Single Valued Neutrosophic Hesitant Fuzzy Rough Set and Its Application

In this paper, we proposed the notion of single valued neutrosophic hesitant fuzzy rough set, by combining single valued neutrosophic hesitant fuzzy set and rough set. The combination of single valued neutrosophic hesitant fuzzy set and rough set is a powerful tool for dealing with uncertainty, granularity and incompleteness of knowledge in information systems. We presented both definition and some basic properties of the proposed model. Finally, we gave a general approach which is applied to a decision making problem in disease diagnoses, and demonstrated the effectiveness of the approach by a numerical example.

A Fuzzy-Rough Feature Selection Based on Binary Shuffled Frog Leaping Algorithm

Feature selection and attribute reduction are crucial problems, and widely used techniques in the field of machine learning, data mining and pattern recognition to overcome the well-known phenomenon of the Curse of Dimensionality. This paper presents a feature selection method that efficiently carries out attribute reduction, thereby selecting the most informative features of a dataset. It consists of two components: 1) a measure for feature subset evaluation, and 2) a search strategy. For the evaluation measure, we have employed the fuzzy-rough dependency degree (FRFDD) of the lower approximation-based fuzzy-rough feature selection (L-FRFS) due to its effectiveness in feature selection. As for the search strategy, a modified version of a binary shuffled frog leaping algorithm is proposed (B-SFLA). The proposed feature selection method is obtained by hybridizing the B-SFLA with the FRDD. Nine classifiers have been employed to compare the proposed approach with several existing methods over twenty two datasets, including nine high dimensional and large ones, from the UCI repository. The experimental results demonstrate that the B-SFLA approach significantly outperforms other metaheuristic methods in terms of the number of selected features and the classification accuracy.

Studies on Properties of Knowledge Dependency and Reduction Algorithm in Tolerance Rough Set Model

Relation between tolerance class and indispensable attribute and knowledge dependency in rough set model with tolerance relation is explored. After giving definitions and concepts of knowledge dependency and knowledge dependency degree for incomplete information system in tolerance rough set model by distinguishing decision attribute containing missing attribute value or not, the result of maintaining reflectivity, transitivity, augmentation, decomposition law and merge law for complete knowledge dependency is proved. Knowledge dependency degrees (not complete knowledge dependency degrees) only satisfy some laws after transitivity, augmentation and decomposition operations. An algorithm to solve attribute reduction in an incomplete decision table is designed. The correctness is checked by an example.

Invariant Characters of Tolerance Class and Reduction under Homomorphism in IIS

Some invariant properties of incomplete information systems homomorphism are studied in this paper. Demand conditions of tolerance class, attribute reduction, indispensable attribute and dispensable attribute being invariant under homomorphism in incomplete information system are revealed and discussed. The existing condition of endohomomorphism on an incomplete information system is also explored. It establishes some theoretical foundations for further investigations on incomplete information systems in rough set theory, like in information systems.

An Improved Limited Tolerance Rough Set Model

Some extended rough set models in incomplete information system cannot distinguish the two objects that have few known attributes and more unknown attributes; some cannot make a flexible and accurate discrimination. In order to solve this problem, this paper suggests an improved limited tolerance rough set model using two thresholds to control what two objects have a relationship between them in limited tolerance relation and to classify objects. Our practical study case shows the model can get fine and reasonable decision results.

Application of Granular Computing Paradigm in Knowledge Induction

This paper illustrates an application of granular computing approach, namely rough set theory in data mining. The paper outlines the formalism of granular computing and elucidates the mathematical underpinning of rough set theory, which has been widely used by the data mining and the machine learning community. A real-world application is illustrated, and the classification performance is compared with other contending machine learning algorithms. The predictive performance of the rough set rule induction model shows comparative success with respect to other contending algorithms.

Generalized Rough Sets Applied to Graphs Related to Urban Problems

Branch of modern mathematics, graphs represent instruments for optimization and solving practical applications in various fields such as economic networks, engineering, network optimization, the geometry of social action, generally, complex systems including contemporary urban problems (path or transport efficiencies, biourbanism, & c.). In this paper is studied the interconnection of some urban network, which can lead to a simulation problem of a digraph through another digraph. The simulation is made univoc or more general multivoc. The concepts of fragment and atom are very useful in the study of connectivity in the digraph that is simulation - including an alternative evaluation of k- connectivity. Rough set approach in (bi)digraph which is proposed in premier in this paper contribute to improved significantly the evaluation of k-connectivity. This rough set approach is based on generalized rough sets - basic facts are presented in this paper.

Properties and Approximation Distribution Reductions in Multigranulation Rough Set Model

Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.

