Search

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]

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]

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]

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]

As we move into the information age, the amount of data in various fields has increased dramatically, and data sources have become increasingly widely distributed. The corresponding phenomenon of missing data is increasingly common, and it leads to the generation of incomplete multi-source information systems. In this context, this paper's proposal aims to address the limitations of rough set theory. We study the method of multi-source fusion in incomplete multi-source systems. This paper presents a method for fusing incomplete multi-source systems based on information entropy; in particular, by comparison with another method, our fusion method is validated. Furthermore, extensive experiments are conducted on six UCI data sets to verify the performance of the proposed method. Additionally, the experimental results indicate that multi-source information fusion approaches significantly outperform other approaches to fusion. [ABSTRACT FROM AUTHOR]

Rough set theory (RST) has been widely used to measure and handle uncertain information; however, the existing RST-based measures are difficult to generalize the results of incomplete information systems to complete information systems. In this paper, some well-justified measures of uncertainty based on discernibility capability of attributes are presented. We first define two single measures and give their useful properties, based on which a new uncertainty measure of rough sets is proposed, which can be consist with human cognition. We then propose three combination measures for multiattribute case and discuss their relationships. Last, we compare our methods with the existing measures to illustrate the physical meaning of the existing measures in RST. Theoretical analysis with numerical examples proves that the new measures will work efficiently on both complete and incomplete information systems. The research results may lead us to a deeper understanding of the essence of uncertainty. [ABSTRACT FROM AUTHOR]

Non-symmetric similarity relation-based rough set model (NS-RSM) is viewed as mathematical tool to deal with the analysis of imprecise and uncertain information in incomplete information systems with '?' values. NS-RSM relies on the concept of non-symmetric similarity relation to group equivalent objects and generate knowledge granules that are then used to approximate the target set. However, NS-RSM results in unpromising approximation space when addressing inconsistent data sets that have lots of boundary objects. This is because objects in the same similarity classes are not necessarily similar to each other and may belong to different target classes. To enhance NS-RSM capability, we introduce the maximal limited similarity-based rough set model (MLS-RSM) which describes the maximal collection of indistinguishable objects that are limited tolerance to each other in similarity classes. This allows accurate computation to be done for the approximation space. Furthermore, approximation accuracy comparisons have been conducted among NS-RSM and MLS-RSM. The results demonstrate that MLS-RSM model outperforms NS-RSM and can approximate the target set more efficiently. [ABSTRACT FROM AUTHOR]

Multigranulation rough sets are desirable features in the field of rough set, where this concept is approximated by multiple granular structures. In this study, we employ belief and plausibility functions from evidence theory to characterize the set approximations and attribute reductions in multigranulation rough set theory. First, we show that in an incomplete information system, the pessimistic multigranulation approximations can be measured by belief and plausibility functions, whereas the optimistic multigranulation approximations do not possess this characteristic in general. We also give a sufficient and necessary condition for the numerical measurement of optimistic multigranulation approximations by belief and plausibility functions. Second, in an incomplete decision system, the pessimistic multigranulation approximations are also measured by belief and plausibility functions. In the end, an attribute reduction algorithm for multigranulation rough sets is proposed based on evidence theory, and its efficiency is examined by an example. Thus, belief and plausibility functions can be employed to numerically characterize the attribute reductions and to construct an attribute reduction algorithm for multigranulation rough sets. [ABSTRACT FROM AUTHOR]

In the field of decision making, three-way decision making has been proven more fruitful for providing scopes to make delayed decision along with acceptance and rejection simultaneously. As a result, the decision risk and loss, which could occur due to take rapid decisions in traditional two-way decision making, are effectively reduced. Accordingly, this paper offers a novel three-way multi-attribute decision making model by combining three-way decision making and multi-attribute decision making under an incomplete information system. The incertitude in the information system is illustrated by introducing interval-valued Fermatean connection number based on interval-valued Fermatean fuzzy number and set pair analysis theory. Thereafter, the achievement of this study is five-fold. First, a possibility dominance relation is developed under incomplete information system in the basis of possibility degree measure of interval-valued Fermatean connection number. Second, we put forward a novel procedure to set up the fuzzy state set. Third, the conditional probability is estimated in light of the fuzzy state set and probability dominance relation. Fourth, the relative utility functions are determined in the virtue of regret theory. Lastly, a three-way multi-attribute decision making model is implemented in incomplete information system and exploited to deal with incomplete multi-attribute decision making problems. Eventually, the propriety, stability and superiority of the proposed model is established via conducting the comparative and experimental analysis. • Introducing a novel uncertainty, namely, interval-valued Fermatean connection number. • Developing a new approach to derive fuzzy state set and conditional probability. • Calculating relative utility functions by using regret theory. • Proposing a novel three-way multi-attribute decision making model. [ABSTRACT FROM AUTHOR]

