Fuzzy Rough Set Approach Research Articles

Another view on tolerance based multigranulation q-rung orthopair fuzzy rough sets with applications

The q-rung orthopair fuzzy sets accommodate more uncertainties than the Pythagorean fuzzy sets and hence their applications are much extensive. Under the q-rung orthopair fuzzy set, the objective of this paper is to develop new types of q-rung orthopair fuzzy lower and upper approximations by applying the tolerance degree on the similarity between two objects. After employing tolerance degree based q-rung orthopair fuzzy rough set approach to it any times, we can get only the six different sets at most. That is to say, every rough set in a universe can be approximated by only six sets, where the lower and upper approximations of each set in the six sets are still lying among these six sets. The relationships among these six sets are established. Furthermore, we propose tolerance degree based multi granulation optimistic/pessimistic q-rung orthopair fuzzy rough sets and investigate some of their properties. Another main contribution of this paper is to disclose the ideas of different kinds of approximations called approximate precision, rough degree, approximate quality and their mutual relationship. Finally a technique is devloped to rank the alternatives in a q-rung orthopair fuzzy information system based on similarity relation. We find that the proposed method/technique is more efficient when compared with other existing techniques.

Neighborhood relation-based variable precision multigranulation Pythagorean fuzzy rough set approach for multi-attribute group decision making

Nowadays, the complexity of real decision-making problem makes people pay more and more attention to the effective evaluation and selection of decision methods. Considering that the Pythagorean fuzzy set (PFS) owing its better capacity can express the uncertainties of human inherent preferences, multigranulation Pythagorean fuzzy rough set (MGPFRS) model is proposed to handle uncertain multi-attribute group decision making (MAGDM) problem. We firstly build the δ−neighborhood relation over multi-attribute Pythagorean fuzzy decision making (MAPFDM) information system based on the distance measurement. Then, combined with the principle of variable precision rough set and PF information, the rough approximation of crisp and inaccuracy concept are discussed. That is, the variable precision multigranulation rough Pythagorean fuzzy set (VMGRPFS). On this basis, given the special case of fuzzy equivalence relation, we propose the variable precision multigranulation Pythagorean fuzzy rough set (VMGPFRS). Furthermore, some fascinating properties for the VMGRPFS and VMGPFRS model are given. The corresponding models of optimistic and pessimistic are deduced respectively. The interrelationship among of the established VMGRPFS and VMGPFRS with the classical multigranulation rough set are discussed in detail. In addition, a new MAGDM method with Pythagorean fuzzy information is proposed by using VMGPFRS and PROMETHEE methods. This method points out the basic principle and algorithm of decision making. Finally, we perform our established method to select the best photovoltaic cell and implement the comparative analysis which can verify the reliability and superiority of our approach.

A noise-aware fuzzy rough set approach for feature selection

Feature selection has aroused extensive attention and aims at selecting features that are highly relevant to classification from raw datasets to improve the performance of a learning model. Fuzzy rough set theory is a powerful mathematical method for feature selection. The classical fuzzy rough set model is very sensitive to the noise while the noise samples in classification data often appear. In addition, fuzzy rough set theory does not fit well when the density distribution of the samples in the dataset varies greatly. Thus, it is of great significance to improve the robustness of fuzzy rough set models and its adaptability to data for feature selection. Inspired by these issues, we focus on the robust fuzzy rough set approach for feature selection. We first propose a robust fuzzy rough set model based on data distribution to achieve the purpose of anti-noise i.e., Noise-aware Fuzzy Rough Sets (NFRS) model. This model proposes a novel search mechanism, which weakens the sensitivity of the approximation operator to noise by considering the distribution of samples in the decision classes to weight the samples, further obtains three kinds of samples, i.e., intra-class samples, boundary samples, and outlier samples. Then, the degrees of relevance of the feature for class is defined by the dependency function based on the NFRS model to evaluate the significance of the feature subset. On this basis, an evaluation function about feature significance is constructed, which simultaneously considers the relevance and redundancy of a candidate feature provided for the selected subset and the remaining feature subset. A novel forward greedy search algorithm is presented to select a feature sequence. The selected features are subsequently evaluated with downstream classification tasks. Experimental using real-world datasets demonstrate the effectiveness of the proposed model and its superiority against comparison baseline methods.

