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With the continuous expansion of databases, the extraction of information has been an urgent research topic in many fields. As an effective method to remove redundant attributes, attribute reduction demonstrates extraordinary ability in simplifying information systems. This paper applies a novel form of conditional entropy to investigate the attribute reduction in incomplete information systems. Firstly, a novel definition of conditional entropy is introduced based on tolerance relation. Additionally, in order to reduce time complexity, we propose a binsearch heuristic attribute-reduction algorithm with conditional entropy as heuristic knowledge. Furthermore, two examples are used to illustrate the feasibility and validity of the reduction algorithm. [ABSTRACT FROM AUTHOR]

Factor selection is crucial for any enterprise to make a quick and accurate quotation decision. For the objects of quotation with missing values, traditional rough sets construct their relations (e.g. tolerance, cover) either with objects having known values, or only with those that also include the missing values of the attribute domains. Such classifications may not work well for reduction in many real-world problems. In this paper, by measuring the similarity of objects, an incomplete covering rough set is proposed to derive a cover for attribute reduction. Firstly, a similarity relation is defined by an approximation degree that tunes the relation in line with the semantics of objects, and then a cover is induced. Secondly, a reduct is derived by the relations of objects with respect to covers; the properties of reduction are proven. Finally, an approach is developed by discernibility matrix. The experimental results of the UCI (University of California Irvine) Repository and real-life quotation data sets show the incomplete covering rough set outperforms the compared rough set in the accuracy of factor selection within the comparable computation time. It is also demonstrated that the proposed quotation model is effective in quote prediction with various proportions of missing data. [ABSTRACT FROM AUTHOR]

With the continuous expansion of databases, the extraction of information has been an urgent research topic in many fields. As an effective method to remove redundant attributes, attribute reduction demonstrates extraordinary ability in simplifying information systems. This paper applies a novel form of conditional entropy to investigate the attribute reduction in incomplete information systems. Firstly, a novel definition of conditional entropy is introduced based on tolerance relation. Additionally, in order to reduce time complexity, we propose a binsearch heuristic attribute-reduction algorithm with conditional entropy as heuristic knowledge. Furthermore, two examples are used to illustrate the feasibility and validity of the reduction algorithm.

Copyright of Journal of Data Acquisition & Processing / Shu Ju Cai Ji Yu Chu Li is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Knowledge reduction of information systems is one of the most important parts of rough set theory in real-world applications. Based on the connections between the rough set theory and the theory of topology, a kind of topological reduction of incomplete information systems is discussed. In this study, the topological reduction of incomplete information systems is characterized by belief and plausibility functions from evidence theory. First, we present that a topological space induced by a pair of approximation operators in an incomplete information system is pseudo-discrete, which deduces a partition. Then, the topological reduction is characterized by the belief and plausibility function values of the sets in the partition. A topological reduction algorithm for computing the topological reducts in incomplete information systems is also proposed based on evidence theory, and its efficiency is examined by an example. Moreover, relationships among the concepts of topological reduct, classical reduct, belief reduct, and plausibility reduct of an incomplete information system are presented.

Aiming at the problems of filling missing information and calculating conditional probability and loss function in incomplete information systems, this paper provides a novel three-way decision model based on incomplete information systems. Firstly, a new information table is obtained by filling in the missing information based on similarity, and the conditional probability calculation method is established by the idea of a TOPSIS combination with the information table. The relative loss function is calculated based on the risk avoidance coefficient under different attributes. Then, we propose the notion of interval relative loss function and give formulae to calculate the interval relative loss function values. In particular, the key steps of constructing the three-way decision model are summarized. Finally, a case study of medical diagnosis is provided to verify the validity of the proposed method. Moreover, the rationality and superiority of the presented method are verified by sensitivity analysis and comparative analysis. [ABSTRACT FROM AUTHOR]

With databases growing at an unrelenting rate, it may be difficult and complex to extract statistics by accessing all of the data in many practical problems. Attribute reduction, as an effective method to remove redundant attributes from massive data, has demonstrated its remarkable capability in simplifying information systems. In this paper, we concentrate on reducing attributes in incomplete information systems. We introduce a novel definition of a binary similarity matrix and present a method to calculate the significance of attributes in correspondence. Secondly, We develop a heuristic attribute reduction algorithm using a binary similarity matrix and attribute significance as heuristic knowledge. In addition, we use a numerical example to showcase the practicality and accuracy of the algorithm. In conclusion, we demonstrate through comparative analysis that our algorithm outperforms some existing attribute reduction methods. [ABSTRACT FROM AUTHOR]

