Decision-theoretic Rough Set Model Research Articles

Minimal decision cost reduct in fuzzy decision-theoretic rough set model

Decision-theoretic rough set model interprets the parameters of existing probabilistic rough sets by introducing Bayesian theory to minimize the risks of classification. It is a representative probabilistic rough set model. As an important extension of decision-theoretic rough set model, fuzzy decision-theoretic rough set model can deal with numerical data directly. To investigate the attribute reduction in fuzzy decision-theoretic rough set model, we propose two attribute reduction approaches: global reduction and local reduction. Global reduction can keep the cost of all the decision classes unchanged or decreased. Moreover, local reduction can make the cost of single decision class unchanged or decreased. In this paper, we use two different heuristic functions to implement heuristic algorithms. Heuristic algorithms are used to find the minimal subset of condition attributes which minimizes the (P) cost, (B) cost and (N) cost in fuzzy decision theoretic-rough set model. Six UCI datasets are employed to test our heuristic algorithms. The experimental results indicate that global reduction and local reduction can minimize the decision cost in fuzzy decision-theoretic rough set model effectively. After reduction, the numbers of condition attributes are reduced greatly. On the other hand, global reduction and local reduction both can decrease the numbers of (P) rule and (B) rule on the whole. The results show that when we reduce the decision cost, we will also reduce the rule numbers as well.

Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information

Decision-theoretic rough sets (DTRSs) as a classic model of three-way decisions have been widely applied in the area of risk decision-making. When we confront the complicated and uncertain environment, one of challenges is to estimate the loss function of DTRSs. As a new generalization of fuzzy sets, dual hesitant fuzzy sets (DHFSs) can handle uncertain information more flexibly in the process of decision making and give a new measure for the determination of loss functions of DTRSs. To have more interesting results in the context of three-way decisions, we introduce the new hesitant format of DHFSs into DTRSs and explore a new three-way decision model. Firstly, we take into account the loss functions of DTRSs with dual hesitant fuzzy elements (DHFEs) and propose a dual hesitant fuzzy DTRS model. In order to satisfy the preconditions of three-way decisions, we analyze the normalized principle of loss functions under the dual hesitant fuzzy environment. Meanwhile, some properties of the expected losses are carefully investigated. Then, we further design two approaches for deriving three-way decisions with the new DTRS model, i.e., Method 1 and Method 2, which mainly relies on the comparisons among the expected losses. Method 1 is a general method based on the scores and the accuracies of DHFEs. Method 2 is a ranking method of possibility degrees with a stochastic strategy and enriches the comparisons among the expected losses. Finally, the assessment of emergency blood transshipment is used to illustrate and compare these proposed methods.

Covering multigranulation trapezoidal fuzzy decision-theoretic rough fuzzy set models and applications

As an extension of the classical Pawlak rough sets, covering multigranulation trapezoidal fuzzy decision-theoretic rough set models have been researched, in which objects approximated are crisp sets or accurate concepts of the universe of discourse, and there are only two states, which are disjoint and opposite each other for an accurate concept of the universe of discourse for a decision-making problem. However, the objects of many decision-making problems can have more than two states in practice. Moreover, the states of the decision object are not necessarily disjoint and opposite each other, but these decision states are fuzzy descriptions of the states of the object on the universe. In order to deal with decision-making problems in which decision states are fuzzy sets, covering multigranulation trapezoidal fuzzy decision-theoretic rough fuzzy set models are proposed in this paper. In addition, the mean, optimistic and pessimistic covering multigranulation trapezoidal fuzzy decision-theoretic rough fuzzy sets are investigated and characterized. Furthermore, the relationships between covering multigranulation trapezoidal fuzzy decision-theoretic rough fuzzy set models and the existing models are discussed. Finally, an example is presented to illustrate the practicality and generality of the proposed models.

Decision-theoretic rough set approach for fuzzy decisions based on fuzzy probability measure and decision making

Most existing studies on decision-theoretic rough set approach focus on crisp decisions. However, in many cases, we need to handle fuzzy concepts. This paper investigates decision-theoretic rough set approach for fuzzy decisions. By introducing fuzzy operators, we extend the traditional decision-theoretic rough set approach with crisp decisions to fuzzy concepts. Decision-theoretic rough set approach with fuzzy concepts is investigated based on fuzzy probabilistic approxi- mation space. Bayesian decision procedure based on fuzzy probabilistic approximation space with fuzzy concepts and fuzzy probabilistic decision systems with fuzzy or continuous decision attributes are studied. The application of the proposed approach in decision making is also illustrated by an example. This study may expand the applications of decision-theoretic rough set model.

