A multi‐attribute decision analysis method based on rough sets dealing with uncertain information

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.

Grade and precision are two important confidence levels. In this paper, the connection and combination between them are studied. The connection between graded approximations and variable precision approximations is studied, and the important formula of conversion is achieved. Approximation of intersection of grade and precision is defined based on logical ”and” operation of grade and precision, and its construction is achieved, which becomes important theory base for decreasing computing complexity and computing quantity of application algorithm of graded rough sets and variable precision rough sets. Graded rough sets and variable precision rough sets are united and included by the approximation of intersection of grade and precision. The study on combination and unity of graded rough sets and variable precision rough sets in this paper, has important value on both theory development and practice application.KeywordsArtificial IntelligenceRough SetsGraded Rough SetsVariable Precision Rough SetsConfidence LevelsGradePrecision

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.

Product service system (PSS) is an important strategy for manufacturing companies to improve competitiveness. The extension of supply range forces the manufacturing companies to select service suppliers to support PSS development due to the constraint of resources and capability. VIKOR approach is applied to evaluate the service suppliers based on compromise programming. To deal with the uncertain evaluation information, evaluation data are expressed as vague values by means of vague set theory. In the vague VIKOR, the maximised group utility and minimised individual regret are obtained based on similarity measure between two vague values. A set of criteria weights is a critical input of VIKOR. The traditional weights-determining approaches are subjective and have higher uncertainty such as analytic hierarchy process and analytic network process. Rough set mining approach can be used to obtain the criteria weights according to the surveyed performance information on each criterion and on the whole. The traditional rough set has poor noise-tolerance capability, the variable precision rough set approach is used to mine the criteria weights, and a mining algorithm is proposed in this paper. A case study of rescue service supplier evaluation in excavator PSS development is presented to illustrate the effectiveness of the proposed approach.

Variable precision rough sets (VPRS), as a extension of rough sets (RS) is adopted to reduce the redundant features for its ability of more useful information adopted compared with RS. The reduced features after VPRS are fed into the improved BP network proposed to inspect the defects of surface quality, which results in short training time and a high classification accuracy with a typical application in defect inspection of wood veneer.

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.

Mobile ad hoc networks are formed dynamically without any infrastructure and each node in the network is responsible for routing information. Rough set theory is a mathematical tool to deal with vagueness and uncertainty. Variable precision rough sets (VPRS) is a generalization of rough sets that allows for a controlled degree of misclassification. This paper proposes extensions in mobile ad hoc routing using VPRS. The performance of the proposed mobile ad hoc routing protocol is compared with that of an existing routing protocol.

A transformer is one of the most important units in the power networks. Thus a breakdown of a transformer faults can cause costly repairs. In this paper, a new transformer fault diagnosis method based on variable precision rough set is presented. The proposed method transforms the continuous attribute values into the fuzzy values by automatically deriving membership functions from a set of data with similarity clustering. With the concepts of fuzzy similarity relation and fuzzy similarity classes, beta-positive region, beta-negative region and beta-boundary region of rough-fuzzy approximation space are given. Also, a fuzzy rough set learning algorithm is given for inducing rules from quantitative data. The application to fault diagnosis of transformer shows the proposed algorithm can find more objective and effective diagnostic rules from the quantitative data and is a good method in application of fault diagnosis.

The aim of feature selection (FS) is to select a small subset of most important and discriminative features. Many FS approaches based on rough set theory up to now, have employed reduct analysis using feature dependency measures. However the critical shortcoming for such approaches is that they are not able to manage useful information that may be destroyed by noise elements. Therefore several extensions to the original theory have been proposed. Three notable extensions are fuzzy rough set (FRS), variable precision rough set (VPRS), and tolerance rough set model (TRSM). Although successful, each of the extensions exhibits a critical shortcoming which makes that extension inapplicable in most of scenarios. For example, FRS is able to describe the existing dependencies between different attributes accurately, but its high run-times makes it inapplicable to larger datasets. As another example, VPR is very fast, but requires more information than contained within the data itself, which is inaccessible for most of the applications. This paper examines a rough set FS technique which uses a noise resistant dependency measure to quantify information that may be hidden due to the noise elements. Experimental results demonstrate that the use of this measure can result more discriminative reducts than those obtained using other RSFS approaches. Moreover, the proposed measure is as fast as VPRS and as accurate as FRS and TRSM, while it need no additional information other than contained within the data.

Quantitative rough sets based on subsethood measures

Rough set theory is studied to manage uncertain and inconsistent information. Because Pawlak’s decision logic for rough sets is based on the classical two-valued logic, it is inconvenient for handling inconsistent information. We propose a bilattice logic as the deduction basis for the decision logic of rough sets to address inconsistent and ambiguous information. To enhance the decision logic to bilattice semantics, we introduce Variable Precision Rough Set (VPRS). As a deductive basis for bilattice decision logic, we define a consequence relation for Belnap’s four-valued semantics and provide a bilattice semantic tableau TB4 for a deduction system. We demonstrate the soundness and completeness of TB4 and enhance it with weak negation.

By the combination of feature and concept hierarchy model and the definition of innovation about concept, the method of structured processing and knowledge hierarchical representation for injection mould repair schemes is put forward under the condition of non-fuzzy or fuzzy data. Rule sets can be provided by knowledge induction for injection mould repairs based on basic rough set, but the rule sets are large-scale and the applicability is poor in practice. Aiming at achieving the rule sets more efficiently and applicably, a new method of knowledge hierarchical induction based on variable precision rough set is proposed. For injection mould repair schemes based on fuzzy data, by the abstraction of innovation about concept from the feature decision tables, feature fuzzy similar matrix is constructed and the feature decision table is divided into some fuzzy equivalent subsets by introducing confidence level vector. Finally, the algorithm of feature reduction and knowledge induction based on fuzzy rough set is put forward by defining single or multi-fuzzy feature equivalence relations. The feasibility and effectiveness of two methods for knowledge hierarchical induction under different data environments are both analyzed.

An expert system for automatically selecting stock portfolio is presented. The expert system involved Grey Relational Analysis (GRA) model, the VPRS-index clustering / classification method, and Variable Precision Rough Set (VPRS) theory. The GRA model is applied to consolidate the 53 financial indices into six financial ratios (Grey Relational Grades (GRGs)) for each stock item. The VPRS-index method is used to determine the optimal number of clusters per GRG. VPRS theory is then applied to identify the stocks within the -lower approximate sets. Finally, the GRGs of each candidate stock item are consolidated to a single GRG indicating the ability of the stock item to maximize the rate of return. The validity and effectiveness of the VPRS-index clustering / classification method is first evaluated prior to that of the expert system. After that, results of this study showed that this expert system yields a higher rate of return than those of several existing portfolio selection systems. Key words: Fuzzy C-Means, VPRS, VPRS-index method, classification, stock portfolio.