Multiple Binary Relations Research Articles

On local multigranulation covering decision-theoretic rough sets

Multi-granulation decision-theoretic rough sets uses the granular structures induced by multiple binary relations to approximate the target concept, which can get a more accurate description of the approximate space. However, Multi-granulation decision-theoretic rough sets is very time-consuming to calculate the approximate value of the target set. Local rough sets not only inherits the advantages of classical rough set in dealing with imprecise, fuzzy and uncertain data, but also breaks through the limitation that classical rough set needs a lot of labeled data. In this paper, in order to make full use of the advantage of computational efficiency of local rough sets and the ability of more accurate approximation space description of multi-granulation decision-theoretic rough sets, we propose to combine the local rough sets and the multigranulation decision-theoretic rough sets in the covering approximation space to obtain the local multigranulation covering decision-theoretic rough sets model. This provides an effective tool for discovering knowledge and making decisions in relation to large data sets. We first propose four types of local multigranulation covering decision-theoretic rough sets models in covering approximation space, where a target concept is approximated by employing the maximal or minimal descriptors of objects. Moreover, some important properties and decision rules are studied. Meanwhile, we explore the reduction among the four types of models. Furthermore, we discuss the relationships of the proposed models and other representative models. Finally, illustrative case of medical diagnosis is given to explain and evaluate the advantage of local multigranulation covering decision-theoretic rough sets model.

Information fusion and numerical characterization of a multi-source information system

The existing research of multi-source information system, pessimistic or optimistic multi-granulation fusion functions, provided by multi-granulation rough set (MGRS) theory, which apply disjunctive and conjunctive operators of multiple binary relations to aggregate multiple granular structures induced by different binary relations, are too relax or too restrictive to solve the practical problems. In this paper, we employ evidence theory, probability theory and information entropy to address the information fusion and numerical characterization of uncertain data in a multi-source information system (MSIS). First, we propose novel definitions of multi-source rough approximations and corresponding multi-granulation rough approximations, probability distribution and basic probability assignment, which can be used to construct the connection between rough approximations and evidence theory. Second, the above ideas are extended to multi-source covering information system (MCIS). Finally, Shannon’s fusion algorithm based on equivalence relations or coverings, involved in the significance degree of condition attributes set with respect to a sample, conditional probability and information entropy, is presented to calculate the uncertainty degree of a decision, respectively. Then, based on the defined conditional probability in this paper, we design a multi-granulation variable precision rough set and consider the relationship with MGRS. And, the illustrative examples are given to elaborate the operation mechanism of the above conclusions. This study will be helpful for integrating the uncertain information come from multiple sources and eventful for creating a route of granular computing.

New and improved: grey multi-granulation rough sets

ABSTRACTRough set has drawn great attention in recent decades, among which multi-granulation rough set (MGRS) is an arresting direction. It constructs a formal theoretical framework to solve complex problems under the circumstance of multiple binary relations. However, the fusion of multi-granulation rough set and grey system for acquiring knowledge is still a gap. Toward this end, we devise a grey multi-granulation rough set (GMGRS) by taking multiple grey relational relations into consideration under the framework of MGRS. In grey information system, the constructed grey relational relation that measures the relationship among objects can be used to further establish multiple binary relations. Based on two different approximate strategies (seeking common reserving difference and seeking common eliminating difference), two types of GMGRS are presented, respectively. After discussing several important properties of GMGRS, we discover that the properties of the proposed GMGRS are synchronous with the classical MGRS. Meanwhile, to obtain the attribute reduction under GMGRS, we reconstruct significance measure and termination criterion based on the θ-precision pessimistic GMGRS. Last but not least, theoretical studies and practical examples demonstrate that our proposed GMGRS largely enrich the MGRS theory and provide a new technique for knowledge discovery, which is practical in real-world scenarios.

