Fuzzy Rough Set Model Research Articles

Fuzzy rough set model for set-valued data

In many practical situations, some of the attribute values for an object may be set-valued. The existing crisp rough set model for set-valued information systems is based on a tolerance relation that examines whether two set values have a non-empty intersection. Some information in the data will be lost according to the tolerance relation. Here we define a fuzzy relation and construct a fuzzy rough set model for set-valued information systems. The concepts of reduct, core, discernibility matrix and discernibility function for set-valued information systems, and relative reduct, core, discernibility matrix and discernibility function for set-valued decision systems are defined and examined. Attribute reduction in set-valued information systems based on discernibility matrices and functions are investigated.

A fuzzy rough set approach to emergency material demand prediction over two universes

Emergency decision-making is still an important issue of unconventional emergency events management. Although many studies are developed on this topic, they remain political and qualitative, and it is difficult to make them operational in practice. Therefore, this article considers a fuzzy rough set over two universes model and approach for solving such a difficulty. As is well known, an exact and scientific emergency material demand prediction can make a quick and efficient emergency rescue and realize the optimal effect. Considering the main characteristics of emergency decision-making with insufficient risk identification, incomplete and inaccuracy of available information and uncertainty of decision-making environment, the fuzzy rough set theory over two universes is used to emergency material demand prediction. We propose a model and approach to emergency material demand prediction, i.e., the fuzzy rough set model of emergency material demand prediction over two universes. We present decision rules and computing methods for the proposed model by using the risk decision-making principle of classical operational research. Finally, the validity of the approach and the applied process of the proposed model is tested by a numerical example with the background of earthquake emergency material demand forecasting.

Attribute Reduction in Interval and Set-Valued Decision Information Systems

In many practical situation, some of the attribute values for an object may be interval and set-valued. This paper introduces the interval and set-valued information systems and decision systems. According to the semantic relation of attribute values, interval and set-valued information systems can be classified into two categories: disjunctive (Type 1) and conjunctive (Type 2) systems. In this paper, we mainly focus on semantic interpretation of Type 1. Then, we define a new fuzzy preference relation and construct a fuzzy rough set model for interval and set-valued information systems. Moreover, based on the new fuzzy preference relation, the concepts of the significance measure of condition attributes and the relative significance measure of condition attributes are given in interval and set-valued decision information systems by the introduction of fuzzy positive region and the dependency degree. And on this basis, a heuristic algorithm for calculating fuzzy positive region reduction in interval and set-valued decision information systems is given. Finally, we give an illustrative example to substantiate the theoretical arguments. The results will help us to gain much more insights into the meaning of fuzzy rough set theory. Furthermore, it has provided a new perspective to study the attribute reduction problem in decision systems.

Interval Type-2 Fuzzy Rough Sets Based on Inclusion Measures

In this paper, a new computation formula of interval type-2 fuzzy inclusion measure is proposed on the basis of the axiom definition of interval type-2 fuzzy inclusion measures. Furthermore, we define an interval type-2 fuzzy rough set model on the basis of inclusion measure and study its basic properties. In the end, the attribute reduction of continuous domain decision information system is discussed and the method on appropriate reduction is given. Further,we present calculation steps of the reduction approach by an example and experimental results demonstrate the feasibility and efectiveness of the reduction algorithm.

Fuzzy rough set models over two universes

The extension of rough set model is an important research direction in rough set theory. The aim of this paper is to present new extensions of the rough set model over two different universes which are rough fuzzy set model in a generalized approximation space, rough set model in a fuzzy approximation space and rough fuzzy set model in a fuzzy approximation space based over two different universes. Moreover, the properties of the approximation operators in these models are investigated. Furthermore, by employing cut set of fuzzy set and fuzzy relation, classical representations of fuzzy rough approximation operators are studied. Finally, the measures of fuzzy rough set models are presented, and the relationships among the fuzzy rough models and rough set model over two universes are investigated.

On Robust Fuzzy Rough Set Models

Rough sets, especially fuzzy rough sets, are supposedly a powerful mathematical tool to deal with uncertainty in data analysis. This theory has been applied to feature selection, dimensionality reduction, and rule learning. However, it is pointed out that the classical model of fuzzy rough sets is sensitive to noisy information, which is considered as a main source of uncertainty in applications. This disadvantage limits the applicability of fuzzy rough sets. In this paper, we reveal why the classical fuzzy rough set model is sensitive to noise and how noisy samples impose influence on fuzzy rough computation. Based on this discussion, we study the properties of some current fuzzy rough models in dealing with noisy data and introduce several new robust models. The properties of the proposed models are also discussed. Finally, a robust classification algorithm is designed based on fuzzy lower approximations. Some numerical experiments are given to illustrate the effectiveness of the models. The classifiers that are developed with the proposed models achieve good generalization performance.