A fuzzy rough set approach to hierarchical feature selection based on Hausdorff distance

A fuzzy rough set approach to hierarchical feature selection based on Hausdorff distance

Tranquility and Anxiety in Multi-Attribute Decision Making Under Hesitant Fuzzy Linguistic Environment with Interactive Attributes: A Set-Valued Fuzzy Rough Set Approach

Tranquility and Anxiety in Multi-Attribute Decision Making Under Hesitant Fuzzy Linguistic Environment with Interactive Attributes: A Set-Valued Fuzzy Rough Set Approach

Prediction of Breast Cancer through Tolerance-based Intuitionistic Fuzzy-rough Set Feature Selection and Artificial Neural Network

The importance of diagnosing breast cancer is one of the most significant issues in medical science. Diagnosing whether the cancer is benign or malignant is extremely essential in ascertaining the type of cure, moreover, to bringing down bills. This study aims to use the tolerance-based intuitionistic fuzzy-rough set approach to pick attributes and data processing with help of machine learning for the classification of breast cancer. The main purpose of selecting a feature is to make a subset of input variables by removing irrelevant variables or variables that lack predictive information. This study shows how to eliminate redundant data in big data and achieve more efficient results. Rough set theory has already been used successfully to set down attributes, but this theory is insufficient to reduce the properties of a real- value dataset because it will possibly drop knowledge through the decomposition procedure. and this prevents us from getting the right results. In this study, we used the tolerance based intuitive fuzzy rough method for attribute selection. In this technique, lower and upper approaches are used to intuitive fuzzy sets from rough sets to remove uncertainty due to having simultaneous membership, non-membership, and hesitation degrees and obtain better results. The used method is demonstrated to be better performing in the shape of chosen attributes.

Fuzzy distance-based filter-wrapper incremental algorithms for attribute reduction when adding or deleting attribute set

Attribute reduction is a critical problem in the data preprocessing step with the aim of minimizing redundant attributes to improve the efficiency of data mining models. The fuzzy rough set theory is considered an effective tool to solve the attribute reduction problem directly on the original decision system, without data preprocessing. With the current digital transformation trend, decision systems are larger in size and updated. To solve the attribute reduction problem directly on change decision systems, a number of recent studies have proposed incremental algorithms to find reducts according to fuzzy rough set approach to reduce execution time. However, the proposed algorithms follow the traditional filter approach. Therefore, the obtained reduct is not optimal in both criteria: the number of attribute of the reducts and the accuracy of classification model. In this paper, we propose incremental algorithms that find reducts following filter-wrapper approach using fuzzy distance measure in the case of adding and deleting attribute set. The experimental results on the sample datasets show that the proposed algorithms significantly reduce the number of attributes in reduct and improve the classification accuracy compared to other algorithms using filter approach

Note on “Tolerance-based intuitionistic fuzzy-rough set approach for attribute reduction”

In this note, we show by counterexamples that Theorem 5.7 and Theorem 5.9 of Tiwari et al. (2018) are incorrect. Further their corrected versions are presented.