Local multigranulation decision-theoretic rough sets

Multigranulation rough sets (MGRSs) where a target concept is approximated by granular structures induced by multiple binary relations have been applied successfully in many domains but they are still affected by two issues. First, similar to other rough set models, calculating the approximation of a target set is extremely time-consuming for larger scale data. Second, MGRSs comprise a supervised learning method, so they often require a large amount of labeled data. However, in the era of big data, labeling all data is almost infeasible in some cases. In this study, to address these issues, we propose the combination of local rough sets with multigranulation decision-theoretic rough sets to obtain local multigranulation decision-theoretic rough sets (LMG-DTRSs) as a semi-unsupervised learning method. We also explore a number of important properties of LMG-DTRSs. In addition, we verify the efficiency of a concept approximation algorithm designed with LMG-DTRS based on theoretical and experimental analyses. Furthermore, we present two types of local MGRS frameworks under PRSs and variable precision rough sets, where the relationships between them and the LMG-DTRS model are also discussed. We show that many local MGRS models can be derived from the LMG-DTRS framework.

Cardiac arrhythmia classification using multi-granulation rough set approaches

Cardiovascular disease is a most important reason for human death in modern society. Electrocardiogram (ECG) signal deals with valuable information about functioning of the heart. For that reason, ECG investigation signifies an efficient way to identification and treat different types of cardiac arrhythmia diseases. Nowadays various pattern classification methods has been developed for the classification of ECG signals. These classification methods helps to physician for diseases diagnosis. A multi-granulation rough set (MGRS) has become a new direction of rough set theory, which is based on multiple binary relations on the universe of discourse. In this present study, Multi-granulation rough set based classification approaches (Pessimistic Multi-Granulation Rough Set (PMGRS) and Optimistic Multi-Granulation Rough Set (OMGRS)) are applied to mine appropriate rules to explore better decision making process. The experiments were conducted on the ECG data from the Physionet arrhythmia database to classify five kinds of normal and abnormal signals. In the classification process, Feature extraction played an important role. And we have used two kinds feature extraction methods (1) Pan Tomkins (PT) feature extraction method. This method used to extract the morphological features are P, Q, R, S, T peak intervals, which is also used to determine heart rate. (2) Wavelet transform (WT) feature extraction method. This method used to extract the wavelet coefficients. Both two methods are successfully applied to (ECG signal) classification. The proposed multi-granulation rough set rule based classification methods is validated using the first 24 channel of the ECG signal records of the MIT-BITH arrhythmia database, and achieves finding high accuracies. Experimental results show that the proposed classification techniques significantly outperforms other well-known techniques.

Pythagorean Fuzzy Multigranulation Rough Set over Two Universes and Its Applications in Merger and Acquisition

Pythagorean fuzzy set, an extension form of intuitionistic fuzzy set, which owns many advantages for dealing with uncertainties, and it has been developed to deal with various complex decision-making problems. Furthermore, based on lower and upper approximations induced by multiple binary relations, the multigranulation rough set has become one of the most promising directions in rough set theory. To combine the two ideas and explore the practical decision-making problems, we develop a new multigranulation rough set model, called Pythagorean fuzzy multigranulation rough set over two universes. In the framework of our study, we introduce the models of Pythagorean fuzzy rough set over two universes and Pythagorean fuzzy multigranulation rough set over two universes, respectively. Both the definition and basic properties are explored. Finally, we give a general algorithm, which is applied to a decision-making problem in merger and acquisition, and the effectiveness of the algorithm is demonstrated by a numerical example.

Multigranulation rough set theory over two universes

Recently, a multigranulation rough set MGRS has become a new direction in rough set theory, which is based on multiple binary relations on the universe of discourse. The existing literature about m...

Multigranulation rough set theory over two universes

Recently, a multigranulation rough set MGRS has become a new direction in rough set theory, which is based on multiple binary relations on the universe of discourse. The existing literature about multigranulation rough set is based on the assumption of the same universe. In reality, however, a good deal of practical decision making may relate to the possibility of two or more different universes. In this paper, we consider the rough approximation of a given concept over two different universes with respect to the multigranulation space formed by different mappings of the two universes, i.e., the multigranulation rough set model. We respectively define the optimistic multigranulation rough set, pessimistic multigranulation rough set and variable precision multigranulation rough set over two universes, each of which can be appropriate to a different real-world decision-making problem in management science. Then several important properties of these models are discussed in detail. Also, the relationship between the multigranulation rough set over two universes and the existing models in the literature is investigated. At last, the entropy and granularity of the binary mapping between two different universes are defined, and then we give an approach to uncertainty measurement based on the granularity of binary mapping for multigranulation rough set over two universes. The multigranulation rough set model over two universes provides a new, effective approach for practical decision problems in management science.