Rough Set and Fuzzy Rough Set Model Based on Decision Criteria

Rough Set and Fuzzy Rough Set Model Based on Decision Criteria

Discovery of factors influencing citation impact based on a soft fuzzy rough set model

In this paper, the machine learning tools were used to identify key features influencing citation impact. Both the papers’ external and quality information were considered in constructing papers’ feature space. Based on the feature space, the soft fuzzy rough set was used to generate a series of associated feature subsets. Then, the KNN classifier was used to find the feature subset with the best classification performance. The results show that citation impact could be predicted by objectively assessed factors. Both the papers’ quality and external features, mainly represented as the reputation of the first author, are contributed to future citation impact.

An Improved Covering Fuzzy Rough Set Model

In this paper, we proposed the covering fuzzy rough set model based on multi-granulations and discussed some interesting properties about the model. The research may enlarge the application range of the rough set theory in real life. The lower and upper approximations of fuzzy set are defined by multi-covering relations on the universe, and some basic properties are introduced. It is shown that the fuzzy rough set model based on multi-covering relations is an extension of the rough set model based on multi-granulations.

Rough set models based on random fuzzy sets and belief function of fuzzy sets

As knowledge blocks in databases are fuzzy and random patterns may emerge, we propose random fuzzy rough set models based on random fuzzy sets and fuzzy logic operators. We give some properties of random fuzzy rough set. We prove that the lower fuzzy measures and the upper fuzzy measures induced by lower approximation and upper approximation of fuzzy set are fuzzy belief measures and fuzzy plausibility measures, respectively, in particular, if a random fuzzy set degenerates a random fuzzy point set, then the lower fuzzy measures and upper fuzzy measures are fuzzy probability measures, and then the lower fuzzy measures and the upper fuzzy measures are exactly the infimum and supremum of the fuzzy probability measures induced by the selections of the random fuzzy set. We investigate the Gödel random fuzzy rough set model in detail, in which the implication operator is chosen as Gödel implication, and prove that a pair of fuzzy belief measure and fuzzy plausibility measure is induced essentially by the lower approximation and the upper approximation of a random fuzzy approximation space.

Bipolar fuzzy rough set model on two different universes and its application

Pawlak initiated the concept of the rough set as a formal tool for modeling and processing incomplete information in information systems. Various fuzzy generalizations of the rough set have been proposed in the literature. In this paper we generalize the fuzzy rough set model on two different universes proposed by Sun and Ma. Concretely, based on the bipolar fuzzy compatible relation R(α,β) (α,β∈(0,1]), the bipolar fuzzy rough set model on two different universes is presented. Some properties of the bipolar fuzzy rough set model are discussed. Two extended models of the bipolar fuzzy rough set model are given, and some related results are obtained. Finally, an example is applied to illustrate the application of the bipolar fuzzy rough set model presented in this paper.

Soft Minimum-Enclosing-Ball Based Robust Fuzzy Rough Sets

The theory of fuzzy rough sets is claimed to be a powerful mathematical tool for dealing with uncertainty in data analysis. Unluckily, the classical model of fuzzy rough sets is sensitive to noisy information. This disadvantage limits the applicability of the model in practice. In this work, we present a robust fuzzy rough set model based on soft minimum enclosing ball, and introduce a new fuzzy dependency function with this model. Some properties of the new model are discussed. Finally, we conduct some experiments to test the effectiveness of the proposed model, and experimental results show that the soft minimum enclosing ball-based fuzzy rough set model is robust to noise.

Soft fuzzy rough sets and its application in decision making

Recently, the theory and applications of soft set has brought the attention by many scholars in various areas. Especially, the researches of the theory for combining the soft set with the other mathematical theory have been developed by many authors. In this paper, we propose a new concept of soft fuzzy rough set by combining the fuzzy soft set with the traditional fuzzy rough set. The soft fuzzy rough lower and upper approximation operators of any fuzzy subset in the parameter set were defined by the concept of the pseudo fuzzy binary relation (or pseudo fuzzy soft set) established in this paper. Meanwhile, several deformations of the soft fuzzy rough lower and upper approximations are also presented. Furthermore, we also discuss some basic properties of the approximation operators in detail. Subsequently, we give an approach to decision making problem based on soft fuzzy rough set model by analyzing the limitations and advantages in the existing literatures. The decision steps and the algorithm of the decision method were also given. The proposed approach can obtain a object decision result with the data information owned by the decision problem only. Finally, the validity of the decision methods is tested by an applied example.

