Showing papers on "Rough set published in 2017"

A survey of decision making methods based on certain hybrid soft set models

Abstract: Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.

On a novel uncertain soft set model

Abstract: Graphical abstractDisplay Omitted HighlightsA novel Z-soft fuzzy rough set model is constructed.Novel idea and new results are different from Meng-SFR-model and Sun-SFR-model.A kind of decision making method based on the Z-SFR-sets is investigated.The comparisons of numerical experimentation are given.An overview of techniques based on some types of soft set models are discussed. In this paper, a kind of novel soft set model called a Z-soft fuzzy rough set is presented by means of three uncertain models: soft sets, rough sets and fuzzy sets, which is an important generalization of Z-soft rough fuzzy sets. As a novel Z-soft fuzzy rough set, its applications in the corresponding decision making problems are established. It is noteworthy that the underlying concepts keep the features of classical Pawlak rough sets. Moreover, this novel approach will involve fewer calculations when one applies this theory to algebraic structures. In particular, an approach for the method of decision making problem with respect to Z-soft fuzzy rough sets is proposed and the validity of the decision making methods is testified by a given example. At the same time, an overview of techniques based on some types of soft set models is investigated. Finally, the numerical experimentation algorithm is developed, in which the comparisons among three types of hybrid soft set models are analyzed.

A novel soft rough set

Abstract: Graphical abstractDisplay Omitted In this paper, we investigate the relationships among rough sets, soft sets and hemirings. The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring. It is pointed out that in this paper, we first apply soft rough sets to algebraic structure-hemirings. Further, we first put forward the concepts of C-soft sets and CC-soft sets, which provide a new research idea for soft rough algebraic research. Moreover, we study roughness in hemirings with respect to MSR-approximation spaces. Some new soft rough operations over hemirings are explored. In particular, lower and upper MSR-hemirings (k-ideal and h-ideal) are investigated. Finally, we put forth an approach for multicriteria group decision making problem based on modified soft rough sets and offer an actual example.

Multigranulation fuzzy rough set over two universes and its application to decision making

Abstract: The original Pawlaks rough set approach based on indiscernibility relation (single granularity) has been extended to multigranulation rough set structure in the recent years. Multigranulation rough set approach has become a flouring research direction in rough set theory. This paper considers rough approximation of a fuzzy concept under the framework of multigranulation over two different universes of discourse, i.e., multigranulation fuzzy rough set models over two universes. We present three types of multigranulation fuzzy rough set over two universes by the constructive approach, respectively. Some interesting properties of the proposed models are discussed and also the interrelationships between the proposed models and the existing rough set models are given. We then propose a new approach to a kind of multiple criteria group decision making problem based on multigranulation fuzzy rough set model over two universes. The decision rules and algorithm of the proposed method are given and an example of handling multiple criteria group decision making problem of clothes ranking illustrates this approach. The main contribution of this paper is twofold. One is to establish the multigranulation fuzzy rough set theory over two universes. Another is to try presenting a new approach to multiple criteria group decision making based on multigranulation fuzzy rough set over two universes. The proposed models not only enrich the theory of multigranulation rough set but also make a tentative to provide a new perspective for multiple criteria group decision making with uncertainty.

Ensemble feature selection using bi-objective genetic algorithm

Abstract: An ensemble parallel processing bi-objective genetic algorithm based feature selection method is proposed.Rough set theory and Mutual information gain are used to select informative data removing the vague one.Parallel processing in genetic algorithm reduces time complexity.The method is compared with the existing state-of-the-art methods using suitable datasets.Classification accuracy and statistical measures outperforms that of other state-of-the-art methods. Feature selection problem in data mining is addressed here by proposing a bi-objective genetic algorithm based feature selection method. Boundary region analysis of rough set theory and multivariate mutual information of information theory are used as two objective functions in the proposed work, to select only precise and informative data from the data set. Data set is sampled with replacement strategy and the method is applied to determine non-dominated feature subsets from each sampled data set. Finally, ensemble of such bi-objective genetic algorithm based feature selectors is developed with the help of parallel implementations to produce much generalized feature subset. In fact, individual feature selector outputs are aggregated using a novel dominance based principle to produce final feature subset. Proposed work is validated using repository especially for feature selection datasets as well as on UCI machine learning repository datasets and the experimental results are compared with related state of art feature selection methods to show effectiveness of the proposed ensemble feature selection method.

