Rough Set Approximations Research Articles

Rough set models in multigranulation spaces

There exist several approaches to rough set approximations in a multigranulation space, namely, a family of equivalence relations. In this paper, we propose a unified framework to classify and compare existing studies. An underlying principle is to explain rough sets in a multigranulation space through rough sets derived by using individual equivalence relations. Two basic models are suggested. One model is based on a combination of a family of equivalence relations into an equivalence relation and the construction of approximations with respect to the combined relation. By combining equivalence relations through set intersection and union, respectively, we construct two sub-models. The other model is based on the construction of a family of approximations from a set of equivalence relations and a combination of the family of approximations. By using set intersection and union to combine a family of approximations, respectively, we again build two sub-models. As a result, we have a total of four models. We examine these models and give conditions under which some of them become the same.

Searching contexts in paraconsistent rough description logic

Query refinement is an interactive process of query modification used to increase or decrease the scope of search results in databases or ontologies. We present a method to obtain optimized query refinements of assertion axioms in the paraconsistent rough description logic $\mathcal {PR_{\textit {ALC}}}$ , a four-valued paraconsistent version of the rough $\mathcal {ALC}$ , which is grounded on Belnap’s Logic. This method is based on the notion of the discernibility matrix commonly used in the process of attribute reduction in the rough set theory. It consists of finding sets of concepts which satisfy the rough set approximation operations in assertion axioms. Consequently, these sets of concepts can be used to restrict or relax queries in this logic. We propose two algorithms to settle this problem of query refinement in $\mathcal {PR_{\textit {ALC}}}$ and show their complexity results. The problem of query restrictions using contextual approximation is proved to have exponential time complexity, while the problem of query relaxations has polynomial space complexity.

Special types of coverings and axiomatization of rough sets based on partial orders

Covering rough sets are a generalization of Pawlak rough sets, in which a partition of the universal set induced by an equivalence relation is replaced by a covering. In this paper, covering rough sets are transformed into generalized rough sets induced by binary relations. The paper discusses three theoretical topics. First, we consider a special type of covering in which the neighborhoods form a reduction of the covering, and we obtain necessary and sufficient conditions for neighborhoods in a covering form a reduction of the covering. Second, we study another special type of covering, and give conditions for the covering lower and upper approximations to be dual to each other. Finally, we give an axiomatic system that characterizes the lower and upper approximations of rough sets based on a partial order.

Applying Dependency of Attributes for Business Data Mining in Information Systems: A Theoretical Framework

This paper presents the applications of dependency of attributes in information systems for data mining from business datasets. Firstly, we present the theoretical framework for data clustering on small business dataset. It is based on a construction of a hierarchical rough set approximation in an information system for data splitting. The hierarchy is defined by the notion of a nested sequence of indiscernibility relations that can be defined from the dependency of attributes. Secondly, an application of such hierarchy for mining maximal association from a business transactional data is presented. It is shown that the dependency provides clear and provable theoretical approach for data clustering and maximal association rules mining.

Update of approximations in composite information systems

In this paper, a new composite rough set model is proposed to process incomplete composite information with criteria and regular attributes. Following that, some strategies for incrementally updating approximations of composite rough sets when adding or removing some objects are discussed and the corresponding incremental algorithms are designed. Several numerical examples illustrate the feasibilities of the composite rough set model and the incremental strategies, respectively. Experimental evaluation shows that the incremental algorithms can effectively reduce the running time than their counterparts.

Accurate Topological Measures for Rough Sets

Data granulation is considered a good tool of decision making in various types of real life applications. The basic ideas of data granulation have appeared in many fields, such as interval analysis, quantization, rough set theory, Dempster-Shafer theory of belief functions, divide and conquer, cluster analysis, machine learning, databases, information retrieval, and many others. Some new topological tools for data granulation using rough set approximations are initiated. Moreover, some topological measures of data granulation in topological information systems are defined. Topological generalizations using dß -open sets and their applications of information granulation are developed.

Fuzzy-Rough-Set-Based Active Learning

Determining the informativeness of unlabeled samples is a key issue in active learning. One solution to this is using the sample's inconsistency between conditional features and decision labels. In this paper, a fuzzy-rough-set-based active learning model is proposed to tackle this problem. First, the consistence degree of a labeled sample is computed by the lower approximations in fuzzy rough set, which reflects its minimum membership in the decision class. Then, the concept of sample covering is proposed to measure the relationship between labeled samples and unlabeled samples. Afterward, the memberships of an unlabeled sample belonging to different decision classes are computed based on the covering degrees of labeled samples on it. Finally, these memberships are used to form a sample selection criterion to measure the sample's inconsistency. By applying Gaussian kernel-based similarity relation to the aforementioned processes, a support vector machine (SVM)-based active learning scheme is developed. Experimental results demonstrate the effectiveness of the proposed model.

