Rough Set Approximations Research Articles

Spherical Linear Diophantine Fuzzy Soft Rough Sets with Multi-Criteria Decision Making

Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs), picture fuzzy sets (PFSs), and spherical fuzzy sets (SFSs) are strong models for MCDM. Nevertheless, these models have certain limitations for three indexes, satisfaction (membership), dissatisfaction (non-membership), refusal/abstain (indeterminacy) grades. A SLDFS with the use of reference parameters becomes an advanced approach to deal with uncertainties in MCDM and to remove strict limitations of above grades. In this approach the decision makers (DMs) have the freedom for the selection of above three indexes in [0,1]. The addition of reference parameters with three index/grades is a more effective approach to analyze DMs opinion. We discuss the concept of spherical linear Diophantine fuzzy numbers (SLDFNs) and certain properties of SLDFSs and SLDFNs. These concepts are illustrated by examples and graphical representation. Some score functions for comparison of LDFNs are developed. We introduce the novel concepts of spherical linear Diophantine fuzzy soft rough set (SLDFSRS) and spherical linear Diophantine fuzzy soft approximation space. The proposed model of SLDFSRS is a robust hybrid model of SLDFS, soft set, and rough set. We develop new algorithms for MCDM of suitable clean energy technology. We use the concepts of score functions, reduct, and core for the optimal decision. A brief comparative analysis of the proposed approach with some existing techniques is established to indicate the validity, flexibility, and superiority of the suggested MCDM approach.

A Novel Concept of Uncertainty Optimization Based Multi-Granular Rough Set and Its Application

Data is generating at an exponential pace with the advancement in information technology. Such data highly contain uncertain and vague information. The rough set approximation is a way to find information in the data-set under uncertainty and to classify objects of the dataset. This work presents a mathematical approach to evaluate the data-sets uncertainties and their application to data reduction. In this work, we have extended the multi-granulation variable precision rough set in the context of uncertainty optimization. We develop an uncertainty optimization-based multi-granular rough set (UOMGRS) to minimize the uncertainties in the data set more effectively. Using UOMGRS, we find the most informative attribute in the feature space. It is desirable to minimize the rough set boundary region using the attribute having the highest approximation quality. Thus we group the attributes whose relative quality of approximation is the maximum to maximize the positive region and to minimize the uncertain region. We compare the UOMGRS with the single granulation rough set (SGRS) and the multi-granular rough set (MGRS). By our proposed method, we require only an average of 62% attributes for approximation whereas, SGRS and MGRS need an average of at least 72% of attributes in the data set for approximation of the concepts in the data-set. Our proposed method requires less amount of data for the classification of objects in the dataset. The method helps minimize the uncertainties in the dataset in a more efficient way.

A dynamic approach for updating the optimal approximation of rough set

The approximate representation and calculation of target concept on approximate space are the foundation of rough set model study. For dynamic attribute reduction and related tasks, it is often necessary to update the approximation of the target concept of rough set theory, and most existing updating approaches are based on the lower and upper approximations of target concepts. This paper presents a dynamic approach for updating the optimal set when a single object is added into the decision table. Aiming at the dynamic change of condition class and decision class caused by the incremental object, the paper discusses the updating mechanisms of optimal approximation set in four different cases and then the dynamic updating algorithm of optimal approximation set is obtained. Finally, the experiments on different data sets from UCI show that the time complexity of optimal approximate updating of decision classes are different for four different cases and the incremental methods are feasible and efficient for decision systems of added one single object.

Analyzing uncertainty in cardiotocogram data for the prediction of fetal risks based on machine learning techniques using rough set

The key focus of this venture is to evaluate the calibration of classifiers built on rules, trees, and functions by exploring the uncertain information that exists in the Cardiotocography (CTG) dataset. Classification is imperative in diagnosing the health of the foetus and new born specifically in critical cases. It facilitates the obstetricians in acquiring the information of foetal well-being in pregnancy, substantially for the woman with complications. The research aims to classify the CTG data points into normal, suspicious and pathologic. Rules, trees, and function-based classifiers are applied in machine learning for predicting the health of the new born. Particle Swarm Optimization (PSO) is used in pre-processing for selecting the relevant features. Rough set approximations are exploited in extracting the uncertain information from the data set. The result reveals the importance of useful information present in the uncertain data during classification. In this paper, the overall highest accuracy is displayed by Random Forest classifier with 99.57% and a tree-based approach has shown its supremacy over other approaches.