Double-quantitative rough fuzzy set based decisions: A logical operations method

As two important expanded quantification rough set models, the probabilistic rough set (PRS) model and the graded rough set (GRS) model are used to measure relative quantitative information and absolute quantitative information between the equivalence classes and a basic concept, respectively. The decision-theoretic rough set (DTRS) model is a special case of PRS model which mainly utilizes the conditional probability to express relative quantification. Since the fuzzy concept is more general than classical concept in real life, how to make decision for a fuzzy concept using relative and absolute quantitative information is becoming a hot topic. In this paper, a couple of double-quantitative decision-theoretic rough fuzzy set (Dq-DTRFS) models based on logical conjunction and logical disjunction operation are proposed. Furthermore, we discuss decision rules and the inner relationship between these two models. Then, an experiment in the medical diagnosis is studied to support the theories. Finally, to apply our methods to solve a pattern recognition problem in big data, experiments on data sets downloaded from UCI are conducted to test the proposed models. In addition, we also offer a comparative analysis using two non-rough set based methods. From the results obtained, one finds that the proposed method is efficient for dealing with practical issues.

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.

Towards scalable rough set based attribute subset selection for intrusion detection using parallel genetic algorithm in MapReduce

Attribute subset selection based on rough sets is a crucial preprocessing step in data mining and pattern recognition to reduce the modeling complexity. To cope with the new era of big data, new approaches need to be explored to address this problem effectively. In this paper, we review recent work related to attribute subset selection in decision-theoretic rough set models. We also introduce a scalable implementation of a parallel genetic algorithm in Hadoop MapReduce to approximate the minimum reduct which has the same discernibility power as the original attribute set in the decision table. Then, we focus on intrusion detection in computer networks and apply the proposed approach on four datasets with varying characteristics. The results show that the proposed model can be a powerful tool to boost the performance of identifying attributes in the minimum reduct in large-scale decision systems.

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. • We propose a multi-objective optimization method for learning thresholds. • Decreasing the size of the boundary region is represented simply. • The penalties in single objective model could be neglected. • Solutions with better classification ability can be improve by F_measures. • Users may select the final solution based on their own preferences.

Quantitative/qualitative region-change uncertainty/certainty in attribute reduction: Comparative region-change analyses based on granular computing

Attribute reduction is a fundamental research theme in rough sets and granular computing (GrC). Its scientific construction originally depends on the region-change law. At present, only region-change non-monotonicity/monotonicity is mined in the quantitative/qualitative model. The in-depth region-change truth and its GrC mechanism have significance, especially for follow-up attribute reduction. This paper commences probing region-change essence, mainly from a novel uncertainty/certainty viewpoint. Concretely, we make comparative region-change analyses based on GrC, by resorting to the qualitative Pawlak-Model and quantitative DTRS-Model (the decision-theoretic rough set model). (1) Knowledge-coarsening is investigated to describe attribute deletion. (2) Granule-merging and its region-distribution are studied to probe region-change functions. (3) Region-change is analyzed in Pawlak-Model to mine qualitative region-change certainty and its relevant properties. (4) Region-change is analyzed in DTRS-Model to mine quantitative region-change uncertainty and its relevant properties. (5) Comparative region-change analyses are summarized, and further experiment verification is provided. Knowledge-coarsening and granule-merging establish GrC mechanisms for extensive region-change analyses. Quantitative/qualitative region-change uncertainty/certainty and relevant principles are discovered via DTRS-Model/Pawlak-Model. By virtue of the GrC technology and comparative strategy, this study reveals region-change uncertainty/certainty to deepen region-change non-monotonicity/monotonicity; furthermore, it underlies attribute reduction, especially with regard to quantitative models.

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.

A fuzzy multigranulation decision-theoretic approach to multi-source fuzzy information systems

Decision-theoretic rough set theory (DTRS) is becoming one of the important research directions for studying set approximations using Bayesian decision procedure and probability theory in rough set community. In this paper, a novel model, fuzzy multigranulation decision-theoretic rough set model (FM-DTRS), is proposed in terms of inclusion measure of fuzzy rough sets in the viewpoint of fuzzy multigranulation. Gaussian kernel is used to compute the similarity between objects, which induces a fuzzy equivalence relation, and then we make use of Tp-norm operator with the property of Hadamart product to aggregate the multiple induced fuzzy equivalence relations. We employ the aggregated relation to fuzzily partition the universe and then obtain multiple fuzzy granulations from the multi-source information system. Moreover, some of its properties are addressed. A comparative study between the proposed fuzzy multigranulation decision-theoretic rough set model and Qian’s multigranulation decision-theoretic rough set model is made. An example is employed to illustrate the effectiveness of the proposed method which may provide an effective approach for multi-source data analysis in real applications.