A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making

Abstract: This paper introduces the notion of Z-soft rough fuzzy sets of hemirings, which is an extended notion of soft rough sets and rough fuzzy sets. It is pointed out that this novel concept removes the limiting condition that full soft sets require in Feng-soft rough fuzzy sets and Meng-soft rough fuzzy sets. We study roughness in hemirings with respect to a ZS-approximation space. Some new soft rough fuzzy operations over hemirings are explored. In particular, Z-lower and Z-upper soft rough fuzzy ideals (k-ideals, h-ideals, strong h-ideals) are investigated. Finally, we put forth an approach for decision making problem based on Z-soft rough fuzzy sets and give an example. Corresponding decision making methods based on Z-soft rough fuzzy sets are analysed.

Online feature selection for high-dimensional class-imbalanced data

Abstract: When tackling high dimensionality in data mining, online feature selection which deals with features flowing in one by one over time, presents more advantages than traditional feature selection methods. However, in real-world applications, such as fraud detection and medical diagnosis, the data is high-dimensional and highly class imbalanced, namely there are many more instances of some classes than others. In such cases of class imbalance, existing online feature selection algorithms usually ignore the small classes which can be important in these applications. It is hence a challenge to learn from high-dimensional and class imbalanced data in an online manner. Motivated by this, we first formalize the problem of online streaming feature selection for class imbalanced data, and then present an efficient online feature selection framework regarding the dependency between condition features and decision classes. Meanwhile, we propose a new algorithm of Online Feature Selection based on the Dependency in K nearest neighbors, called K-OFSD. In terms of Neighborhood Rough Set theory, K-OFSD uses the information of nearest neighbors to select relevant features which can get higher separability between the majority class and the minority class. Finally, experimental studies on seven high-dimensional and class imbalanced data sets show that our algorithm can achieve better performance than traditional feature selection methods with the same numbers of features and state-of-the-art online streaming feature selection algorithms in an online manner.

Incorporating Diversity and Informativeness in Multiple-Instance Active Learning

Abstract: Multiple-instance active learning (MIAL) is a paradigm to collect sufficient training bags for a multiple-instance learning (MIL) problem, by selecting and querying the most valuable unlabeled bags iteratively. Existing works on MIAL evaluate an unlabeled bag by its informativeness with regard to the current classifier, but neglect the internal distribution of its instances, which can reflect the diversity of the bag. In this paper, two diversity criteria, i.e., clustering-based diversity and fuzzy rough set based diversity, are proposed for MIAL by utilizing a support vector machine (SVM) based MIL classifier. In the first criterion, a kernel $k$ -means clustering algorithm is used to explore the hidden structure of the instances in the feature space of the SVM, and the diversity degree of an unlabeled bag is measured by the number of unique clusters covered by the bag. In the second criterion, the lower approximations in fuzzy rough sets are used to define a new concept named dissimilarity degree, which depicts the uniqueness of an instance so as to measure the diversity degree of a bag. By incorporating the proposed diversity criteria with existing informativeness measurements, new MIAL algorithms are developed, which can select bags with both high informativeness and diversity. Experimental comparisons demonstrate the feasibility and effectiveness of the proposed methods.

Matrix-based dynamic updating rough fuzzy approximations for data mining

Abstract: In a dynamic environment, the data collected from real applications varies not only with the amount of objects but also with the number of features, which will result in continuous change of knowledge over time. The static methods of updating knowledge need to recompute from scratch when new data are added every time. This makes it potentially very time-consuming to update knowledge, especially as the dataset grows dramatically. Calculation of approximations is one of main mining tasks in rough set theory, like frequent pattern mining in association rules. Considering the fuzzy descriptions of decision states in the universe under fuzzy environment, this paper aims to provide an efficient approach for computing rough approximations of fuzzy concepts in dynamic fuzzy decision systems (FDS) with simultaneous variation of objects and features. We firstly present a matrix-based representation of rough fuzzy approximations by a Boolean matrix associated with a matrix operator in FDS. While adding the objects and features concurrently, incremental mechanisms for updating rough fuzzy approximations are introduced, and the corresponding matrix-based dynamic algorithm is developed. Unlike the static method of computing approximations by updating the whole relation matrix, our new approach partitions it into sub-matrices and updates each sub-matrix locally by utilizing the previous matrix information and the interactive information of each sub-matrix to avoid unnecessary calculations. Experimental results on six UCI datasets shown that the proposed dynamic algorithm achieves significantly higher efficiency than the static algorithm and the combination of two reference incremental algorithms.