An Improved Variable Tolerance RSM with a Proportion Threshold

In rough set models, tolerance relation, similarity relation and limited tolerance relation solve different situation problems for incomplete information systems in which there exists a phenomenon of missing value. If two objects have the same few known attributes and more unknown attributes, they cannot distinguish them well. In order to solve this problem, we presented two improved limited and variable precision rough set models. One is symmetric, the other one is non-symmetric. They all use more stringent condition to separate two small probability equivalent objects into different classes. The two models are needed to engage further study in detail. In the present paper, we newly form object classes with a different respect comparing to the first suggested model. We overcome disadvantages of non-symmetry regarding to the second suggested model. We discuss relationships between or among several models and also make rule generation. The obtained results by applying the second model are more accurate and reasonable.

Cost Sensitive Feature Selection in Decision-Theoretic Rough Set Models for Customer Churn Prediction: The Case of Telecommunication Sector Customers

In recent days, there is a change and the ongoing development of the telecommunications sector in the global market. In this sector, churn analysis techniques are commonly used for analysing why some customers terminate their service subscriptions prematurely. In addition, customer churn is utmost significant in this sector since it causes to important business loss. Many companies make various researches in order to prevent losses while increasing customer loyalty. Although a large quantity of accumulated data is available in this sector, their usefulness is limited by data quality and relevance. In this paper, a cost-sensitive feature selection framework is developed aiming to obtain the feature reducts to predict customer churn. The framework is a cost based optional pre-processing stage to remove redundant features for churn management. In addition, this cost-based feature selection algorithm is applied in a telecommunication company in Turkey and the results obtained with this algorithm.

Upgraded Rough Clustering and Outlier Detection Method on Yeast Dataset by Entropy Rough K-Means Method

Rough set theory is used to handle uncertainty and incomplete information by applying two accurate sets, Lower approximation and Upper approximation. In this paper, the rough clustering algorithms are improved by adopting the Similarity, Dissimilarity–Similarity and Entropy based initial centroids selection method on three different clustering algorithms namely Entropy based Rough K-Means (ERKM), Similarity based Rough K-Means (SRKM) and Dissimilarity-Similarity based Rough K-Means (DSRKM) were developed and executed by yeast dataset. The rough clustering algorithms are validated by cluster validity indexes namely Rand and Adjusted Rand indexes. An experimental result shows that the ERKM clustering algorithm perform effectively and delivers better results than other clustering methods. Outlier detection is an important task in data mining and very much different from the rest of the objects in the clusters. Entropy based Rough Outlier Factor (EROF) method is seemly to detect outlier effectively for yeast dataset. In rough K-Means method, by tuning the epsilon (ᶓ) value from 0.8 to 1.08 can detect outliers on boundary region and the RKM algorithm delivers better results, when choosing the value of epsilon (ᶓ) in the specified range. An experimental result shows that the EROF method on clustering algorithm performed very well and suitable for detecting outlier effectively for all datasets. Further, experimental readings show that the ERKM clustering method outperformed the other methods.

Fuzzy Population-Based Meta-Heuristic Approaches for Attribute Reduction in Rough Set Theory

One of the global combinatorial optimization problems in machine learning is feature selection. It concerned with removing the irrelevant, noisy, and redundant data, along with keeping the original meaning of the original data. Attribute reduction in rough set theory is an important feature selection method. Since attribute reduction is an NP-hard problem, it is necessary to investigate fast and effective approximate algorithms. In this paper, we proposed two feature selection mechanisms based on memetic algorithms (MAs) which combine the genetic algorithm with a fuzzy record to record travel algorithm and a fuzzy controlled great deluge algorithm, to identify a good balance between local search and genetic search. In order to verify the proposed approaches, numerical experiments are carried out on thirteen datasets. The results show that the MAs approaches are efficient in solving attribute reduction problems when compared with other meta-heuristic approaches.

Pruning Algorithm for the Minimum Rule Reduct Generation

In this paper we consider the rule reduct generation problem. Rule Reduct Generation (RG) and Modified Rule Generation (MRG) algorithms, that are used to solve this problem, are well-known. Alternative to these algorithms, we develop Pruning Rule Generation (PRG) algorithm. We compare the PRG algorithm with RG and MRG.

Frequent Itemset Mining Using Rough-Sets

Frequent pattern mining is the process of finding a pattern (a set of items, subsequences, substructures, etc.) that occurs frequently in a data set. It was proposed in the context of frequent itemsets and association rule mining. Frequent pattern mining is used to find inherent regularities in data. What products were often purchased together? Its applications include basket data analysis, cross-marketing, catalog design, sale campaign analysis, Web log (click stream) analysis, and DNA sequence analysis. However, one of the bottlenecks of frequent itemset mining is that as the data increase the amount of time and resources required to mining the data increases at an exponential rate. In this investigation a new algorithm is proposed which can be uses as a pre-processor for frequent itemset mining. FASTER (FeAture SelecTion using Entropy and Rough sets) is a hybrid pre-processor algorithm which utilizes entropy and roughsets to carry out record reduction and feature (attribute) selection respectively. FASTER for frequent itemset mining can produce a speed up of 3.1 times when compared to original algorithm while maintaining an accuracy of 71%.