On quick attribute reduction in decision-theoretic rough set models

Compared with the Pawlak rough set model, decision-theoretic rough set (DTRS) models have relatively powerful data processing capability for complex and low quality data. However, the non-monotonicity of the criteria used in DTRS models causes many problems, particularly the inefficiency of attribute reduction algorithms, which greatly narrows their applications. Few systematic studies have been reported on how to construct efficient reduction methods for DTRS models. This paper discusses this problem and constructs an efficient reduction algorithm for DTRS models incorporating three aspects: taking advantage of common characteristics of data sets and employing division techniques, a fast division approach to computing equivalence classes is proposed, which is the most frequently used and the most time-consuming basic operation in the reduction algorithm; extracting a “monotonic ingredient” from decision systems, an effective heuristic function is constructed for the reduction algorithm, which can guide searches for the algorithm and has better ability to find shorter super-reducts; a novel algorithm is proposed to search the power set space of a given super-reduct, which has a shorter average search length than the existing backtracking methods. Finally, the reduction algorithm is proposed that combines these improvements. Experimental results demonstrate that these improvements are effective and the proposed reduction algorithm is relatively efficient.

Two Bayesian approaches to rough sets

Bayesian inference and probabilistic rough sets (PRSs) provide two methods for data analysis. Both of them use probabilities to express uncertainties and knowledge in data and to make inference about data. Many proposals have been made to combine Bayesian inference and rough sets. The main objective of this paper is to present a unified framework that enables us (a) to review and classify Bayesian approaches to rough sets, (b) to give proper perspectives of existing studies, and (c) to examine basic ingredients and fundamental issues of Bayesian approaches to rough sets. By reviewing existing studies, we identify two classes of Bayesian approaches to PRSsand three fundamental issues. One class is interpreted as Bayesian classification rough sets, which is built from decision-theoretic rough set (DTRS) models proposed by Yao, Wong and Lingras. The other class is interpreted as Bayesian confirmation rough sets, which is built from parameterized rough set models proposed by Greco, Matarazzo and Słowiński. Although the two classes share many similarities in terms of making use of Bayes’ theorem and a pair of thresholds to produce three regions, their semantic interpretations and, hence, intended applications are different. The three fundamental issues are the computation and interpretation of thresholds, the estimation of required conditional probabilities, and the application of derived three regions. DTRS models provide an interpretation and a method for computing a pair of thresholds according to Bayesian decision theory. Naive Bayesian rough set models give a practical technique for estimating probability based on Bayes’ theorem and inference. Finally, a theory of three-way decisions offers a tool for building ternary classifiers. The main contribution of the paper lies in weaving together existing results into a coherent study of Bayesian approaches to rough sets, rather than introducing new specific results.

Multigranulation decision-theoretic rough sets in incomplete information systems

We study multigranulation decision-theoretic rough sets in incomplete information systems. Based on Bayesian decision procedure, we propose the notions of weighted mean multigranulation decision-theoretic rough sets, optimistic multigranulation decision-theoretic rough sets, and pessimistic multigranulation decision-theoretic rough sets in an incomplete information system. We investigate the relationships between the proposed multigranulation decision-theoretic rough set models and other related rough set models. We also study some basic properties of these models. We give an example to illustrate the application of the proposed models.

Decision-theoretic rough sets under dynamic granulation

Decision-theoretic rough set theory is quickly becoming a research direction in rough set theory, which is a general and typical probabilistic rough set model with respect to its threshold semantics and decision features. However, unlike the Pawlak rough set, the positive region, the boundary region and the negative region of a decision-theoretic rough set are not monotonic as the number of attributes increases, which may lead to overlapping and inefficiency of attribute reduction with it. This may be caused by the introduction of a probabilistic threshold. To address this issue, based on the local rough set and the dynamic granulation principle proposed by Qian et al., this study will develop a new decision-theoretic rough set model satisfying the monotonicity of positive regions, in which the two parameters α and β need to dynamically update for each granulation. In addition to the semantic interpretation of its thresholds itself, the new model not only ensures the monotonicity of the positive region of a target concept (or decision), but also minimizes the local risk under each granulation. These advantages constitute important improvements of the decision-theoretic rough set model for its better and wider applications.

