Variable Precision Rough Set Approach to Multiple Decision Tables

Variable Precision Rough Set (VPRS) model is one of the most important extensions of the Classical Rough Set (RS) theory. It employs a majority inclusion relation mechanism in order to make the Classical RS model become more fault tolerant, and therefore the generalization of the model is improved. This paper can be viewed as an extension of previous investigations on attribution reduction problem in VPRS model. In our investigation, we illustrated with examples that the previously proposed reduct definitions may spoil the hidden classification ability of a knowledge system by ignoring certian essential attributes in some circumstances. Consequently, by proposing a new ß-consistent notion, we analyze the relationship between the structures of Decision Table (DT) and different definitions of reduct in VPRS model. Then we give a new notion of /3-complement reduct that can avoid the defects of reduct notions defined in previous literatures. We also supply the method to obtain the /3- complement reduct using a decision table splitting algorithm, and finally demonstrate the feasibility of our approach with sample instances.

A generalization of the original idea of rough sets and variable precision rough sets is introduced. This generalization is based on the concept of absolute and relative rough membership. Similarly to variable precision rough set model, the generalization called parameterized rough set model, is aimed at modeling data relationships expressed in terms of frequency distribution rather than in terms of a full inclusion relation used in the classical rough set approach. However, differently from variable precision rough set model, one or more parameters modeling the degree to which the condition attribute values confirm the decision attribute value, are considered. The properties of this extended model are investigated and compared to the classical rough set model and the variable precision rough set model.

Variable precision rough set model, as an important probabilistic approach to rough set theory, can deal with many practical problems which involve noise data and cannot be effectively handled by Pawlak's rough set model. Generally, rough set theory based knowledge reduction includes attribute reduction and attribute value reduction. Attribute reduction in variable precision rough set model has been attracted many researchers' attentions. However, attribute value reduction in variable precision rough set model was rarely discussed. In this paper, an approach to attribute value reduction in variable precision rough set model is presented, with which the redundant information in the given decision table can be effectively removed and the properties of the acquired rules, namely deterministic or probabilistic, can be preserved well.

PurposeThe purpose of this paper is to acquire doubly variable precision‐based knowledge rules from incomplete decision tables (IDTs) in the framework of pansystems methodology. It suggests a new variable precision limited tolerance – a special pansystems relation – rough set model with precision inclusion and a reduct procedure in which it overcomes the non‐monotony in forming tolerance classes when reducing an attribute from attribute set.Design/methodology/approachThrough introducing variable precision and limited tolerance relation in IDT, it constructs symmetric binary relation, dissimilar to non‐symmetric relation proposed by others, and then forms tolerance classes. It proposes a new reduction procedure with absolute value calculation to avoid tolerance classes being non‐monotone. Using variable inclusion, it obtains lower and upper approximations with noises.FindingsTolerance classes are not monotone with the reduction of attribute from attribute set in the proposed variable precision and limited tolerance relation, but it remains symmetry. Proposed reduction procedure with absolute value calculation is a new approach in adjudging whether a reduct equals to the original whole attribute set within a error range or not.Practical implicationsUsing variable precision and limited rough set model with variable inclusion to mine deep knowledge from IDT is a paradise in knowledge discovery in dealing with non‐determinative and vague problems.Originality/valueThe formation of symmetric tolerance relation is natural. The reduction procedure with absolute value calculation is new and not similar to those existed in literatures.

An illustration of variable precision rough sets model: an analysis of the findings of the UK Monopolies and Mergers Commission

The variable precision rough set (VPRS) model generalizes the Pawlak rough set model with variable parameters. The Bayesian rough set (BRS) model improves the VPRS model with non-parametric modification by using the prior probability as a reference. This paper presents two research results related to rough set model and rough vague sets. One is a modification to the Bayesian rough set model and the other is a modification to rough vague sets. First, the Bayesian rough set model is analyzed and discussed. Second, a modification to this model is proposed and verified. Finally, a modification to rough vague sets is presented and its related properties are discussed..

Traditional rough set of noise data, the lack of adaptability, lack of flexibility or robustness, for the engineering data can not distinguish between equivalence classes of edge region of overlap with the collection, resulting in loss of many valuable engineering information. Strong noise in the actual engineering data over-fitting due to reduced ability to distinguish the object, its limitations limits its further application. In this paper, variable precision rough set model (VPRS, the variable precision Rough set Model), allows a certain threshold level of classification rate exists, in order to better solve the engineering data, no functional relationship between attributes of interference data classification problem, it Overcome the standard rough set model on the shortcomings of the data is too sensitive to noise, thereby enhancing the data analysis and processing robustness. Finally, simulation results show that using variable precision rough set theory to solve the data uncertainty of similar projects under the influence of the extraction is feasible.

Variable precision rough set model is the extension of rough set model, which introduce theβparameter based on the basic rough set theory, that is, allows a certain degree of misclassification rate existing. This paper presents the web mining algorithm based on variable precision rough set in e-commerce, analyzes the limitation of the reduction methods based on variable precision rough set theory. The experiment shows the CPU Time in the attribute numbers, indicating that VPRS is superior to normal algorithm in web mining in e-commerce. The experiments show the algorithm could flexibly and dynamically web mining and therefore provide a valuable addition to the field.