Telecom fraud detection is of great significance in online social networks. Yet the massive, redundant, incomplete, and uncertain network information makes it a challenging task to handle. Hence, this paper mainly uses the correlation of attributes by entropy function to optimize the data quality and then solves the problem of telecommunication fraud detection with incomplete information. First, to filter out redundancy and noise, we propose an attribute reduction algorithm based on max-correlation and max-independence rate (MCIR) to improve data quality. Then, we design a rough-gain anomaly detection algorithm (MCIR-RGAD) using the idea of maximal consistent blocks to deal with missing incomplete data. Finally, the experimental results on authentic telecommunication fraud data and UCI data show that the MCIR-RGAD algorithm provides an effective solution for reducing the computation time, improving the data quality, and processing incomplete data. [ABSTRACT FROM AUTHOR]

Dealing with an incomplete information has been a major issue in the theory of soft sets. In this paper, we have presented an approach to deal with incomplete soft set, incomplete fuzzy soft set and incomplete intuitionistic fuzzy soft set. For this purpose, we have introduced the notion of distance between two objects (parameters) which will be used to compute the degree of interdependence between them. This approach will use the full information of known data and the relationships between them. Data filling converts an incomplete soft set into a complete one which makes the soft sets applicable not only to decision making but also to other fields. [ABSTRACT FROM AUTHOR]

Decision-making problem is a fundamental activity in human life every day. Regarding group decision-making, individuals have insufficient comprehension of the decision objects owing to the limited experience and knowledge and drawback the evaluation process. Therefore, the evaluation information is missing and the group cannot get the precise information for decision objects resulting in the generation of incomplete information systems. It is meaningful for individuals finding an approach to Leverage and tap into existing information. On the basis, the work presented in this paper focuses on group decision-making problems (GDM) with incomplete information. Under the framework of group decision-making, a GDM approach with an incomplete information system is presented combining the formal concept analysis and rough set theory. Firstly, we propose a concept called formal decision context and discuss the properties of the formal decision context, which could divide the incomplete information system into many cognitive units, and the definitions of cognitive units will be given. Then, the property and the relations of various cognitive units will be discussed. Additionally, the upper and lower approximation space under the formal decision context is founded considering the risk attitudes integrating fuzzy rough set and formal concept context. Considering the order relation of various cognitive units and decision objects, we introduce the dominance relation and the importance degree of each cognitive unit under the framework of formal decision context. Furthermore, a theoretical framework of the multi-criteria decision-making problem is presented and two models for the multi-criteria group decision-making problem are discussed combined with fuzzy rough set and formal decision context from two perspectives, including qualitative analysis and quantitative analysis. Finally, an illustrated example is applied to verify the validity and effectiveness of the proposed models. The contributions of this paper include two aspects. On the one hand, this paper provides a new perspective and paradigm considering MCGDM problems with the incomplete information system from the perspective of group consensus. On the other hand, this paper gives two approaches for group decision-making problems from sorting and set theory by the perspective of multi-granular rough set and group consensus. • A model of formal decision context with incomplete information to describe the cognitive situation. • An approach to MCDM problem combined rough set with formal decision context with incomplete information. • Two approaches to MCGDM problem from qualitative analysis and quantitative analysis. [ABSTRACT FROM AUTHOR]

As a new method of granular computing, the three-way decision (3WD) approach has unique advantages in handling uncertain and imprecise problems. Based on decision-theoretic rough sets (DTRSs) and Bayesian minimum risk theory, conditional probability and loss function are the key research issues in 3WD. Many approaches for handling deterministic and complete information have been developed. However, few studies have focused on the construction of an intuitionistic fuzzy three-way decision (IF3WD) model for an intuitionistic fuzzy incomplete information system (IFIIS). In this paper, an IF3WD model based on an IFIIS is proposed to improve the ability to process complex fuzzy incomplete information systems, which extends the application range of the traditional 3WD. Concretely, we first propose a calculation method to measure the degree of information retention of missing data and describe it in two dimensions: coarse-grained and fine-grained. Next, an intuitionistic fuzzy number approximation (IFNA) strategy for missing data is presented. Then, a loss function with three states is given. Furthermore, combined with the Choquet integral, the interaction and influence between acceptance, rejection, and delay decision costs are investigated, and the corresponding IF3WD rules are induced. Finally, the rationality and effectiveness of our proposed model are verified through case analysis and are compared with those of existing methods. [ABSTRACT FROM AUTHOR]

In this paper, attribute reduction of incomplete information system is studied. Firstly, optimistic and pessimistic generalized variable precision rough set models based on maximal consistent blocks are constructed. The relationship between the two models and their main properties are analyzed. After that β-lower optimistic (pessimistic) and β-upper distribution attribute reduction is defined, and the corresponding judgement theorem is given. Boolean method of attribute reduction is obtained, and it can keep the upper (lower) approximation distribution of the decision class unchanged. This method of constructing discernibility set between maximal consistent blocks reduces the size of the discernibility matrix, and the process of computing attribute reduction is simplified, which can effectively save computing time and storage space. Then two examples of incomplete information systems with “lost” “don't care” values and only “don't care” values are employed to illustrate the proposed method. Finally, 5 sets of incomplete information data sets from UCI data set are used to validate its effectiveness.