Object-First Incremental Algorithms for Updating Approximations in Multi-Granulation Fuzzy Probabilistic Rough Sets Over Two Universes

Multi-granulation fuzzy probabilistic rough set (MFPRS) model over two universes has various applications in recent years. However, data are typically changing with time in real-life applications. When data changes, people have to spend a lot of unnecessary time to recalculate the approximations in MFPRS over two universes. To address this problem, we design incremental algorithms based on the object-first approach for updating approximations in MFPRS over two universes while the objects are added into or removed from the two universes. Firstly, considering a case where the equivalence class of the object with respect to the fuzzy relation could be empty, we introduce a model of type-empty MFPRS over two universes. Then, based on the matrix, a traditional algorithm is introduced to calculate approximations in MFPRS over two universes. In addition, by optimizing the traditional algorithm, we design the object-first algorithm which could calculate approximations more efficient in MFPRS over two universes. After that, based on the object-first algorithm, four object-first incremental algorithms are designed for updating approximations in MFPRS over two universes while the objects are added into or removed from two universes. Finally, experimental results show that the proposed object-first incremental algorithms for updating approximations in MFPRS over two universes are more efficient in comparison with the non-incremental algorithms and the traditional incremental algorithms.

INCREMENTALLY UPDATING APPROXIMATION IN INCOMPLETE INFORMATION SYSTEMS UNDER THE VARIATION OF OBJECTS

Rough membership functions in covering approximation space not only give numerical characterizations of covering-based rough set approximations, but also establish the relationship between covering-based rough sets and fuzzy covering-based rough sets. In this paper, we introduce a new method to update the approximation sets with rough membership functions in covering approximation space. Firstly, we present the third types of rough membership functions and study their properties. And then, we consider the change of them while simultaneously adding and removing objects in the information system. Based on that change, we propose a method for updating the approximation sets when the objects vary over time.

Rough set reasoning using answer set programs

Reasoning about uncertainty is one of the main cornerstones of Knowledge Representation. Formal representations of uncertainty are numerous and highly varied due to different types of uncertainty intended to be modeled such as vagueness, imprecision and incompleteness. There is a rich body of theoretical results that has been generated for many of these approaches. It is often the case though, that pragmatic tools for reasoning with uncertainty lag behind this rich body of theoretical results. Rough set theory is one such approach for modeling incompleteness and imprecision based on indiscernibility and its generalizations. In this paper, we provide a pragmatic tool for constructively reasoning with generalized rough set approximations that is based on the use of Answer Set Programming (Asp). We provide an interpretation of answer sets as (generalized) approximations of crisp sets (when possible) and show how to use Asp solvers as a tool for reasoning about (generalized) rough set approximations situated in realistic knowledge bases. The paper includes generic Asp templates for doing this and also provides a case study showing how these techniques can be used to generate reducts for incomplete information systems. Complete, ready to run clingoAsp code is provided in the Appendix, for all programs considered. These can be executed for validation purposes in the clingoAsp solver.

Matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation

Multigranulation rough set model (MGRS) uses multiple equivalence relations on the universe to calculate the approximations, which can solve problem in mutigranulation spaces. In practical applications, information systems often dynamically update due to the variation of objects, attributes or attribute values. Incremental approach is an effective method to calculate approximations for dynamically updated information system. However, existing incremental updating approximations in MGRS mainly focus on single-dimensional variation of objects, attributes or attribute values respectively, without considering multi-dimensional variation of objects, attributes and attribute values. In this paper, we propose matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation of objects, attributes and attribute values. One is the simultaneous variation of objects and attributes (VOA). The other is the simultaneous variation of objects and attribute values (VOV). First, we give the incremental approaches to update the relevant matrices for the dynamically updated information system due to VOA and VOV. Second, based on the updated matrices, we propose two matrix-based incremental algorithms to update approximations. Finally, examples and experimental results demonstrate the effectiveness of the proposed algorithms for incremental updating approximations in multigranulation rough set under two-dimensional variation.

Distributed approach for computing rough set approximations of big incomplete information systems

The size of information gathered from real world applications today is staggering. To make matters worse, this information may also be incomplete, due to errors in measurement or lack of discipline. The two phenomena give rise to a big incomplete information system (IIS). The processing of a big IIS is difficult because of its two problems, big size and incompleteness, and the present work introduces an approach that addresses both. Specifically, we develop an efficient rough set theoretic (RST) algorithm to compute the approximation space of the IIS, which addresses the incompleteness problem. Then we distribute the computational chores of the algorithm using the MapReduce framework, which addresses the size problem. The approach is explained fully, and a detailed illustrative example is provided. For validation and performance analysis, the approach has been implemented and tested on four publicly-accessible big IISs for many metrics including sizeup, scaleup, and speedup. The experimental results attest to its validity, accuracy and efficiency. A comparison test with similar approaches shows that it has superior performance.