A comparative study of rough sets for hybrid data

To discover knowledge from hybrid data using rough sets, researchers have developed several fuzzy rough set models and a neighborhood rough set model. These models have been applied to many hybrid data processing applications for a particular purpose, thus neglecting the issue of selecting an appropriate model. To address this issue, this paper mainly concerns the relationships among these rough set models. Investigating fuzzy and neighborhood hybrid granules reveals an important relationship between these two granules. Analyzing the relationships among rough approximations of these models shows that Hu’s fuzzy rough approximations are special cases of neighborhood and Wang’s fuzzy rough approximations, respectively. Furthermore, one-to-one correspondence relationships exist between Wang’s fuzzy and neighborhood rough approximations. This study also finds that Wang’s fuzzy and neighborhood rough approximations are cut sets of Dubois’ fuzzy rough approximations and Radzikowska and Kerre’s fuzzy rough approximations, respectively.

Multi-granulation Fuzzy Rough Sets in a Fuzzy Tolerance Approximation Space

Based on the analysis of the rough set model on a tolerance relation and the fuzzy rough set, two types of fuzzy rough sets models on tolerance relations are constructed and researched. Then we propose the optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing. In these models, the fuzzy lower and upper approximations of a fuzzy set are defined on multiple fuzzy tolerance relations. It follows the research on the properties of the fuzzy lower and upper approximations of the new models. The fuzzy rough set model, rough set model on a tolerance relation and multi-granulation rough sets models are special cases of the new ones from the perspective of the considered concepts, related relations and granular computing. The new models are meaningful generalizations of the classical rough sets.

Approximation operators based on vague relations and roughness measures of vague sets

Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approximation operators of vague sets based on vague relations, and investigate the basic properties of approximation operators on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transitive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.

Kernelized Fuzzy Rough Sets and Their Applications

Kernel machines and rough sets are two classes of commonly exploited learning techniques. Kernel machines enhance traditional learning algorithms by bringing opportunities to deal with nonlinear classification problems, rough sets introduce a human-focused way to deal with uncertainty in learning problems. Granulation and approximation play a pivotal role in rough sets-based learning and reasoning. However, a way how to effectively generate fuzzy granules from data has not been fully studied so far. In this study, we integrate kernel functions with fuzzy rough set models and propose two types of kernelized fuzzy rough sets. Kernel functions are employed to compute the fuzzy T-equivalence relations between samples, thus generating fuzzy information granules in the approximation space. Subsequently fuzzy granules are used to approximate the classification based on the concepts of fuzzy lower and upper approximations. Based on the models of kernelized fuzzy rough sets, we extend the measures existing in classical rough sets to evaluate the approximation quality and approximation abilities of the attributes. We discuss the relationship between these measures and feature evaluation function ReliefF, and augment the ReliefF algorithm to enhance the robustness of these proposed measures. Finally, we apply these measures to evaluate and select features for classification problems. The experimental results help quantify the performance of the KFRS.

Transformation of bipolar fuzzy rough set models

In this paper, the notions of the union, the intersection, and the inverse of bipolar fuzzy approximation spaces are first introduced, respectively, and some related results are obtained. Then, the composition of bipolar fuzzy approximation spaces are proposed, and some properties are discussed. Finally, we give two examples to illustrate the applications of bipolar fuzzy rough set models’ transformation in multiple criteria decision making.

Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets

Fuzzy rough sets are considered as an effective tool to deal with uncertainty in data analysis, and fuzzy similarity relations are used in fuzzy rough sets to calculate similarity between objects. On the other hand in kernel tricks, a kernel maps data into a higher dimensional feature space where the resulting structure of the learning task is linearly separable, while the kernel is the inner product of this feature space and can also be viewed as a similarity function. It has been reported there is an overlap between family of kernels and collection of fuzzy similarity relations. This fact motivates the idea in this paper to use some kernels as fuzzy similarity relations and develop kernel based fuzzy rough sets. First, we consider Gaussian kernel and propose Gaussian kernel based fuzzy rough sets. Second we introduce parameterized attribute reduction with the derived model of fuzzy rough sets. Structures of attribute reduction are investigated and an algorithm with discernibility matrix to find all reducts is developed. Finally, a heuristic algorithm is designed to compute reducts with Gaussian kernel fuzzy rough sets. Several experiments are provided to demonstrate the effectiveness of the idea.

Robust fuzzy rough classifiers

Fuzzy rough sets, generalized from Pawlak's rough sets, were introduced for dealing with continuous or fuzzy data. This model has been widely discussed and applied these years. It is shown that the model of fuzzy rough sets is sensitive to noisy samples, especially sensitive to mislabeled samples. As data are usually contaminated with noise in practice, a robust model is desirable. We introduce a new model of fuzzy rough set model, called soft fuzzy rough sets, and design a robust classification algorithm based on the model. Experimental results show the effectiveness of the proposed algorithm.