Incremental updating approximations in probabilistic rough sets under the variation of attributes

The attribute set in an information system evolves in time when new information arrives. Both lower and upper approximations of a concept will change dynamically when attributes vary. Inspired by the former incremental algorithm in Pawlak rough sets, this paper focuses on new strategies of dynamically updating approximations in probabilistic rough sets and investigates four propositions of updating approximations under probabilistic rough sets. Two incremental algorithms based on adding attributes and deleting attributes under probabilistic rough sets are proposed, respectively. The experiments on five data sets from UCI and a genome data with thousand attributes validate the feasibility of the proposed incremental approaches.

Incremental Approach for Updating Approximations of Variable Precision Rough Set Based on Dominance Relations

Variable precision rough set (VPRS) based on dominance relation is an extension of traditional rough set by which can handle preference-ordered information flexibly. This paper focuses on the maintenance of approximations in dominance based VPRS when the objects in an information system vary over time. The incremental updating principles are given as inserting or deleting an object, and some experimental evaluations validates the effectiveness of the proposed method.

A short note on rough set over dual-universes

To extend the utilisation and flexibility of rough set extension on universes, we modify rough set over dual-universes model by comparing rough set extension on universes based on compatibility relation and rough set over dual-universes in the aspect of theories and applications. Instance in daily life is advanced to indicate shortcomings of rough set extension on universes based on compatibility relation and rough set over dual-universes. The similarities and differences between rough set over dual-universes and rough set extension models on universes based on compatibility relation are analysed from the view of approximation operators. New lower and upper approximations of rough set over dual-universes are designed by introducing set-valued map. An improved rough set model is constructed. The conclusion is that rough set over dual-universes in this article has a standard description and could solve practical problems well compared with rough set extension models on universes based on compatibility relation.

Forward approximation and backward approximation in fuzzy rough sets

It is general to obtain rules by attribute reduction in fuzzy information systems. Instead of obtaining rules by attribute reduction, which may have a negative effect on inducting good rules, the objective of this paper is to extract rules without computing attribute reducts. Forward and backward approximations in fuzzy rough sets are first defined, and their important properties are discussed. Two algorithms based on forward and backward approximations, namely, mine rules based on the forward approximation (MRBFA) and mine rules based on the backward approximation (MRBBA), are proposed for rule extraction . The two algorithms are evaluated by several data sets from the UC Irvine Machine Learning Repository. The experimental results show that both MRBFA and MRBBA achieve better classification performances than the method based on attribute reduction.

A kind of approximations of generalized rough set model

In this paper, we investigate the approximation problem of generalized rough set model. In generalized rough sets, the binary relation on one universe is always unknown and needed to be induced by the other already-known relation. In order to evaluate the induced binary relation, we propose a pair of generalized approximations called generalized lower and upper approximations by which the induced binary relation and the already-known binary relation can be connected. We also assert that the pair of generalized approximations are related to the definitions of approximations of classical rough sets. Their algebraic properties and topology structures are first studied. More important, we both give some comparisons of the relations in the same generalized rough set model and the approximations among different generalized rough set models. In the end, some applications of the proposed approximations in covering based rough sets are presented.

Detecting overlapping protein complexes by rough-fuzzy clustering in protein-protein interaction networks.

In this paper, we present a novel rough-fuzzy clustering (RFC) method to detect overlapping protein complexes in protein-protein interaction (PPI) networks. RFC focuses on fuzzy relation model rather than graph model by integrating fuzzy sets and rough sets, employs the upper and lower approximations of rough sets to deal with overlapping complexes, and calculates the number of complexes automatically. Fuzzy relation between proteins is established and then transformed into fuzzy equivalence relation. Non-overlapping complexes correspond to equivalence classes satisfying certain equivalence relation. To obtain overlapping complexes, we calculate the similarity between one protein and each complex, and then determine whether the protein belongs to one or multiple complexes by computing the ratio of each similarity to maximum similarity. To validate RFC quantitatively, we test it in Gavin, Collins, Krogan and BioGRID datasets. Experiment results show that there is a good correspondence to reference complexes in MIPS and SGD databases. Then we compare RFC with several previous methods, including ClusterONE, CMC, MCL, GCE, OSLOM and CFinder. Results show the precision, sensitivity and separation are 32.4%, 42.9% and 81.9% higher than mean of the five methods in four weighted networks, and are 0.5%, 11.2% and 66.1% higher than mean of the six methods in five unweighted networks. Our method RFC works well for protein complexes detection and provides a new insight of network division, and it can also be applied to identify overlapping community structure in social networks and LFR benchmark networks.