RS-HeRR: a rough set-based Hebbian rule reduction neuro-fuzzy system

Interpretabilty is one of the desired characteristics in various classification task. Rule-based system and fuzzy logic can be used for interpretation in classification. The main drawback of rule-based system is that it may contain large complex rules for classification and sometimes it becomes very difficult in interpretation. Rule reduction is also difficult for various reasons. Removing important rules may effect in classification accuracy. This paper proposes a hybrid fuzzy-rough set approach named RS-HeRR for the generation of effective, interpretable and compact rule set. It combines a powerful rule generation and reduction fuzzy system, called Hebbian-based rule reduction algorithm (HeRR) and a novel rough-set-based attribute selection algorithm for rule reduction. The proposed hybridization leverages upon rule reduction through reduction in partial dependency as well as improvement in system performance to significantly reduce the problem of redundancy in HeRR, even while providing similar or better accuracy. RS-HeRR demonstrates these characteristics repeatedly over four diverse practical classification problems, such as diabetes identification, urban water treatment monitoring, sonar target classification, and detection of ovarian cancer. It also demonstrates excellent performance for highly biased datasets. In addition, it competes very well with established non-fuzzy classifiers and outperforms state-of-the-art methods that use rough sets for rule reduction in fuzzy systems.

Scalable Fuzzy Rough Set Reduct Computation Using Fuzzy Min–Max Neural Network Preprocessing

A fuzzy rough set (FRS) is a hybridization of rough sets and fuzzy sets and provides a framework for reduct (feature subset selection) computation for hybrid decision systems. However, the existing FRS-based feature selection approaches are intractable for large decision systems due to the space complexity of the FRS methodology. We propose a novel fuzzy min–max neural network (FMNN)-FRS reduct computation approach utilizing the FMNN to enhance the scalability of FRS approaches. The FMNN provides a single pass epoch learning of arriving at granules of objects in the form of fuzzy hyperboxes for multiple decision classes. In the proposed approach, the FMNN model is used to reconstruct the object-based decision system into a fuzzy hyperbox-based interval-valued decision system. Then, a novel way of constructing the fuzzy discernibility matrix (FDM) from the interval-valued decision system is introduced. A fuzzy rough approximate reduct computation algorithm is developed with the induced FDM. The FMNN-FRS approach reduces the space complexity of FRS reduct computation significantly and results in enhanced scalability. Comparative experimental analysis has been done with the existing FRS reduct approaches on benchmark hybrid decision systems and established the relevance of the FMNN-FRS approach. The FMNN-FRS approach obtained the exact reduct in most of the datasets in much lesser computational time than existing FRS approaches while preserving similar classification accuracy. The FMNN-FRS method achieved enhanced scalability to such large decision systems, at which it is not possible to obtain reduct by existing FRS approaches.

Weight selection strategies for ordered weighted average based fuzzy rough sets

Fuzzy rough set theory models both vagueness and indiscernibility in data, which makes it a very useful tool for application to various machine learning tasks. In this paper, we focus on one of its robust generalisations, namely ordered weighted average based fuzzy rough sets. This model uses a weighted approach in the definition of the fuzzy rough operators. Although its efficacy and competitiveness with state-of-the-art machine learning approaches has been well established in several studies, its main drawback is the difficulty in choosing an appropriate weighting scheme. Several options exist and an adequate choice can greatly enhance the suitability of the ordered weighted average based fuzzy rough operators. In this work, we develop a clear strategy for the weighting scheme selection based upon the underlying characteristics of the data. The advantages of the approach are presented in a detailed experimental study focusing. Rather than to propose a classifier, our aim is to present a strategy to select a suitable weighting scheme for ordered weighted average based fuzzy rough sets in general. Our weighting scheme selection process allows users to take full advantage of the versatility offered by this model and performance improvements over the traditional fuzzy rough set approaches.

Heterogeneous multigranulation fuzzy rough set-based multiple attribute group decision making with heterogeneous preference information

Abstract This study proposes a heterogeneous attribute multigranulation fuzzy rough set approach to the problem of multiple attribute group decision-making (MAGDM) under uncertainty. We first present the definition of heterogeneous attribute multi-source information systems and then construct the heterogeneous multigranulation approximation space using the arbitrary binary relation classes generated by different categories attribute. We then give the rough approximation of a fuzzy decision-making object with respect to heterogeneous multigranulation approximation space, i.e., the heterogeneous attribute multigranulation fuzzy rough set model over multi-source information system. Meanwhile, we investigate some interesting properties and conclusions for the proposed new model and also discuss the interrelationship between the proposed heterogeneous attribute multigranulation fuzzy rough set model and the existing generalized rough set models. After that, we construct a new approach to MAGDM problems based on heterogeneous attribute multigranulation fuzzy rough set theory. The decision-making procedure and the methodology as well as the algorithm of the proposed method are given and a detailed comparison of the traditional methods to MAGDM problems illustrates the advantages and limitations. Finally, an example of handling MAGDM problem of evaluation of emergency plans for unconventional emergency events illustrates this approach.

