too much distortion to the original knowledge. Therefore, we set an upper limit for information distortion, which represents the maximum degree of information distortion we allow. Under this upper limit of distortion, we seek to find the summary table with the highest compression. This paper proposes two algorithms. The first is to find all summary tables that satisfy the maximum distortion constraint, while the second is to further select the summary table with the greatest degree of compression from these tables.

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Yang, Tian, Zhaowen Li, and Xiaoqing Yang. "A Granular Reduction Algorithm Based on Covering Rough Sets." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/970576.

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The granular reduction is to delete dispensable elements from a covering. It is an efficient method to reduce granular structures and get rid of the redundant information from information systems. In this paper, we develop an algorithm based on discernability matrixes to compute all the granular reducts of covering rough sets. Moreover, a discernibility matrix is simplified to the minimal format. In addition, a heuristic algorithm is proposed as well such that a granular reduct is generated rapidly.

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Ferone, Alessio, and Antonio Maratea. "Adaptive Quick Reduct for Feature Drift Detection." Algorithms 14, no. 2 (2021): 58. http://dx.doi.org/10.3390/a14020058.

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Data streams are ubiquitous and related to the proliferation of low-cost mobile devices, sensors, wireless networks and the Internet of Things. While it is well known that complex phenomena are not stationary and exhibit a concept drift when observed for a sufficiently long time, relatively few studies have addressed the related problem of feature drift. In this paper, a variation of the QuickReduct algorithm suitable to process data streams is proposed and tested: it builds an evolving reduct that dynamically selects the relevant features in the stream, removing the redundant ones and adding the newly relevant ones as soon as they become such. Tests on five publicly available datasets with an artificially injected drift have confirmed the effectiveness of the proposed method.

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Yanagisawa, Hideyoshi, and Shuichi Fukuda. "Interactive Reduct Evolutional Computation for Aesthetic Design." Journal of Computing and Information Science in Engineering 5, no. 1 (2005): 1–7. http://dx.doi.org/10.1115/1.1846055.

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We propose a method of evolving designs based on the user’s personal preferences. The method works through an interaction between the user and a computer system. The method’s objective is to help the customer to set design parameters via a simple evaluation of displayed samples. An important feature is that the design attributes to which the user pays more attention (favored features) are estimated using reducts in rough set theory and reflected when refining the design. New design candidates are generated by the user’s evaluation of design samples generated at random. The values of attributes estimated as favored features are fixed in the refined samples, while other attributes are generated at random. This interaction continues until the samples converge to a satisfactory design. In this manner, the design process efficiently evaluates personal and subjective preferences. The method is applied to design a 3D cylinder model such as a cup or vase. The method is then compared with an Interactive GA.

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Jia, Xiuyi, Lin Shang, Bing Zhou, and Yiyu Yao. "Generalized attribute reduct in rough set theory." Knowledge-Based Systems 91 (January 2016): 204–18. http://dx.doi.org/10.1016/j.knosys.2015.05.017.

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Blok, W. J. "On interpretations of varieties with semilattice reduct." Algebra Universalis 27, no. 2 (1990): 299–303. http://dx.doi.org/10.1007/bf01182463.

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Zhao, Xianzhong. "Idempotent semirings with a commutative additive reduct." Semigroup Forum 64, no. 2 (2001): 289–96. http://dx.doi.org/10.1007/s002330010048.

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Ganesan, Jothi, Hannah H. Inbarani, Ahmad Taher Azar, and Kemal Polat. "Tolerance rough set firefly-based quick reduct." Neural Computing and Applications 28, no. 10 (2016): 2995–3008. http://dx.doi.org/10.1007/s00521-016-2514-2.

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Gao, Yuan, Xiangjian Chen, Xibei Yang, Pingxin Wang, and Jusheng Mi. "Ensemble-Based Neighborhood Attribute Reduction: A Multigranularity View." Complexity 2019 (November 11, 2019): 1–17. http://dx.doi.org/10.1155/2019/2048934.