A new approach for discretizing continuous attributes in learning systems

Discretization is a process to convert continuous attributes into discrete format to represent signals for further data processing in learning systems. The main concern in discretization techniques is to find an optimal representation of continuous values with limited number of intervals that can effectively characterize the data and meanwhile minimize information loss. In this paper, we propose a novel class-attribute interdependency discretization algorithm (termed as NCAIC), which takes account of data distribution and the interdependency between all classes and attributes. In our proposed solution, the upper approximation of rough sets as a prime part of the discretization algorithm is applied, and the class-attribute mutual information is used to automatically control and adjust the scope of the discretization of continuous attributes. Some experiments with comparison to five other discretization algorithms are reported, where 13 benchmarked datasets extracted from UCI database and the well-known C4.5 decision tree tool are employed in this study. Results demonstrate that in general our proposed algorithm outperforms other tested discretization algorithms in terms of classification performance.

Realization of Rough Set Approximation Toplogical Operations Based on Formal Concept Analysis

There is an intimate correlation between rough set theory and formal concept analysis theory, so rough set approximations can be realized by means of formal concept analysis. For any given multiple valued information system, the realization of rough set approximation operation has two major steps, firstly convert the information system from multiple valued one to single valued formal context, secondly realize rough set approximation operations aided by concept lattice, which is equivalent to a query operation under some necessary conditions.

Rough Sets, Kernel Set, and Spatiotemporal Outlier Detection

Nowadays, the high availability of data gathered from wireless sensor networks and telecommunication systems has drawn the attention of researchers on the problem of extracting knowledge from spatiotemporal data. Detecting outliers which are grossly different from or inconsistent with the remaining spatiotemporal data set is a major challenge in real-world knowledge discovery and data mining applications. In this paper, we deal with the outlier detection problem in spatiotemporal data and describe a rough set approach that finds the top outliers in an unlabeled spatiotemporal data set. The proposed method, called Rough Outlier Set Extraction (ROSE), relies on a rough set theoretic representation of the outlier set using the rough set approximations, i.e., lower and upper approximations. We have also introduced a new set, named Kernel Set, that is a subset of the original data set, which is able to describe the original data set both in terms of data structure and of obtained results. Experimental results on real-world data sets demonstrate the superiority of ROSE, both in terms of some quantitative indices and outliers detected, over those obtained by various rough fuzzy clustering algorithms and by the state-of-the-art outlier detection methods. It is also demonstrated that the kernel set is able to detect the same outliers set but with less computational time.

Incremental Maintenance of Rough Fuzzy Set Approximations under the Variation of Object Set

The lower and upper approximations in rough set theory will change dynamically over time due to the variation of the information system. Incremental methods for updating approximations in rough set theory and its extensions have received much attention recently. Most existing incremental methods have difficulties in dealing with fuzzy decision systems which decision attributes are fuzzy. This paper introduces an incremental algorithm for updating approximations of rough fuzzy sets under the variation of the object set in fuzzy decision systems. In experiments on 6 data sets from UCI, comparisons of the incremental and non-incremental methods for updating approximations are conducted. The experimental results show that the incremental method effectively reduces the computational time.

Comparison between rough set approximations based on different topologies

Considering the generalised approximation space, this paper aims to introduce and study eight approaches for approximating rough sets. The approximations are based on different topologies. Comparisons between the accuracy of these types of approximations are superimposed. Some fundamental properties of the suggested approximation operators are obtained.

Evidence-theory-based numerical algorithms of attribute reduction with neighborhood-covering rough sets

Covering rough sets generalize traditional rough sets by considering coverings of the universe instead of partitions, and neighborhood-covering rough sets have been demonstrated to be a reasonable selection for attribute reduction with covering rough sets. In this paper, numerical algorithms of attribute reduction with neighborhood-covering rough sets are developed by using evidence theory. We firstly employ belief and plausibility functions to measure lower and upper approximations in neighborhood-covering rough sets, and then, the attribute reductions of covering information systems and decision systems are characterized by these respective functions. The concepts of the significance and the relative significance of coverings are also developed to design algorithms for finding reducts. Based on these discussions, connections between neighborhood-covering rough sets and evidence theory are set up to establish a basic framework of numerical characterizations of attribute reduction with these sets.

Rough Sets for Bias Field Correction in MR Images Using Contraharmonic Mean and Quantitative Index

One of the challenging tasks for magnetic resonance (MR) image analysis is to remove the intensity inhomogeneity artifact present in MR images, which often degrades the performance of an automatic image analysis technique. In this regard, the paper presents a novel approach for bias field correction in MR images. It judiciously integrates the merits of rough sets and contraharmonic mean. While the contraharmonic mean is used in low-pass averaging filter to estimate the bias field in multiplicative model, the concept of lower approximation and boundary region of rough sets deals with vagueness and incompleteness in filter structure definition. A theoretical analysis is presented to justify the use of both rough sets and contraharmonic mean for bias field estimation. The integration enables the algorithm to estimate optimum or near optimum bias field. Some new quantitative indexes are introduced to measure intensity inhomogeneity artifact present in a MR image. The performance of the proposed approach, along with a comparison with other approaches, is demonstrated on both simulated and real MR images for different bias fields and noise levels.