Linear approximation fuzzy model for fault detection in cyber-physical system for supply chain management

ABSTRACT The paper’s goal is to propose an IoT assisted Cyber-Physical System with a fault detection technique using a fuzzy algorithm for the supply chain management (SCM). Mathematical models are important for detecting faults. Devicescan contribute to device vulnerabilities. Propertiesof the components in an embedded application can identify defective components in cyber systems of SCM. In this paper linear approximation Boolean fuzzifier model can detect faults in cyber systems of SCM. The rough-set approximation principle with the fuzzy membership functions not only eliminates the ambiguity in the detection method, whereas it helps to classify faulty components in IoT assisted Cyber-Physical System.

High-performance attribute reduction on graphics processing unit

ABSTRACT Recently, graphics processing unit (GPU) gained lots of attention from academia and industry for its applicability in high-performance computing. It has been successfully applied to many fields, such as image processing, machine learning, object detection, etc. In our previous work, GPU was adopted to accelerate the computation of rough set approximation (RSA), which is the core step in most of the rough sets based tasks, e.g. attribute reduction. The method is essentially a CPU-GPU cooperative paradigm. That is to say, there are lots of data exchanged between host memory and GPU memory, which greatly degrades the performance of the system. This paper introduces a unified GPU framework for parallel attribute reduction, in which two critical steps in attribute reduction, i.e. computation of equivalence class and attributes significance, are both executed on GPU. Moreover, the algorithm is well designed by exploiting the architectural characteristics of the modern GPU architecture. Experiments were carried out on data sets with different sizes. The results show that the proposed algorithm can outperform the CPU-GPU cooperative algorithm on large data sets.

Relative relation matrix-based approaches for updating approximations in multigranulation rough sets

Multigranulation rough set (MGRS) theory has attracted much attention. However, with the advent of big data era, the attribute values may often change dynamically, which leads to high computational complexity when handling large and complex data. How to effectively obtain useful knowledge from the dynamic information system becomes an important issue in MGRS. Motivated by this requirement, in this paper, we propose relative relation matrix approaches for computing approximations in MGRS and updating them dynamically. A simplified relative relation matrix is used to calculate approximations in MGRS, it is showed that the space and time complexities are no more than that of the original method. Furthermore, relative relation matrix-based approaches for updating approximations in MGRS while refining or coarsening attribute values are proposed. Several incremental algorithms for updating approximations in MGRS are designed. Finally, experiments are conducted to evaluate the efficiency and validity of the proposed methods.

The Symmetry of Lower and Upper Approximations, Determined by a Cyclic Hypergroup, Applicable in Control Theory

In the first part of our paper, we construct a cyclic hypergroup of matrices using the Ends Lemma. Its properties are then, in the second part of the paper, used to describe the symmetry of lower and upper approximations in certain rough sets with respect to invertible subhypergroups of this cyclic hypergroup. Since our approach is widely used in autonomous robotic systems, we suggest an application of our results for the study of detection sensors, which are used especially in mobile robot mapping.

Indices for rough set approximation and the application to confusion matrices

Confusion matrices and their associated statistics are a well established tool in machine learning to evaluate the accuracy of a classifier. In the present study, we define a rough confusion matrix based on a very general classifier, and derive various statistics from it which are related to common rough set estimators. In other words, we perform a rough set–like analysis on a confusion matrix, which is the converse of the usual procedure; in particular, we consider upper approximations. A suitable index for measuring the tightness of the upper bound uses a ratio of odds. Odds ratios offer a symmetric interpretation of lower and upper precision, and remove the bias in the upper approximation. We investigate rough odds ratios of the parameters obtained from the confusion matrix; to guard against undue random influences, we also approximate their standard errors.

An efficient feature selection based Bayesian and Rough set approach for intrusion detection

The exponential growth of network size leads to increase attacks and intrusions. Detection of these attacks from the network has turned into a noteworthy issue of security. An intrusion detection system is an important approach to achieves high detection rate. A high dimensional dataset increase complexities of detection systems. In this paper, we have designed a novel intelligent system that comprises the feature selection with a hybrid approach of the Rough set theory and the Bayes theorem. The proposed feature selection computed core features and ranked them based on estimated probability. In a decision system, an object may belong to a single or multiple decision, and a feature contains a set of objects that occurrences compute an estimated probability. The rough set theory is being applied to classify information into lower and upper approximations. Uncertain information is distinguished using rough set approximations and solved by the Bayes theorem. In this research work, it has also been highlighted the quantitative realism of recently generated dataset and compared to publicly available datasets. This approach reduces false alarm rate, computational complexity, training complexity and increases detection rate. Comparisons with relevant classifiers are also tabled that show proposed method performs better than existing classifiers.

