Probabilistic graded rough set and double relative quantitative decision-theoretic rough set

The probabilistic rough set (PRS) model ignores absolute quantitative information i.e., overlap between equivalence class and basic set. And graded rough set (GRS) model cannot reflect the distinctive degrees of information. In order to overcome these defects, this paper proposes the probabilistic graded rough set (PGRS), which is an extension of Pawlak's rough set and GRS. What is more, we propose double relative quantitative decision-theoretic rough set (Drq-DTRS) models, which essentially indicate the relative and absolute quantification.     

Probabilistic rough set over two universes and rough entropy

In this paper, we discuss the properties of the probabilistic rough set over two universes in detail. We present the parameter dependence or the continuous of the lower and upper approximations on parameters for probabilistic rough set over two universes. We also investigate some properties of the uncertainty measure, i.e., the rough degree and the precision, for probabilistic rough set over two universes. Meanwhile, we point out the limitation of the uncertainty measure for the traditional method and then define the general Shannon entropy of covering-based on universe. Then we discuss the uncertainty measure of the knowledge granularity and rough entropy for probabilistic rough set over two universes by the proposed concept. Finally, the validity of the methods and conclusions is tested by a numerical example.     

Sampling aspects of rough set theory

Rough Set Theory (RST) originated as an approach to approximating a given set, but has found its main applications in the statistical domain of classification problems. It generates classification rules, and can be seen in general terms as a technique for rule induction. Expositions of RST often stress that it is robust in requiring no (explicit) assumptions of a statistical nature. The argument here, however, is that this apparent strength is also a weakness which prevents establishment of general statistical properties and comparison with other methods. A sampling theory is developed for the first time, using both the original RST model and its probabilistic extension, Variable Precision Rough Sets. This is applied in the context of examples, one of which involves Fishers Iris data.Bruce Curry: The author is grateful to two anonymous referees for various helpful suggestions     

Neighborhood based decision-theoretic rough set models

As an extension of Pawlak rough set model, decision-theoretic rough set model (DTRS) adopts the Bayesian decision theory to compute the required thresholds in probabilistic rough set models. It gives a new semantic interpretation of the positive, boundary and negative regions by using three-way decisions. DTRS has been widely discussed and applied in data mining and decision making. However, one limitation of DTRS is its lack of ability to deal with numerical data directly. In order to overcome this disadvantage and extend the theory of DTRS, this paper proposes a neighborhood based decision-theoretic rough set model (NDTRS) under the framework of DTRS. Basic concepts of NDTRS are introduced. A positive region related attribute reduct and a minimum cost attribute reduct in the proposed model are defined and analyzed. Experimental results show that our methods can get a short reduct. Furthermore, a new neighborhood classifier based on three-way decisions is constructed and compared with other classifiers. Comparison experiments show that the proposed classifier can get a high accuracy and a low misclassification cost.     

Variable-precision dominance-based rough set approach and attribute reduction

In this paper, a variable-precision dominance-based rough set approach (VP-DRSA) is proposed together with several VP-DRSA-based approaches to attribute reduction. The properties of VP-DRSA are shown in comparison to previous dominance-based rough set approaches. An advantage of VP-DRSA over variable-consistency dominance-based rough set approach in decision rule induction is emphasized. Some relations among the VP-DRSA-based attribute reduction approaches are investigated.     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.     

Bayesian rough set model: A further investigation

Bayesian rough set model (BRSM), as the hybrid development between rough set theory and Bayesian reasoning, can deal with many practical problems which could not be effectively handled by original rough set model. In this paper, the equivalence between two kinds of current attribute reduction models in BRSM for binary decision problems is proved. Furthermore, binary decision problems are extended to multi-decision problems in BRSM. Some monotonic measures of approximation quality for multi-decision problems are presented, with which attribute reduction models for multi-decision problems can be suitably constructed. What is more, the discernibility matrices associated with attribute reduction for binary decision and multi-decision problems are proposed, respectively. Based on them, the approaches to knowledge reduction in BRSM can be obtained which corresponds well to the original rough set methodology.     

Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables

In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a valued dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of a data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.     

A sequential pattern mining algorithm using rough set theory

Sequential pattern mining is a crucial but challenging task in many applications, e.g., analyzing the behaviors of data in transactions and discovering frequent patterns in time series data. This task becomes difficult when valuable patterns are locally or implicitly involved in noisy data. In this paper, we propose a method for mining such local patterns from sequences. Using rough set theory, we describe an algorithm for generating decision rules that take into account local patterns for arriving at a particular decision. To apply sequential data to rough set theory, the size of local patterns is specified, allowing a set of sequences to be transformed into a sequential information system. We use the discernibility of decision classes to establish evaluation criteria for the decision rules in the sequential information system.     