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Recently, multigranularity has been an interesting topic, since different levels of granularity can provide different information from the viewpoint of Granular Computing (GrC). However, established researches have focused less on investigating attribute reduction from multigranularity view. This paper proposes an algorithm based on the multigranularity view. To construct a framework of multigranularity attribute reduction, two main problems can be addressed as follows: (1) The multigranularity structure can be constructed firstly. In this paper, the multigranularity structure will be constructed based on the radii, as different information granularities can be induced by employing different radii. Therefore, the neighborhood-based multigranularity can be constructed. (2) The attribute reduction can be designed and realized from the viewpoint of multigranularity. Different from traditional process which computes reduct through employing a fixed granularity, our algorithm aims to obtain reduct from the viewpoint of multigranularity. To realize the new algorithm, two main processes are executed as follows: (1) Considering that different decision classes may require different key condition attributes, the ensemble selector is applied among different decision classes; (2) to accelerate the process of attribute reduction, only the finest and the coarsest granularities are employed. The experiments over 15 UCI data sets are conducted. Compared with the traditional single-granularity approach, the multigranularity algorithm can not only generate reduct which can provide better classification accuracy, but also reduce the elapsed time. This study suggests new trends for considering both the classification accuracy and the time efficiency with respect to the reduct.

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Demetrovics, János, Vu Duc Thi, Nguyen Long Giang, and Tran Huy Duong. "On the Time Complexity of the Problem Related to Reducts of Consistent Decision Tables." Serdica Journal of Computing 9, no. 2 (2016): 167–76. http://dx.doi.org/10.55630/sjc.2015.9.167-176.

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In recent years, rough set approach computing issues concerning reducts of decision tables have attracted the attention of many researchers. In this paper, we present the time complexity of an algorithmcomputing reducts of decision tables by relational database approach. LetDS = (U, C ∪ {d}) be a consistent decision table, we say that A ⊆ C is arelative reduct of DS if A contains a reduct of DS. Let s = <C ∪ {d} , F>be a relation schema on the attribute set C ∪ {d}, we say that A ⊆ C isa relative minimal set of the attribute d if A contains a minimal set of d.Let Qd be the family of all relative reducts of DS, and Pd be the family ofall relative minimal sets of the attribute d on s. We prove that the problem whether Qd ⊆ Pd is co-NP-complete. However, the problem whether Pd ⊆ Qd is in P .

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Ognjenovic, Visnja, Vladimir Brtka, Jelena Stojanov, Eleonora Brtka, and Ivana Berkovic. "The Cuts Selection Method Based on Histogram Segmentation and Impact on Discretization Algorithms." Entropy 24, no. 5 (2022): 675. http://dx.doi.org/10.3390/e24050675.

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The preprocessing of data is an important task in rough set theory as well as in Entropy. The discretization of data as part of the preprocessing of data is a very influential process. Is there a connection between the segmentation of the data histogram and data discretization? The authors propose a novel data segmentation technique based on a histogram with regard to the quality of a data discretization. The significance of a cut’s position has been researched on several groups of histograms. A data set reduct was observed with respect to the histogram type. Connections between the data histograms and cuts, reduct and the classification rules have been researched. The result is that the reduct attributes have a more irregular histogram than attributes out of the reduct. The following discretization algorithms were used: the entropy algorithm and the Maximal Discernibility algorithm developed in rough set theory. This article presents the Cuts Selection Method based on histogram segmentation, reduct of data and MD algorithm of discretization. An application on the selected database shows that the benefits of a selection of cuts relies on histogram segmentation. The results of the classification were compared with the results of the Naïve Bayes algorithm.

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Tan, Hai Zhong. "A New Criterion for Attribute Reduction Based on Variable Precision Rough Set Model." Applied Mechanics and Materials 121-126 (October 2011): 1579–84. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.1579.