A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model

Abstract: Smarandache initiated neutrosophic sets (NSs) as a tool for handling undetermined information. Wang et al. proposed single valued neutrosophic sets (SVNSs) that is an especial NSs and can be used expediently to deal with real-world problems. In this paper, we propose single valued neutrosophic rough sets by combining single valued neutrosophic sets and rough sets. We study the hybrid model by constructive and axiomatic approaches. Firstly, by using the constructive approach, we propose the lower/upper single valued neutrosophic approximation operators and illustrate the connections between special single valued neutrosophic relations (SVNRs) and the lower/upper single valued neutrosophic approximation operators. Then, by using the axiomatic approach, we discuss the operator-oriented axiomatic characterizations of single valued neutrosophic rough sets. We obtain that different axiom sets of the lower/upper single valued neutrosophic set-theoretic operators guarantee the existence of different classes of SVNRs which produce the same operators. Finally, we introduce single valued neutrosophic rough sets on two-universes and an algorithm of decision making based on single valued neutrosophic rough sets on two-universes, and use an illustrative example to demonstrate the application of the proposed model.

Attribute Selection for Partially Labeled Categorical Data By Rough Set Approach

Abstract: Attribute selection is considered as the most characteristic result in rough set theory to distinguish itself to other theories. However, existing attribute selection approaches can not handle partially labeled data. So far, few studies on attribute selection in partially labeled data have been conducted. In this paper, the concept of discernibility pair based on rough set theory is raised to construct a uniform measure for the attributes in both supervised framework and unsupervised framework. Based on discernibility pair, two kinds of semisupervised attribute selection algorithm based on rough set theory are developed to handle partially labeled categorical data. Experiments demonstrate the effectiveness of the proposed attribute selection algorithms.

Three-way decisions in ordered decision system

Abstract: As a natural extension of three-way decisions, this paper presents a novel three-way decision model with order information. First, we do some comparative analysis between ordered three-way decisions and decision-theoretic rough sets, and then present some important properties of the proposed model. Second, a hybrid decision table consisted both of the “order information” and “loss function”, is utilized to solve the ordered three-way decisions with two classification problem. Two order sets (dominating set and dominated set generated by order relation) and three risk strategies (optimistic strategy, equable strategy, pessimistic strategy) are induced to construct the model and design the algorithm of ordered three-way decisions. At last, an illustrative example of salary administration validates the reasonability and effectiveness of our approach.

Bipolar neutrosophic soft sets and applications in decision making

Abstract: Neutrosophic set, proposed by Smarandache considers a truth membership function, an indeterminacy membership function and a falsity membership function. Soft set, proposed by Molodtsov is a mathematical framework which has the ability of independency of parameterizations inadequacy, syndrome of fuzzy set, rough set, probability. Those concepts have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, game theory, pattern recognition, and computer vision. Nonetheless, there are many problems in real-world applications containing indeterminate and inconsistent information that cannot be effectively handled by the neutrosophic set and soft set. In this paper, we propose the notation of bipolar neutrosophic soft sets that combines soft sets and bipolar neutrosophic sets. Some algebraic operations of the bipolar neutrosophic set such as the complement, union, intersection are examined. We then propose an aggregation bipolar neutrosophic soft operator of a bipolar neutrosophic soft set and develop a decision making algorithm based on bipolar neutrosophic soft sets. Numerical examples are given to show the feasibility and effectiveness of the developed approach.