Relative Reduction of Neighborhood-Covering Pessimistic Multigranulation Rough Set Based on Evidence Theory

Relative reduction of multiple neighborhood-covering with multigranulation rough set has been one of the hot research topics in knowledge reduction theory. In this paper, we explore the relative reduction of covering information system by combining the neighborhood-covering pessimistic multigranulation rough set with evidence theory. First, the lower and upper approximations of multigranulation rough set in neighborhood-covering information systems are introduced based on the concept of neighborhood of objects. Second, the belief and plausibility functions from evidence theory are employed to characterize the approximations of neighborhood-covering multigranulation rough set. Then the relative reduction of neighborhood-covering information system is investigated by using the belief and plausibility functions. Finally, an algorithm for computing a relative reduction of neighborhood-covering pessimistic multigranulation rough set is proposed according to the significance of coverings defined by the belief function, and its validity is examined by a practical example.

Incremental updating approximations for double-quantitative decision-theoretic rough sets with the variation of objects

Double-quantitative decision-theoretic rough sets (Dq-DTRS) provide more comprehensive description methods for rough approximations of concepts, which lay foundations for the development of attribute reduction and rule extraction of rough sets. Existing researches on concept approximations of Dq-DTRS pay more attention to the equivalence class of each object in approximating a concept, and calculate concept approximations from the whole data set in a batch. This makes the calculation of approximations time consuming in dynamic data sets. In this paper, we first analyze the variations of equivalence classes, decision classes, conditional probability, internal grade and external grade in dynamic data sets while objects vary sequentially or simultaneously over time. Then we propose the updating mechanisms for the concept approximations of two types of Dq-DTRS models from incremental perspective in dynamic decision information systems with the sequential and batch variations of objects. Meanwhile, we design incremental sequential insertion, sequential deletion, batch insertion, batch deletion algorithms for two Dq-DTRS models. Finally, we present experimental comparisons showing the feasibility and efficiency of the proposed incremental approaches in calculating approximations and the stability of the incremental updating algorithms from the perspective of the runtime under different inserting and deleting ratios and parameter values.

Classification of Land Cover from Remote Sensing Images using Morphological Linear Contact Distributions and Rough Sets.

Remote sensing image classification plays an essential role in computer vision and image processing to address the problems in the areas of agriculture, forest monitoring, urban development, environment protection, etc. A lot of literature is available on remote sensing image classification. But, it is still a research task even today because of the multitude of problems. RTBFCA (Rough Texture Based Features Classification Algorithm), a new classification algorithm has been proposed in this paper. This paper aims at classifying the remote sensing images into various cover types using mathematical morphology and rough sets. Morphological texture features (linear contact distributions) along with first order statistics are used to identify the pixels of various classes and the concepts of lower and upper approximations of rough sets are used for clustering the features of the pixels and then are finally classified to display the classified image. The proposed method was tested on Google Earth images and is able to classify even various crops patterns of a land cover image. The algorithm is compared with other algorithms like ”GLCM with rough sets”, ”intensity values with rough sets” and with ”linear contact distributions with rough sets”.

Matrix-based approaches for updating approximations in neighborhood multigranulation rough sets while neighborhood classes decreasing or increasing

Matrix-based approaches for updating approximations in neighborhood multigranulation rough sets while neighborhood classes decreasing or increasing

Construction Of Opinion Models For E-Learning Courses By Rough Set Theory And Text Mining

Extracting knowledge through the machine learning techniques in general lacks in its predictions the level of perfection with minimal error or accuracy. Recently, researchers have been enjoying the fruits of Rough Set Theory (RST) to uncover the hidden patterns with its simplicity and expressive power. In RST mainly the issue of attribute reduction is tackled through the notion of ‘reducts’ using lower and upper approximations of rough sets based on a given information table with conditional and decision attributes. Hence, while researchers go for dimension reduction they propose many methods among which RST approach shown to be simple and efficient for text mining tasks. The area of text mining has focused on patterns based on text files or corpus, initially preprocessed to identify and remove irrelevant and replicated words without inducing any information loss for the classifying models later generated and tested. In this current work, this hypothesis are taken as core and tested on feedbacks for e-learning courses using RST’s attribution reduction and generating distinct models of n-grams and finally the results are presented for selecting final efficient model.