Tolerance-based intuitionistic fuzzy-rough set approach for attribute reduction

Due to technological advancement and the explosive growth of electrically stored information, automated methods are required to aid users in maintaining and processing this huge amount of information. Experts, as well as machine learning processes on large volumes of data, are the main sources of knowledge. Knowledge extraction is an important step in framing expert and intelligent systems. However, the knowledge extraction phase is very slow or even impossible due to noise and large size of data. To enhance the productivity of machine learning algorithms, feature selection or attribute reduction plays a key role in the selection of relevant and non-redundant features to improve the performance of classifiers and interpretability of data. Many areas like machine learning, image processing, data mining, natural language processing and Bioinformatics, etc., which have high relevancy to expert and intelligent systems, are applications of feature selection.Rough set theory has been successfully applied for attribute reduction, but this theory is inadequate in the case of attribute reduction of real-valued data set as it may lose some information during the discretization process. Fuzzy and rough set theories have been combined and various attribute selection techniques were proposed, which can easily handle the real-valued data. An intuitionistic fuzzy set possesses a strong ability to represent information and better describing the uncertainty when compared to the classical fuzzy set theory as it considers positive, negative and hesitancy degree simultaneously for an object to belong to a set. This paper proposes a novel mechanism of attribute selection using tolerance-based intuitionistic fuzzy rough set theory. For this, we present tolerance-based intuitionistic fuzzy lower and upper approximations and formulate a degree of dependency of decision features over the set of conditional features. Moreover, the basic results on lower and upper approximations based on rough sets are extended for intuitionistic fuzzy rough sets and analogous results are established. In the end, the proposed algorithm is applied to an example data set and the comparison between tolerance-based fuzzy rough and intuitionistic fuzzy rough sets approaches for feature selection is presented. The proposed concept is found to be better performing in the form of selected attributes.

Dominance-based fuzzy rough set approach for incomplete interval-valued data

Dominance-based fuzzy rough set approach for incomplete interval-valued data

Dynamic affinity-based classification of multi-class imbalanced data with one-versus-one decomposition: a fuzzy rough set approach

Class imbalance occurs when data elements are unevenly distributed among classes, which poses a challenge for classifiers. The core focus of the research community has been on binary-class imbalance, although there is a recent trend toward the general case of multi-class imbalanced data. The IFROWANN method, a classifier based on fuzzy rough set theory, stands out for its performance in two-class imbalanced problems. In this paper, we consider its extension to multi-class data by combining it with one-versus-one decomposition. The latter transforms a multi-class problem into two-class sub-problems. Binary classifiers are applied to these sub-problems, after which their outcomes are aggregated into one prediction. We enhance the integration of IFROWANN in the decomposition scheme in two steps. Firstly, we propose an adaptive weight setting for the binary classifier, addressing the varying characteristics of the sub-problems. We call this modified classifier IFROWANN- $${{\mathcal {W}}_{\mathrm{IR}}}$$ . Second, we develop a new dynamic aggregation method called WV–FROST that combines the predictions of the binary classifiers with the global class affinity before making a final decision. In a meticulous experimental study, we show that our complete proposal outperforms the state-of-the-art on a wide range of multi-class imbalanced datasets.