With databases growing at an unrelenting rate, it may be difficult and complex to extract statistics by accessing all of the data in many practical problems. Attribute reduction, as an effective method to remove redundant attributes from massive data, has demonstrated its remarkable capability in simplifying information systems. In this paper, we concentrate on reducing attributes in incomplete information systems. We introduce a novel definition of a binary similarity matrix and present a method to calculate the significance of attributes in correspondence. Secondly, We develop a heuristic attribute reduction algorithm using a binary similarity matrix and attribute significance as heuristic knowledge. In addition, we use a numerical example to showcase the practicality and accuracy of the algorithm. In conclusion, we demonstrate through comparative analysis that our algorithm outperforms some existing attribute reduction methods.

Combined with air material consumption features，this paper proposes a method combining the rough set（RS） and the support vector machine（SVM） for air material consumption prediction. Through attribute reduction of the incomplete information system of RS，redundant quantitative factors in the air material consumption information system are eliminated. On the basis of the importance of attributes，seven factors are reduced to three，and the core knowledge of the system is retained. After the introduction of SVM improved by the particle swarm optimization（PSO）model，this approach obtains the optimized parameter combination and establises the forecast model of air material consumption. The case study demonstrates that the prediction accuracy of the RS-PSO-SVM model is better than those of the PSO-SVM model or the RSback propagation（ BP）model. [ABSTRACT FROM AUTHOR]

Telecom fraud detection is of great significance in online social networks. Yet the massive, redundant, incomplete, and uncertain network information makes it a challenging task to handle. Hence, this paper mainly uses the correlation of attributes by entropy function to optimize the data quality and then solves the problem of telecommunication fraud detection with incomplete information. First, to filter out redundancy and noise, we propose an attribute reduction algorithm based on max-correlation and max-independence rate (MCIR) to improve data quality. Then, we design a rough-gain anomaly detection algorithm (MCIR-RGAD) using the idea of maximal consistent blocks to deal with missing incomplete data. Finally, the experimental results on authentic telecommunication fraud data and UCI data show that the MCIR-RGAD algorithm provides an effective solution for reducing the computation time, improving the data quality, and processing incomplete data.

Copyright of Journal of Zhengzhou University (Natural Science Edition) is the property of Journal of Zhengzhou University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Rough set theory is one of the mathematical models for dealing with a vague, imprecise, and fuzzy knowledge that has been successfully used to handle incomplete information systems. Since, in fact in the real-world problems, often found the conditions that are the user can not provide all the necessary preference values. In this research, an implementation of extension technique of rough set theory that called limited tolerance relation is used to overcome incomplete information systems in student data at Telkom University. Based on the obtained results, the limited tolerance relation technique successfully used to handle that problem. The results show that the technique achieved the accuracy of 96.04% with an execution time of 3.1830 seconds.

Copyright of Journal of Frontiers of Computer Science & Technology is the property of Beijing Journal of Computer Engineering & Applications Journal Co Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In recent years, rough set theory has been considered as a strong solution to solve artificial intelligence problem such as data mining. But, the classic rough set theory is not effective in the case of attribute reduction in incomplete information systems. Since there are null values for some of attributes in a data set, an incomplete information system is created. In this paper, a novel method proposed to solve attribute reduction in incomplete information system based on rough set theory by combining and modifying imperialist competitive algorithm with fuzzy logic. Utilizing the fuzzy logic to control the parameters of the algorithm was useful and generated better solutions compared to its classic draft. In this research, no changes imposed on incomplete data, and it was just considered as a complete systems. The fuzzy imperialist competitive algorithm acted intelligently to reduce the number of attribute in incomplete information system, providing appropriate results that is worthy of attention.

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, when predicting the unknown attribute value of an object, it regards the frequency of an attribute value approximately as the probability of appearance of this value, without considering the effects of other known attribute values of this object on predicting the unknown attribute value. In this paper, considering both the frequency of the known attribute values and the influence weight to predict the unknown attribute values. Modified data-driven valued tolerance relation (MDVT) is defined. On this basis, an extended rough set model based on modified data-driven valued tolerance relation is proposed. Some properties of the new model are analyzed. Experimental results show that the MDVT can get better classification results than other generalized indiscernibility relations. [ABSTRACT FROM AUTHOR]

Copyright of Computer Measurement & Control is the property of Magazine Agency of Computer Measurement & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Telecommunication Engineering is the property of Telecommunication Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Aiming at the classification of incomplete information system, we improve the relationship of discernibility and perfect the tolerance relationship based on rough set theory, and propose an improved extended rough set model. To eliminate the noise in incomplete information system, we also introduced the variable precision rough set in the incomplete information system Finally, based on the improved discernibility relationship, this paper constructs an extended rough set model of variable precision whose feasibility and validity of the method are verified by empirical analysis. [ABSTRACT FROM AUTHOR]