A rough set approach to the characterization of transversal matroids

Rough sets are efficient for data pre-processing during data mining. However, some important problems such as attribute reduction in rough sets are NP-hard and the algorithms required to solve them are mostly greedy ones. The transversal matroid is an important part of matroid theory, which provides well-established platforms for greedy algorithms. In this study, we investigate transversal matroids using the rough set approach. First, we construct a covering induced by a family of subsets and we propose the approximation operators and upper approximation number based on this covering. We present a sufficient condition under which a subset is a partial transversal, and also a necessary condition. Furthermore, we characterize the transversal matroid with the covering-based approximation operator and construct some types of circuits. Second, we explore the relationships between closure operators in transversal matroids and upper approximation operators based on the covering induced by a family of subsets. Finally, we study two types of axiomatic characterizations of the covering approximation operators based on the set theory and matroid theory, respectively. These results provide more methods for investigating the combination of transversal matroids with rough sets.     

Technical diagnostic of a fleet of vehicles using rough set theory

The paper presents a process of technical diagnostic applied to a fleet of vehicles utilized in the delivery system of express mail. It is focused on evaluation of diagnostic capacity of particular characteristics, reduction of a set of initially selected characteristics to a minimal and satisfactory subset, recognition of a technical condition of vehicles resulting in their condition-based classification. In addition, the decision rules facilitating technical diagnostic and management of a fleet of vehicles are generated and utilized. N-fold cross validation is applied to estimate the efficiency of the decision rules. The rough set theory is applied to support the diagnostic process of vehicles. Classical rough set (CRS) theory is compared with the dominance-based rough set (DRS) approach. The results of computational experiments for both approaches are compared.     

An exact feature selection algorithm based on rough set theory

Feature reduction based on rough set theory is an effective feature selection method in pattern recognition applications. Finding a minimal subset of the original features is inherent in rough set approach to feature selection. As feature reduction is a Nondeterministic Polynomial‐time‐hard problem, it is necessary to develop fast optimal or near‐optimal feature selection algorithms. This article aims to propose an exact feature selection algorithm in rough set that is efficient in terms of computation time. The proposed algorithm begins the examination of a solution tree by a breadth‐first strategy. The pruned nodes are held in a version of the trie data structure. Based on the monotonic property of dependency degree, all subsets of the pruned nodes cannot be optimal solutions. Thus, by detecting these subsets in trie, it is not necessary to calculate their dependency degree. The search on the tree continues until the optimal solution is found. This algorithm is improved by selecting an initial search level determined by the hill‐climbing method instead of searching the tree from the level below the root. The length of the minimal reduct and the size of data set can influence which starting search level is more efficient. The experimental results using some of the standard UCI data sets, demonstrate that the proposed algorithm is effective and efficient for data sets with more than 30 features. © 2014 Wiley Periodicals, Inc. Complexity 20: 50–62, 2015     

Multi-objective optimization method for learning thresholds in a decision-theoretic rough set model

For decision-theoretic rough sets, a key issue is determining the thresholds for the probabilistic rough set model by setting appropriate cost functions. However, it is not easy to obtain correct cost functions because of a lack of prior knowledge and few previous studies have addressed the determination of learning thresholds and cost functions from datasets. In the present study, a multi-objective optimization model is proposed for threshold learning. In our model, we integrate an objective function that minimizes the decision cost with another that decreases the size of the boundary region. The ranges of the thresholds and two types of F_measure are used as constraints. In addition, a multi-objective genetic algorithm is employed to obtain the Pareto optimal set. We used 12 UCI datasets to validate the performance of our method, where the experimental results demonstrated the trade-off between the two objectives as well as showing that the thresholds obtained by our method were more intuitive than those obtained using other methods. The classification abilities of the solutions were improved by the F_measure constraints.     

On uniqueness of （fuzzy） relation in some generalized rough set model

In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.     

Integration of particle swarm optimization-based fuzzy neural network and artificial neural network for supplier selection

This study is intended to develop an intelligent supplier decision support system which is able to consider both the quantitative and qualitative factors. It is composed of (1) the collection of quantitative data such as profit and productivity, (2) a particle swarm optimization (PSO)-based fuzzy neural network (FNN) to derive the rules for qualitative data, and (3) a decision integration model for integrating both the quantitative data and fuzzy knowledge decision to achieve the optimal decision. The results show that the decision support system developed in this study make more precise and favorable judgments in selecting suppliers after taking into account both qualitative and quantitative factors.     

Smart case-based indexing in worsted roving process: Combination of rough set and case-based reasoning

Rough set data analysis (RSDA) has been primarily studied in order to obtain knowledge rules. Taking one group of data as an example, according to the simplified attributes and extractive rules a case was established; using case-based reasoning (CBR), another case was established based on the parameters influencing on the roving quality. In addition, RSDA was combined with CBR to build the case library. This allowed unimportant parameters to be removed and the case library to be simplified; in turn allowing easier, more efficient searching of attributes from the simplified case library. The union of Rule-Based Reasoning (RBR) and CBR means that complicated calculations around similar cases and the associated error can be avoided. Using RSDA one is able to reveal characteristic attributes and deduce knowledge rules associated with the model/problem in order to build a case library directly from historical data. So using the above procedure, allows machine settings to be defined and the prediction and control of the end-product quality to be easier.