As a natural extension of three-way decisions with incomplete information, this paper provides a novel three-way decision model based on incomplete information system. First, we define a new relation to describe the similarity degree of incomplete information. Then, in view of the missing values presented in incomplete information system, we utilize interval number to acquire the loss function. A hybrid information table which consist both of the incomplete information and loss function, is used to deal with the new three-way decision model. The key steps and algorithm for constructing the integrated three-way decision model are also carefully investigated. An empirical study of medical diagnosis validates the reasonability and effectiveness of our proposed model. [ABSTRACT FROM AUTHOR]

Considering the incompleteness and uncertainty of information systems, this paper combines the incomplete information systems with interval-valued fuzzy sets, and defines the incomplete interval-valued fuzzy information systems. The basic rough set theory for incomplete interval-valued fuzzy information systems is also discussed in this paper. [ABSTRACT FROM AUTHOR]

Decision-theoretic rough sets in two kinds of incomplete information systems are discussed in this paper. One is for the classical decision attribute and the other for the fuzzy decision attribute. In complete information system, the universe is partitioned with the equivalence relation. Given a concept, we get a pair of approximations of the concept using rough set theory, and the universe can be partitioned into three regions for making a decision. An incomplete information table can be expressed as a family of complete information tables. The universe is partitioned by the equivalence relation for each complete information table. The probability of each object belonging to the concept can be calculated in a completion from incomplete information system, and then the total probability of the object belonging to the concept can be obtained. Decision rules are derived using total probability instead of conditional probability in decision-theoretic rough sets. Finally, the universe is divided into three regions according to the total probability. A similar approach to fuzzy incomplete information system is examined and the universe is also divided into three regions. [ABSTRACT FROM AUTHOR]

The neighborhood system based rough set is a generalization of Pawlak's rough set model since the former uses the neighborhood system instead of the partition for constructing target approximation. In this paper, the neighborhood system based rough set approach is employed to deal with the incomplete information system. By the coverings induced by the maximal consistent blocks and the support sets of the descriptors, respectively, two neighborhood systems based rough sets are explored. By comparing with the original maximal consistent block and descriptor based rough sets, the neighborhood system based rough sets hold the same lower approximations and the smaller upper approximations. Furthermore, the concept of attribute reduction is introduced into the neighborhood systems and the corresponding rough sets. The judgement theorems and discernibility functions to compute reducts are also presented. Some numerical examples are employed to substantiate the conceptual arguments. [ABSTRACT FROM AUTHOR]

Abstract: Neighborhood system formalized the ancient intuition, infinitesimals, which led to the invention of calculus, topology and non-standard analysis. In this paper, the neighborhood system is researched from the view point of knowledge engineering and then each neighborhood is considered as a basic unit with knowledge. By using these knowledge in neighborhood system, the rough approximations and the corresponding properties are discussed. It is shown that in the incomplete information system, the smaller upper approximations can be obtained by neighborhood system based rough sets than by the methods in [Y. Leung, D.Y. Li, Maximal consistent block technique for rule acquisition in incomplete information systems, Information Sciences 115 (2003) 85–106] and [Y. Leung, W.Z. Wu, W.X. Zhang, Knowledge acquisition in incomplete information systems: a rough set approach, European Journal of Operational Research 168 (2006) 164–180]. Furthermore, a new knowledge operation is discussed in the neighborhood system, from which more knowledge can be derived from the initial neighborhood system. By such operations, the regions of lower and upper approximations are further expanded and narrowed, respectively. Some numerical examples are employed to substantiate the conceptual arguments. [Copyright &y& Elsevier]

The purpose of this paper is to present a new rough set model for generating negative rules from the incomplete information system. A negative rule indicates that if an object does not satisfy the attribute-value pairs in the condition part, then we can exclude the decision part from such object. The proposed rough set model is constructed on the basis of a difference relation. Such difference relation is a binary relation without any constraints. Moreover, to simplify the negative rules generated from the difference relation-based rough approximations, the concepts of lower, upper approximate and rough reducts are also proposed. Some numerical examples are employed to substantiate the conceptual arguments. [ABSTRACT FROM AUTHOR]

Rough set theory is a relatively new mathematical tool for computer applications in circumstances characterized by vagueness and uncertainty. In this paper, we address uncertainty of rough sets for incomplete information systems. An axiom definition of knowledge granulation for incomplete information systems is obtained, under which a measure of uncertainty of a rough set is proposed. This measure has some nice properties such as equivalence, maximum and minimum. Furthermore, we prove that the uncertainty measure is effective and suitable for measuring roughness and accuracy of rough sets for incomplete information systems. [ABSTRACT FROM AUTHOR]