Fuzzy Rough Set Theory Research Articles

Credit scoring analysis using a fuzzy probabilistic rough set model

Credit scoring analysis is an important activity, especially nowadays after a huge number of defaults has been one of the main causes of the financial crisis. Among the many different tools used to model credit risk, the recent development of rough set models has proved effective. The original development of rough set theory has been widely generalized and combined with other approaches to uncertain reasoning, especially probability and fuzzy set theories. Since coherent conditional probability assessments cope well with the problem of unifying these different approaches, a merging of fuzzy rough set theory with this subjectivist approach is proposed. Specifically, expert partial probabilistic evaluations are encompassed inside a gradual decision rule structure, with coherence of the conclusion as a guideline. In line with Bayesian rough set models, credibility degrees of multiple premises are introduced through conditional probability assessments. Nonetheless, discernibility with this method remains too fine. Therefore, the basic partition is coarsened by equivalence classes based on the arity of positively, negatively and neutrally related criteria. A membership function, which grades the likelihood of default, is introduced by a peculiar choice of t-norms and t-conorms. To build and test the model, real data related to a sample of firms are used.

A Novel Recommender System Based on Fuzzy Set and Rough Set Theory

Recommender System is an effective means of handling information overload and can provide personalized service as a useful information tool in e-commerce. In this paper, a novel automatic recommender system is proposed based on fuzzy c-means algorithm and rough set theory, including three main steps: data discretization, rules establishing and fuzzy reasoning. A method for fitting the results of FCM clustering is put forward by membership function and using it with attributes to achieve data discretization, in order to avoid the processing that each input data have to carry clustering operation for discretization. Using rough set theory, it can accelerate the speed of fuzzy reasoning through rules reduction with choosing closely relating attributes for commodity. Fuzzy reasoning method is also applied into commodity recommender system. Lastly, a case study conducted by the presented method is given, and the results show that this model can provide valuable advice for potential users and it is also an effective way for recommendation.

Fuzzy-rough nearest neighbour classification and prediction

Nearest neighbour (NN) approaches are inspired by the way humans make decisions, comparing a test object to previously encountered samples. In this paper, we propose an NN algorithm that uses the lower and upper approximations from fuzzy-rough set theory in order to classify test objects, or predict their decision value. It is shown experimentally that our method outperforms other NN approaches (classical, fuzzy and fuzzy-rough ones) and that it is competitive with leading classification and prediction methods. Moreover, we show that the robustness of our methods against noise can be enhanced effectively by invoking the approximations of the Vaguely Quantified Rough Set (VQRS) model, which emulates the linguistic quantifiers “some” and “most” from natural language.

Fuzzy rough set based attribute reduction for information systems with fuzzy decisions

Fuzzy rough set is a generalization of crisp rough set to deal with data sets with real value attributes. A primary use of fuzzy rough set theory is to perform attribute reduction for decision systems with numerical conditional attribute values and crisp (symbolic) decision attributes. In this paper we define inconsistent fuzzy decision system and their reductions, and develop discernibility matrix-based algorithms to find reducts. Finally, two heuristic algorithms are developed and comparison study is provided with the existing algorithms of attribute reduction with fuzzy rough sets. The proposed method in this paper can deal with decision systems with numerical conditional attribute values and fuzzy decision attributes rather than crisp ones. Experimental results imply that our algorithm of attribute reduction with general fuzzy rough sets is feasible and valid.

The incremental method for fast computing the rough fuzzy approximations

Abstract The lower and upper approximations are basic concepts in rough fuzzy set theory. The effective computation of approximations is very important for improving the performance of related algorithms. This paper proposed and proved two incremental methods for fast computing the rough fuzzy approximations, one starts from the boundary set, the other is based on the cut sets of a fuzzy set. Then some illustrative examples are conducted. Consequently, two algorithms corresponding to the two incremental methods are put forward respectively. In order to test the efficiency of algorithms, some experiments are made on a large soybean data set from UCI. The experimental results show that the two incremental methods effectively reduce the computing time in comparison with the traditional non-incremental method [1].

English

Rough set model with lower and upper approximations based on lattice theory is defined and for the new model some properties are given. Lattice theory plays an important role in rough set theory and fuzzy set theory, so the new rough set model over lattice theory in this paper may be a new tool to study the relationship between fuzzy set theory and rough set theory.

Fuzzy–Rough Supervised Attribute Clustering Algorithm and Classification of Microarray Data

One of the major tasks with gene expression data is to find groups of coregulated genes whose collective expression is strongly associated with sample categories. In this regard, a new clustering algorithm, termed as fuzzy-rough supervised attribute clustering (FRSAC), is proposed to find such groups of genes. The proposed algorithm is based on the theory of fuzzy-rough sets, which directly incorporates the information of sample categories into the gene clustering process. A new quantitative measure is introduced based on fuzzy-rough sets that incorporates the information of sample categories to measure the similarity among genes. The proposed algorithm is based on measuring the similarity between genes using the new quantitative measure, whereby redundancy among the genes is removed. The clusters are refined incrementally based on sample categories. The effectiveness of the proposed FRSAC algorithm, along with a comparison with existing supervised and unsupervised gene selection and clustering algorithms, is demonstrated on six cancer and two arthritis data sets based on the class separability index and predictive accuracy of the naive Bayes' classifier, the K-nearest neighbor rule, and the support vector machine.