Intelligent Assistive Methods for Diagnosis of Rheumatoid Arthritis Using Histogram Smoothing and Feature Extraction of Bone Images

Advances in the field of image processing envision a new era of evaluation techniques and application of procedures in various different fields. One such field being considered is the biomedical field for prognosis as well as diagnosis of diseases. This plethora of methods though provides a wide range of options to select from, it also proves confusion in selecting the apt process and also in finding which one is more suitable. Our objective is to use a series of techniques on bone scans, so as to detect the occurrence of rheumatoid arthritis (RA) as accurately as possible. Amongst other techniques existing in the field our proposed system tends to be more effective as it depends on new methodologies that have been proved to be better and more consistent than others. Computer aided diagnosis will provide more accurate and infallible rate of consistency that will help to improve the efficiency of the system. The image first undergoes histogram smoothing and specification, morphing operation, boundary detection by edge following algorithm and finally image subtraction to determine the presence of rheumatoid arthritis in a more efficient and effective way. Using preprocessing noises are removed from images and using segmentation, region of interest is found and Histogram smoothing is applied for a specific portion of the images. Gray level co-occurrence matrix (GLCM) features like Mean, Median, Energy, Correlation, Bone Mineral Density (BMD) and etc. After finding all the features it stores in the database. This dataset is trained with inflamed and noninflamed values and with the help of neural network all the new images are checked properly for their status and Rough set is implemented for further reduction.

Some Properties of IF Rough Relational Algebraic Operators in Medical Databases

Some properties of Intuitionistic Fuzzy (IF) rough relational algebraic operators under an IF rough relational data model are investigated and illustrated using diabetes and heart disease databases. These properties are important and desirable for processing queries in an effective and efficient manner.  

Data Mining to Capture User-Experience: A Case Study in Notebook Product Appearance Design

In the era of rapidly increasing notebook market, consumer electronics manufacturers are facing a highly dynamic and competitive environment. In particular, the product appearance is the first part for user to distinguish the product from the product of other brands. Notebook product should differ in its appearance to engage users and contribute to the user experience (UX). The UX evaluates various product concepts to find the design for user needs; in addition, help the designer to further understand the product appearance preference of different market segment. However, few studies have been done for exploring the relationship between consumer background and the reaction of product appearance. This study aims to propose a data mining framework to capture the user’s information and the important relation between product appearance factors. The proposed framework consists of problem definition and structuring, data preparation, rules generation, and results evaluation and interpretation. An empirical study has been done in Taiwan that recruited 168 subjects from different background to experience the appearance performance of 11 different portable computers. The results assist the designers to develop product strategies based on the characteristics of consumers and the product concept that related to the UX, which help to launch the products to the right customers and increase the market shares. The results have shown the practical feasibility of the proposed framework.

Rough Neural Networks in Adapting Cellular Automata Rule for Reducing Image Noise

The reduction or removal of noise in a color image is an essential part of image processing, whether the final information is used for human perception or for an automatic inspection and analysis. This paper describes the modeling system based on the rough neural network model to adaptive cellular automata for various image processing tasks and noise remover. In this paper, we consider the problem of object processing in colored image using rough neural networks to help deriving the rules which will be used in cellular automata for noise image. The proposed method is compared with some classical and recent methods. The results demonstrate that the new model is capable of being trained to perform many different tasks, and that the quality of these results is comparable or better than established specialized algorithms.

Simultaneous Clustering and Feature Selection Method for Gene Expression Data

Microarrays are made it possible to simultaneously monitor the expression profiles of thousands of genes under various experimental conditions. It is used to identify the co-expressed genes in specific cells or tissues that are actively used to make proteins. This method is used to analysis the gene expression, an important task in bioinformatics research. Cluster analysis of gene expression data has proved to be a useful tool for identifying co-expressed genes, biologically relevant groupings of genes and samples. In this work K-Means algorithms has been applied for clustering of Gene Expression Data. Further, rough set based Quick reduct algorithm has been applied for each cluster in order to select the most similar genes having high correlation. Then the ACV measure is used to evaluate the refined clusters and classification is used to evaluate the proposed method. They could identify compact clusters with feature selection method used to genes are selected.

A New Hybrid K-Mean-Quick Reduct Algorithm for Gene Selection

Feature selection is a process to select features which are more informative. It is one of the important steps in knowledge discovery. The problem is that all genes are not important in gene expression data. Some of the genes may be redundant, and others may be irrelevant and noisy. Here a novel approach is proposed Hybrid K-Mean-Quick Reduct (KMQR) algorithm for gene selection from gene expression data. In this study, the entire dataset is divided into clusters by applying K-Means algorithm. Each cluster contains similar genes. The high class discriminated genes has been selected based on their degree of dependence by applying Quick Reduct algorithm to all the clusters. Average Correlation Value (ACV) is calculated for the high class discriminated genes. The clusters which have the ACV value as 1 is determined as significant clusters, whose classification accuracy will be equal or high when comparing to the accuracy of the entire dataset. The proposed algorithm is evaluated using WEKA classifiers and compared. The proposed work shows that the high classification accuracy.