Pessimistic rough set based decisions: A multigranulation fusion strategy

Multigranulation rough sets (MGRS) is one of desirable directions in rough set theory, in which lower/upper approximations are approximated by granular structures induced by multiple binary relations. It provides a new perspective for decision making analysis based on rough set theory. In decision making analysis, people often adopt the decision strategy “Seeking common ground while eliminating differences” (SCED). This strategy implies that one reserves common decisions while deleting inconsistent decisions. From this point of view, the objective of this study is to develop a new multigranulation rough set based decision model based on SCED strategy, called pessimistic multigranulation rough sets. We study this model from three aspects, which are lower/upper approximation and their properties, decision rules and attribute reduction, in this paper.

Multi-Granulation Entropy and Its Applications

In the view of granular computing, some general uncertainty measures are proposed through single-granulation by generalizing Shannon’s entropy. However, in the practical environment we need to describe concurrently a target concept through multiple binary relations. In this paper, we extend the classical information entropy model to a multi-granulation entropy model (MGE) by using a series of general binary relations. Two types of MGE are discussed. Moreover, a number of theorems are obtained. It can be concluded that the single-granulation entropy is the special instance of MGE. We employ the proposed model to evaluate the significance of the attributes for classification. A forward greedy search algorithm for feature selection is constructed. The experimental results show that the proposed method presents an effective solution for feature analysis.

Multigranulation decision-theoretic rough sets

The Bayesian decision-theoretic rough sets propose a framework for studying rough set approximations using probabilistic theory, which can interprete the parameters from existing forms of probabilistic approaches to rough sets. Exploring rough sets in the viewpoint of multigranulation is becoming one of desirable directions in rough set theory, in which lower/upper approximations are approximated by granular structures induced by multiple binary relations. Through combining these two ideas, the objective of this study is to develop a new multigranulation rough set model, called a multigranulation decision-theoretic rough set. Many existing multigranulation rough set models can be derived from the multigranulation decision-theoretic rough set framework.

NMGRS: Neighborhood-based multigranulation rough sets

Recently, a multigranulation rough set (MGRS) has become a new direction in rough set theory, which is based on multiple binary relations on the universe. However, it is worth noticing that the original MGRS can not be used to discover knowledge from information systems with various domains of attributes. In order to extend the theory of MGRS, the objective of this study is to develop a so-called neighborhood-based multigranulation rough set (NMGRS) in the framework of multigranulation rough sets. Furthermore, by using two different approximating strategies, i.e., seeking common reserving difference and seeking common rejecting difference, we first present optimistic and pessimistic 1-type neighborhood-based multigranulation rough sets and optimistic and pessimistic 2-type neighborhood-based multigranulation rough sets, respectively. Through analyzing several important properties of neighborhood-based multigranulation rough sets, we find that the new rough sets degenerate to the original MGRS when the size of neighborhood equals zero. To obtain covering reducts under neighborhood-based multigranulation rough sets, we then propose a new definition of covering reduct to describe the smallest attribute subset that preserves the consistency of the neighborhood decision system, which can be calculated by Chen’s discernibility matrix approach. These results show that the proposed NMGRS largely extends the theory and application of classical MGRS in the context of multiple granulations.

A consulting system for data base design

This paper proposes a methodology for automated data base design based on a set of managerial reports. We introduce the notion of report schemata, specified in terms of record types and binary relations, as a framework for analyzing report structures and interactions among reports. Four classes of binary relations are identified, each being characteristic of a certain type of elementary report. Multiple binary relations are used to specify more complex reports. We also discuss concepts such as report covering and the maximal members for transforming reports to a parsimonious representation for data base design. Finally, we formulate this report-driven data base design methodology as an expert consulting system in Artificial Intelligence.