The Application of Fuzzy Theory and Gray-Based Rough Set Theory in the Supplier Selection Decision Making

This work presents the combination of fuzzy theory and rough set theory to solve facility location selection problems under the condition of involving different objective/subjective attributes. We try to utilize individual merits for each method and combine it to form a reliable selection of alternative suppliers. An empirical example is illustrated to show the effectiveness of the integrated method. Our results showed that the integrated method can allow decision makers to get the best candidate of supplier location, and is recommended in the practice therefore.

Membership evaluation and feature selection for fuzzy support vector machine based on fuzzy rough sets

A fuzzy support vector machine (FSVM) is an improvement in SVMs for dealing with data sets with outliers. In FSVM, a key step is to compute the membership for every training sample. Existing approaches of computing the membership of a sample are motivated by the existence of outliers in data sets and do not take account of the inconsistency between conditional attributes and decision classes. However, this kind of inconsistency can affect membership for every sample and has been considered in fuzzy rough set theory. In this paper, we develop a new method to compute membership for FSVMs by using a Gaussian kernel-based fuzzy rough set. Furthermore, we employ a technique of attribute reduction using Gaussian kernel-based fuzzy rough sets to perform feature selection for FSVMs. Based on these discussions we combine the FSVMs and fuzzy rough sets methods together. The experimental results show that the proposed approaches are feasible and effective.

Fuzzy–Rough Sets for Information Measures and Selection of Relevant Genes From Microarray Data

Several information measures such as entropy, mutual information, and f-information have been shown to be successful for selecting a set of relevant and nonredundant genes from a high-dimensional microarray data set. However, for continuous gene expression values, it is very difficult to find the true density functions and to perform the integrations required to compute different information measures. In this regard, the concept of the fuzzy equivalence partition matrix is presented to approximate the true marginal and joint distributions of continuous gene expression values. The fuzzy equivalence partition matrix is based on the theory of fuzzy-rough sets, where each row of the matrix represents a fuzzy equivalence partition that can automatically be derived from the given expression values. The performance of the proposed approach is compared with that of existing approaches using the class separability index and the predictive accuracy of the support vector machine. An important finding, however, is that the proposed approach is shown to be effective for selecting relevant and nonredundant continuous-valued genes from microarray data.

MODELING OF COGNITIVE STRUCTURE OF UNCERTAIN SCIENTIFIC CONCEPTS USING FUZZY-ROUGH SETS AND INTUITIONISTIC FUZZY SETS: EXAMPLE OF THE LIFE CONCEPT

In this study, using fuzzy-rough set and intuitionistic fuzzy set approaches, we propose a cognitive structural model for the concept of life for which a certain definition can not be made because of scientific uncertainty as well as moral, legal, and theological aspects. Total 191 first-year students from seven different high schools in a large western city in Turkey participated in the study. An open-ended conceptual understanding (CULC) test, developed by the researcher, was used for data collection. Semi-structured interviews were carried out with 14 students and their biology teachers to clarify ambiguous points in students' responses to the CULC test. The results of analyses indicated that students constructed the concept of life by associating it predominantly with 'human'. Motion appeared as the most frequently associated term with the concept of life. The results suggest that the life concept has been constructed using animistic-anthropocentric cognitive schemes. In the next step, we evaluated the data obtained from the CULC test using the fuzzy-rough set and intuitionistic fuzzy set theories. Consequently, we propose an 'animistic-anthropocentric structural model' about cognitive construction of the concept of life.

Attribute selection with fuzzy decision reducts

Rough set theory provides a methodology for data analysis based on the approximation of concepts in information systems. It revolves around the notion of discernibility: the ability to distinguish between objects, based on their attribute values. It allows to infer data dependencies that are useful in the fields of feature selection and decision model construction. In many cases, however, it is more natural, and more effective, to consider a gradual notion of discernibility. Therefore, within the context of fuzzy rough set theory, we present a generalization of the classical rough set framework for data-based attribute selection and reduction using fuzzy tolerance relations. The paper unifies existing work in this direction, and introduces the concept of fuzzy decision reducts, dependent on an increasing attribute subset measure. Experimental results demonstrate the potential of fuzzy decision reducts to discover shorter attribute subsets, leading to decision models with a better coverage and with comparable, or even higher accuracy.

Data Mining Based on Fuzzy Rough Set Theory and Its Application in the Glass Identification

To overcome the disadvantage of determining artificially the class number, fuzzy C means clustering is introduced to fuzzify the continual attribute, and the best minute class number is obtained by cluster validity analysis. The relationship of glass composition and its application is excavated using data mining method in this paper.