About a Fuzzy Distance between Two Fuzzy Partitions and Application in Attribute Reduction Problem

Abstract According to traditional rough set theory approach, attribute reduction methods are performed on the decision tables with the discretized value domain, which are decision tables obtained by discretized data methods. In recent years, researches have proposed methods based on fuzzy rough set approach to solve the problem of attribute reduction in decision tables with numerical value domain. In this paper, we proposeafuzzy distance between two partitions and an attribute reduction method in numerical decision tables based on proposed fuzzy distance. Experiments on data sets show that the classification accuracy of proposed method is more efficient than the ones based fuzzy entropy.

A Variable Precision Fuzzy Rough Set Approach to a Fuzzy-Rough Decision Table

In a real world, non-empty boundaries between classes may be both rough and fuzzy. In order to make decision in fuzzy approximation space, a fuzzy VPRS (variable precision rough set) approach is proposed based on substitution of the indiscernibility relation by a fuzzy indiscernibility relation in the rough approximation of decision classes, which can obtain probabilistic rules from fuzzy decision tables. Some set theoretic properties of the proposed approach are discussed.

A Fuzzy-Rough Set Approach for Evaluating the Microfinance Performance of Bank

Microfinance has entered the phase of rapid development and it has become one of the most important businesses in commercial banks. This study set up an evaluation system based on the balanced scorecard and used the fuzzy-rough set approach to evaluate the microfinance performance. Firstly, this study designed the performance evaluation system from five dimensions according to the principals of balanced scorecard. It needs an objective and scientific method to allocate the weight of indicators of bank's microfinance evaluation system. How to overcome the fuzziness problem and lack of objectivity becomes the point of the research. Then this study used the fuzzy comprehensive evaluation method which is based on the rough set to determine the weight of indicators. Finally this study made an empirical study by using above method and got the fuzzy evaluation results. The effectiveness and practicability of the method were verified by the empirical results.

Fuzzy based Feature Selection Scheme through Transductive SVM Technique for Cancer Pattern Classification and Prediction

Objectives: A reliable and precise classification of tumor types is of great importance and essential for successful Diagnosis and Drug Discovery. Methods: Gene expression profiling has shown a great prospective in the outcome prediction of different types of Cancers, with the innovation of Microarray Technology. Microarray cancer data, which have been organized as samples versus genes fashion, are being exploited for the tissue sample classification. They are also useful for identifying potential gene markers in each subtype of cancer, that helps to analyze a particular cancer type in a successful manner. Findings: In this paper a new method for classification based on Fuzzy Rough-Set Feature Selection Approach through Transductive SVM Technique, which is called as FFS+TSVM is proposed. Moreover recently, for Cancer Pattern Classification, a combined Consistency based Feature Selection Approach through Transductive Support Vector Machine (CBFS+TSVM) has proposed and its prediction accuracy has encouraged than that of existing other Classifiers. However, from the literature survey, it is revealed that the performance of the existing scheme can be improved if Fuzzy Rough Set Approach for Gene Feature Selection with Transductive Support Vector Machine is employed. The present work is implemented with the help of Bio Weka and studied thoroughly in terms of Computational Cost, Dimensionality Reduction, Threshold, Classification Error and Classification Accuracy. Applications/Improvements: The proposed work outperforms the existing Transductive Support Vector Machine (TSVM) in terms of Dimensionality Reduction, Threshold, Classification Error and Classification Accuracy for various Cancer Patterns.

A fuzzy rough set approach for incremental feature selection on hybrid information systems

In real-applications, there may exist many kinds of data (e.g., boolean, categorical, real-valued and set-valued data) and missing data in an information system which is called as a Hybrid Information System (HIS). A new Hybrid Distance (HD) in HIS is developed based on the value difference metric, and a novel fuzzy rough set is constructed by combining the HD distance and the Gaussian kernel. Considering the information systems often vary with time, the updating mechanisms for attribute reduction (feature selection) are analyzed with the variation of the attribute set. Fuzzy rough set approaches for incremental feature selection on HIS are presented. Then two corresponding incremental algorithms are proposed, respectively. Finally, extensive experiments on eight datasets from UCI and an artificial dataset show that the incremental approaches significantly outperform non-incremental approaches with feature selection in the computational time.