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The rule set which is acquired based on rough set theory can be classified into two categories: deterministic rules and probabilistic rules. Traditional attribute reduction definitions in variable precision rough set model cannot guarantee the rule properties, namely deterministic or probabilistic. In this paper, a new criterion for attribute reduction is put forward based on variable precision rough set model. The rule properties can be preserved during the process of attribute reduction. The relationships between the new reduct definition and available definitions, including Ziarko’s reduct definition and β lower distribution reduct definition are also discussed.

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Nübling, Herwig. "Reducts of stable, CM-trivial theories." Journal of Symbolic Logic 70, no. 4 (2005): 1025–36. http://dx.doi.org/10.2178/jsl/1129642113.

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Wang, Jin, Yuxin Liu, Jianjun Chen, and Xibei Yang. "An Ensemble Framework to Forest Optimization Based Reduct Searching." Symmetry 14, no. 6 (2022): 1277. http://dx.doi.org/10.3390/sym14061277.

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Essentially, the solution to an attribute reduction problem can be viewed as a reduct searching process. Currently, among various searching strategies, meta-heuristic searching has received extensive attention. As a new emerging meta-heuristic approach, the forest optimization algorithm (FOA) is introduced to the problem solving of attribute reduction in this study. To further improve the classification performance of selected attributes in reduct, an ensemble framework is also developed: firstly, multiple reducts are obtained by FOA and data perturbation, and the structure of those multiple reducts is symmetrical, which indicates that no order exists among those reducts; secondly, multiple reducts are used to execute voting classification over testing samples. Finally, comprehensive experiments on over 20 UCI datasets clearly validated the effectiveness of our framework: it is not only beneficial to output reducts with superior classification accuracies and classification stabilities but also suitable for data pre-processing with noise. This improvement work we have performed makes the FOA obtain better benefits in the data processing of life, health, medical and other fields.

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Giang, Nguyen Long, Le Hoang Son, Nguyen Anh Tuan, Tran Thi Ngan, Nguyen Nhu Son, and Nguyen Truong Thang. "Filter-Wrapper Incremental Algorithms for Finding Reduct in Incomplete Decision Systems When Adding and Deleting an Attribute Set." International Journal of Data Warehousing and Mining 17, no. 2 (2021): 39–62. http://dx.doi.org/10.4018/ijdwm.2021040103.

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The tolerance rough set model is an effective tool to solve attribute reduction problem directly on incomplete decision systems without pre-processing missing values. In practical applications, incomplete decision systems are often changed and updated, especially in the case of adding or removing attributes. To solve the problem of finding reduct on dynamic incomplete decision systems, researchers have proposed many incremental algorithms to decrease execution time. However, the proposed incremental algorithms are mainly based on filter approach in which classification accuracy was calculated after the reduct has been obtained. As the results, these filter algorithms do not get the best result in term of the number of attributes in reduct and classification accuracy. This paper proposes two distance based filter-wrapper incremental algorithms: the algorithm IFWA_AA in case of adding attributes and the algorithm IFWA_DA in case of deleting attributes. Experimental results show that proposed filter-wrapper incremental algorithm IFWA_AA decreases significantly the number of attributes in reduct and improves classification accuracy compared to filter incremental algorithms such as UARA, IDRA.

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Shi, Ying, Hui Qi, Xiaofang Mu, and Mingxing Hou. "Adjustable Fuzzy Rough Reduction: A Nested Strategy." Computational Intelligence and Neuroscience 2021 (July 22, 2021): 1–15. http://dx.doi.org/10.1155/2021/5513722.

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As a crucial extension of Pawlak's rough set, a fuzzy rough set has been successfully applied in real-valued attribute reduction. Nevertheless, the traditional fuzzy rough set is not provided with adjustable ability due to the maximal and minimal operators. It follows that the associated measure for attribute evaluation is not always appropriate. To alleviate such problems, a novel adjustable fuzzy rough set model is presented and further introduced into the parameterized attribute reduction. Additionally, the inner relationship between the appointed parameter and the reduct result is discovered, and thereby a nested mechanism is adopted to accelerate the searching procedure of reduct. Experiments demonstrate that the proposed heuristic algorithm can offer us more stable reducts with higher computational efficiency as compared with the traditional approaches.

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