In order to effectively handle the real-valued data sets in practice, it is valuable from theoretical and practical aspects to combine fuzzy rough set and variable precision rough set so that a powerful tool can be developed. That is, the model of fuzzy variable precision rough set, which not only can handle numerical data but also is less sensitive to misclassification and perturbation,In this paper, we propose a new variable precision rough fuzzy set by introducing the variable precision parameter to generalized rough fuzzy set, i.e., the variable precision rough fuzzy set based on general relation. We, respectively, define the variable precision rough lower and upper approximations of any fuzzy set and it level set with variable precision parameter by constructive approach. Also, we present the properties of the proposed model in detail. Meanwhile, we establish the relationship between the variable precision rough approximation of a fuzzy set and the rough approximation of the level set for a fuzzy set. Furthermore, we give a new approach to uncertainty measure for variable precision rough fuzzy set established in this paper in order to overcome the limitations of the traditional methods. Finally, some numerical example are used to illuminate the validity of the conclusions given in this paper.

An integration method of variable precision rough set and neural network for fault diagnosis is presented and used in rotary machinery fault diagnosis. The method integrates the ability of variable precision rough set on reduction of diagnosis information system and that of neural network for fault classification. Typical faults of rotating machinery were simulated in our rotor test-bed. The power spectrum data are used as rotating machinery fault diagnosis signal. For inconsistent data and noise data in power spectrum, variable precision rough set model allows a flexible region of lower approximations by precision variables. By attribute reduction based on variable precision rough set, redundant attributes are identified and removed. The reduction results are used as the input of neural network. The diagnosis results show that the proposed approach for input dimension reduction in neural network is very effective and has better learning efficiency and diagnosis accuracy.

Radar emitter information detected by multisensor system takes on uncertainty, illegibility and contradiction. In real reconnaissance environment, the patterns of radar classes often overlap, the accurate classification of the Pawlak rough set model restricts its application in the real world. In order to solve emitter recognition problem, a new method of finding decision rules is presented to classify radar emitter from the new point of view of variable precision rough set. This method is according to dependent degree of decision attributes on condition attributes. The decision rules proposed are more straightforward. At last, example of recognizing the radar emitter purposes is selected. During the experiment, discretization is conducted on extracted index data of radar emitter and metrical radar characteristic parameter firstly. Then, positive region of each condition attribute are calculated under the given error parameter, which is the basis of decision rules. Experimental results demonstrate this new radar emitter recognition method by finding decision rules based on variable precision rough set model is effective and feasibility

Precision and grade are two important quantitative indexes. The purpose of this paper is to combine precision and grade, and explore new extended rough set model. Based on logical difference operation of grade and precision, this paper proposes model of logical difference operation of grade upper approximation operator and variable precision lower approximation operator. In the new model, fundamental structure and properties are obtained by transformation formulas between variable precision approximations and graded approximations, furthermore regular algorithm and structural algorithm are proposed and analyzed. Finally a practical example is given to illustrate the model and the algorithms. The new model has extended variable precision rough set model, graded rough set model and classical rough set model, and so these models have obtained similar properties of approximation operators.

Precision and grade are two important quantitative indexes. The purpose of this paper is to combine precision and grade, and explore new extended rough set model. Based on logical OR operation of precision and grade, this paper proposes model of logical OR operation of variable precision lower approximation operator and grade upper approximation operator. In the new model, fundamental structure and properties are obtained by transformation formulas between variable precision approximations and graded approximations, furthermore regular algorithm and structural algorithm are proposed and analyzed. Finally a practical example is given to illustrate the model and the algorithms. The new model has extended variable precision rough set model, graded rough set model and classical rough set model, and so these models have obtained similar properties of approximation operators.

Precision and grade are two important quantitative indexes. This paper is to combine precision and grade, and explore new extended rough set model. Based on logical OR requirement of precision and grade, this paper proposes logical OR model of variable precision upper approximation operator and grade lower approximation operator. In the new model, basic structure and properties are obtained by transformation formulas between variable precision approximations and grade approximations, furthermore regular algorithm and structural algorithm are proposed and analyzed. Finally a practical example is given to illustrate the model and the algorithms. The new model has extended variable precision rough set model, graded rough set model and classical rough set model, and so these models have obtained corresponding properties of approximation operators.

Precision and grade are two important quantitative indexes. The purpose of this paper is to combine precision and grade, and explore new extended rough set model. Based on logical difference operation of precision and grade, this paper proposes model of logical difference operation of variable precision upper approximation operator and grade lower approximation operator. In the new model, fundamental structure and properties are obtained by transformation formulas between variable precision approximations and graded approximations, furthermore regular algorithm and structural algorithm are proposed and analyzed. Finally a practical example is given to illustrate the model and the algorithms. The new model has extended variable precision rough set model, graded rough set model and classical rough set model, and so these models have obtained similar properties of approximation operators.