Multigranulation Decision-theoretic Rough Set in Ordered Information System

The decision-theoretic rough set model based on Bayesian decision theory is a main development tendency in the research of rough sets. To extend the theory of decision-theoretic rough set, the article devotes this study to presenting multigranulation decision-theoretic rough set model in ordered information systems. This new multigranulation decision-theoretic rough set approach is characterized by introducing the basic set assignment function in an ordered information system. It is addressed about how to construct probabilistic rough set and multigranulation decision-theoretic rough set models in an ordered information system. Moreover, three kinds of multigranulation decision-theoretic rough set model are analyzed carefully in an ordered information system. In order to explain probabilistic rough set model and multigranulation decision-theoretic rough set models in an ordered information system, an illustrative example is considered, which is helpful for applying these theories to deal with practical issues.

Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making

Based on decision-theoretic rough set model of three-way decisions, we augment the existing model by introducing linguistic terms. Considering the two types of parameters being used in the three-way decisions with linguistic assessment, a certain type of novel three-way decisions based on the Bayesian decision procedure is constructed. In this way, three-way decisions with decision-theoretic rough sets are extended to the qualitative environment. With the aid of multi-attribute group decision making, the values of these parameters are determined. An adaptive algorithm supporting consistency improvement of multi-attribute group decision making is designed. Then, we optimize the scales of the linguistic terms with the use of particle swarm optimization. The values of these parameters of three-way decisions are aggregated when proceeding with group decision making. Finally, the proposed model of three-way decisions with linguistic assessment is applied to the selection process of new product ideas.

Attribute Reduction in Decision-Theoretic Rough Set Model using Particle Swarm Optimization with the Threshold Parameters Determined using LMS Training Rule

Abstract Decision-theoretic rough set model is the probabilistic generalization of the Pawlak rough set model. In this paper, we have analyzed decision-theoretic rough set model (DTRSM) in the context of attribute reduction. DTRSM is based on Bayesian decision theory for classifying an object into a particular category. The risk associated with classifying an object is defined in terms of loss functions and conditional probabilities. We have used least mean squares learning algorithm to determine the Bayesian loss functions by taking expected overall risk as the learning function. With the loss functions ready, DTRSM can be applied to classification problems. We have proposed attribute reduction in DTRSM by optimizing the expected overall risk using particle swarm optimization algorithm. The proposed algorithm was tested on various data sets found in University of California, machine learning repository. The proposed algorithm has given good results for the cardinality of the reduct and classification accuracy during tests performed on the data sets. Experimental results obtained by the proposed algorithm have been found to give better reduced length of the reduct and classification accuracy in comparison to the results obtained by the consistency subset evaluation feature selection algorithm described in the literature.

Region-based quantitative and hierarchical attribute reduction in the two-category decision theoretic rough set model

Quantitative attribute reduction exhibits applicability but complexity when compared to qualitative reduction. According to the two-category decision theoretic rough set model, this paper mainly investigates quantitative reducts and their hierarchies (with qualitative reducts) from a regional perspective. (1) An improved type of classification regions is proposed, and its preservation reduct (CRP-Reduct) is studied. (2) Reduction targets and preservation properties of set regions are analyzed, and the set-region preservation reduct (SRP-Reduct) is studied. (3) Separability of set regions and rule consistency is verified, and the quantitative and qualitative double-preservation reduct (DP-Reduct) is established. (4) Hierarchies of CRP-Reduct, SRP-Reduct, and DP-Reduct are explored with two qualitative reducts: the Pawlak-Reduct and knowledge-preservation reduct (KP-Reduct). (5) Finally, verification experiments are provided. CRP-Reduct, SRP-Reduct, and DP-Reduct expand layer by layer Pawlak-Reduct and exhibit quantitative applicability, and the experimental results indicate their effectiveness and hierarchies regarding Pawlak-Reduct and KP-Reduct.

Decision-theoretic rough fuzzy set model and application

This article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space. We propose the probabilistic rough fuzzy set by defining the conditional probability of a fuzzy event. Then we establish the model of probabilistic rough fuzzy set and discuss several properties in detail. Furthermore, three generalizations of probabilistic rough fuzzy set, namely, 0.5-probabilistic rough fuzzy set, variable precision probabilistic rough fuzzy set and Bayesian rough fuzzy set are reported. In order to give a systematic method of selecting parameters for the probabilistic rough fuzzy set, we propose a decision-theoretic rough fuzzy set. That is, we formulate a non-parametric definition of the probabilistic rough fuzzy set. Moreover, we illustrate the motivation and verify the validity of the decision-theoretic rough fuzzy set by using a credit card applicant decision-making problem. Furthermore, the interrelationship between the decision-theoretic rough fuzzy set and the probabilistic rough fuzzy set is explained. The main contribution of this paper is twofold. One is to extend the probabilistic rough set to fuzzy environment, i.e., the probabilistic rough fuzzy set model. Another is to present an approach to select parameters needed in probabilistic rough fuzzy set modeling by using the process of decision-making under conditions of risk.