Measures of uncertainty for neighborhood rough sets

Abstract: Uncertainty measures are critical evaluating tools in machine learning fields, which can measure the dependence and similarity between two feature subsets and can be used to judge the significance of features in classifying and clustering algorithms. In the classical rough sets, there are some uncertainty tools to measure a feature subset, including accuracy, roughness, information entropy, rough entropy, etc. These measures are applicable to discrete-valued information systems, but not suitable to real-valued data sets. In this paper, by introducing the neighborhood rough set model, each object is associated with a neighborhood subset, named a neighborhood granule. Several uncertainty measures of neighborhood granules are proposed, which are neighborhood accuracy, information quantity, neighborhood entropy and information granularity in the neighborhood systems. Furthermore, we prove that these uncertainty measures satisfy non-negativity, invariance and monotonicity. The maximum and minimum of these measures are also given. Theoretical analysis and experimental results show that information quantity, neighborhood entropy and information granularity measures are better than the neighborhood accuracy measure in the neighborhood systems.

Active Sample Selection Based Incremental Algorithm for Attribute Reduction With Rough Sets

Abstract: Attribute reduction with rough sets is an effective technique for obtaining a compact and informative attribute set from a given dataset. However, traditional algorithms have no explicit provision for handling dynamic datasets where data present themselves in successive samples. Incremental algorithms for attribute reduction with rough sets have been recently introduced to handle dynamic datasets with large samples, though they have high complexity in time and space. To address the time/space complexity issue of the algorithms, this paper presents a novel incremental algorithm for attribute reduction with rough sets based on the adoption of an active sample selection process and an insight into the attribute reduction process. This algorithm first decides whether each incoming sample is useful with respect to the current dataset by the active sample selection process. A useless sample is discarded while a useful sample is selected to update a reduct. At the arrival of a useful sample, the attribute reduction process is then employed to guide how to add and/or delete attributes in the current reduct. The two processes thus constitute the theoretical framework of our algorithm. The proposed algorithm is finally experimentally shown to be efficient in time and space.

A brief review of modeling approaches based on fuzzy time series

Abstract: Recently, there seems to be increased interest in time series forecasting using soft computing (SC) techniques, such as fuzzy sets, artificial neural networks (ANNs), rough set (RS) and evolutionary computing (EC). Among them, fuzzy set is widely used technique in this domain, which is referred to as “Fuzzy Time Series (FTS)”. In this survey, extensive information and knowledge are provided for the FTS concepts and their applications in time series forecasting. This article reviews and summarizes previous research works in the FTS modeling approach from the period 1993–2013 (June). Here, we also provide a brief introduction to SC techniques, because in many cases problems can be solved most effectively by integrating these techniques into different phases of the FTS modeling approach. Hence, several techniques that are hybridized with the FTS modeling approach are discussed briefly. We also identified various domains specific problems and research trends, and try to categorize them. The article ends with the implication for future works. This review may serve as a stepping stone for the amateurs and advanced researchers in this domain.

A Comparative Study of Statistical and Rough Computing Models in Predictive Data Analysis

Abstract: Information and technology revolution has brought a radical change in the way data are collected. The data collected is of no use unless some useful information is derived from it. Therefore, it is essential to think of some predictive analysis for analyzing data and to get meaningful information. Much research has been carried out in the direction of predictive data analysis starting from statistical techniques to intelligent computing techniques and further to hybridize computing techniques. The prime objective of this paper is to make a comparative analysis between statistical, rough computing, and hybridized techniques. The comparative analysis is carried out over financial bankruptcy data set of Greek industrial bank ETEVA. It is concluded that rough computing techniques provide better accuracy 88.2% as compared to statistical techniques whereas hybridized computing techniques provides still better accuracy 94.1% as compared to rough computing techniques.

Uncertainty measurement for incomplete interval-valued information systems based on α-weak similarity

Abstract: Rough set theory is a powerful mathematical tool to deal with uncertainty in data analysis. Interval-valued information systems are generalized models of single-valued information systems. Recently, uncertainty measures for complete interval-valued information systems or complete interval-valued decision systems have been developed. However, there are few studies on uncertainty measurements for incomplete interval-valued information systems. This paper aims to investigate the uncertainty measures in incomplete interval-valued information systems based on an α -weak similarity. Firstly, the maximum and the minimum similarity degrees are defined when interval-values information systems are incomplete based on the similarity relation. The concept of α -weak similarity relation is also defined. Secondly, the rough set model is constructed. Based on this model, accuracy, roughness and approximation accuracy are given to evaluate the uncertainty in incomplete interval-valued information systems. Furthermore, experimental analysis shows the effectiveness of the constructed uncertainty measures for incomplete interval-valued information systems.