Ant colony feature selection based on fuzzy rough set information entropy

Most heuristic feature selection algorithms converge easily to local-best, which cannot search the whole feature space effectively. In order to improve the parallel search ability to feature space, the information entropy theory of fuzzy rough set was introduced to ant colony model, and the ant search strategy, pheromone updating and state transition rules of the model have been modified to realize ant colony model based feature selection. UCI datasets experiments indicate that the proposed algorithm is effective to feature subset selection compared with three classical feature selection algorithms.

Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches

Computational Intelligence and Feature Selection provides a high level audience with both the background and fundamental ideas behind feature selection with an emphasis on those techniques based on rough and fuzzy sets, including their hybridizations. It introduces set theory, fuzzy set theory, rough set theory, and fuzzy-rough set theory, and illustrates the power and efficacy of the feature selection described through the use of real-world applications and worked examples. Program files implementing major algorithms covered, together with the necessary instructions and datasets, are available on the Web.

Reasoning within intuitionistic fuzzy rough description logics

It is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are suitable, well-known logics for managing structured knowledge that have gained considerable attention the last decade. The current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in DLs are analyzed in this paper. An integration between the theories of intuitionistic fuzzy DLs and rough DLs has been attempted by providing intuitionistic fuzzy rough DLs based on intuitionistic fuzzy rough set theory. The syntax, semantics and properties of intuitionistic fuzzy rough DLs are given. It is proved that the satisfiability, subsumption, entailment and ABox consistency reasoning in intuitionistic fuzzy rough DLs may be reduced to the corresponding satisfiability, subsumption, entailment and ABox consistency reasoning in fuzzy DL over complete lattice, respectively.

Reasoning within expressive fuzzy rough description logics

It is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are suitable, well-known logics for managing structured knowledge that have gained considerable attention the last decade. The current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in DLs are analyzed in this paper. An integration between the theories of fuzzy DLs and rough DLs has been attempted by providing fuzzy rough DLs based on fuzzy rough set theory. The syntax, semantics and properties of fuzzy rough DLs are given. It is proved that the satisfiability, subsumption, entailment and ABox consistency reasoning in fuzzy rough DLs may be reduced to the ABox consistency reasoning in the corresponding fuzzy DLs.

Fuzzy-rough attribute reduction via mutual information with an application to cancer classification

Establishing a classification model for cancer recognition based on DNA microarrays is useful for cancer diagnosis. Feature selection is a key step to perform cancer classification with DNA microarrays, for there is a large number of genes from which to predict classes and a relatively small number of samples. Automatic methods must be developed for extracting relevant genes which are essential for classification. This paper proposes a novel approach for reducing data redundancy based on fuzzy rough set theory and information theory. A mutual information-based algorithm for attribute reduction is suggested. The method is applied to the problem of gene selection for cancer classification. Experimental results show that the algorithm is more effective than conventional rough sets based approaches.

A Novel Methodology to Manage Uncertainty for Multidisciplinary Design and Optimization in Conceptual Design

Uncertainty in design and simulation affects the quality of product directly during the process of MDO, which should be considered to help designers to make the design decisions, especially at conceptual design stage. In traditional approaches, this uncertainty is ignored in the hope that it is not significant to the decision making. In this investigation, firstly, three main uncertainties in MDO of conceptual design are pointed out and carefully analyzed. Then, an innovative methodology integrating extract knowledge and probabilistic method to manage these uncertainties is presented. Considering practical application and eliminating the uncertainty in configuration, we propose a promising method combining Fuzzy c-means algorithm (FCM) and Rough Sets theory (RST) to deduce the configuration rule. Furthermore, probabilistic kriging model is utilized as an approximation model to reduce global computational expense of complex product. Sensitivity analysis (SA) is used to reduce uncertainty of inputs of simulation, and mean square error (MSE) is employed to assess model error to reduce model uncertainty. Finally, the validity and necessity of this methodology are demonstrated through the conceptual design of bulk carrier.

Uncertainty representation of ocean fronts based on fuzzy-rough set theory

Analysis of ocean fronts’ uncertainties indicates that they result from indiscernibility of their spatial position and fuzziness of their intensity. In view of this, a flow hierarchy for uncertainty representation of ocean fronts is proposed on the basis of fuzzy-rough set theory. Firstly, raster scanning and blurring are carried out on an ocean front, and the upper and lower approximate sets, the indiscernible relation in fuzzy-rough theories and related operators in fuzzy set theories are adopted to represent its uncertainties, then they are classified into three sets: with members one hundred percent belonging to the ocean front, belonging to the ocean front’s edge and definitely not belonging to the ocean front. Finally, the approximate precision and roughness degree are utilized to evaluate the ocean front’s degree of uncertainties and the precision of the representation. It has been proven that the method is not only capable of representing ocean fronts’ uncertainties, but also provides a new theory and method for uncertainty representation of other oceanic phenomena.