4,196 research outputs found

    Parameter Selection and Uncertainty Measurement for Variable Precision Probabilistic Rough Set

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    In this paper, we consider the problem of parameter selection and uncertainty measurement for a variable precision probabilistic rough set. Firstly, within the framework of the variable precision probabilistic rough set model, the relative discernibility of a variable precision rough set in probabilistic approximation space is discussed, and the conditions that make precision parameters α discernible in a variable precision probabilistic rough set are put forward. Concurrently, we consider the lack of predictability of precision parameters in a variable precision probabilistic rough set, and we propose a systematic threshold selection method based on relative discernibility of sets, using the concept of relative discernibility in probabilistic approximation space. Furthermore, a numerical example is applied to test the validity of the proposed method in this paper. Secondly, we discuss the problem of uncertainty measurement for the variable precision probabilistic rough set. The concept of classical fuzzy entropy is introduced into probabilistic approximation space, and the uncertain information that comes from approximation space and the approximated objects is fully considered. Then, an axiomatic approach is established for uncertainty measurement in a variable precision probabilistic rough set, and several related interesting properties are also discussed. Thirdly, we study the attribute reduction for the variable precision probabilistic rough set. The definition of reduction and its characteristic theorems are given for the variable precision probabilistic rough set. The main contribution of this paper is twofold. One is to propose a method of parameter selection for a variable precision probabilistic rough set. Another is to present a new approach to measurement uncertainty and the method of attribute reduction for a variable precision probabilistic rough set

    Rough sets, their extensions and applications

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    Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge. Despite its recency, the theory and its extensions have been widely applied to many problems, including decision analysis, data-mining, intelligent control and pattern recognition. This paper presents an outline of the basic concepts of rough sets and their major extensions, covering variable precision, tolerance and fuzzy rough sets. It also shows the diversity of successful applications these theories have entailed, ranging from financial and business, through biological and medicine, to physical, art, and meteorological

    AN EFFICIENT MULTI-CRITERIA DECISION-MAKING APPROACH BASED ON HYBRIDIZING DATA MINING TECHNIQUES AN EFFICIENT MULTI-CRITERIA DECISION-MAKING APPROACH BASED ON HYBRIDIZING DATA MINING TECHNIQUES

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    Multiple-criteria decision-making (MCDM) that deals with multiple criteria in decision-making environments has been explicitly applied to various decision-making fields. Nevertheless, the critical issues of uncertainty and inaccuracy generally and gradually exists in the majority of the MCDM processes because of (1) prejudice and preference of decision-makers or experts as well as (2) the insufficiency information of the input and output. Therefore, this research efficiently proposed a novel method, FVM-index method, to resolve the limitations happened when MCDM is applied. The FVM-index approach, which consists of the fuzzy set theory (FST), the variable precision rough set (VPRS), and the cluster validity index (CVI) function, not only provides optimized classification results for the datasets but also filters out the uncertainty and inaccuracy instances from surveyed datasets by VPRS theory. Because the datasets are refined by the proposed FVM-index method, the decision makers will be able to effectively obtain the suitable results of MCD

    Data Reduction with Rough Sets

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    Rough Set Theory for Real Estate Appraisal: An Application to Directional District of Naples

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    This paper proposes an application of Rough Set Theory (RST) to the real estate field, in order to highlight its operational potentialities for mass appraisal purposes. RST allows one to solve the appraisal of real estate units regardless of the deterministic relationship between characteristics that contribute to the formation of the property market price and the same real estate prices. RST was applied to a real estate sample (office units located in Directional District of Naples) and was also integrated with a functional extension so-called Valued Tolerance Relation (VTR) in order to improve its flexibility. A multiple regression analysis (MRA) was developed on the same real estate sample with the aim to compare RST and MRA results. The case study is followed by a brief discussion on basic theoretical connotations of this methodology

    Rough approximation quality revisited

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    AbstractIn rough set theory, the approximation quality γ is the traditional measure to evaluate the classification success of attributes in terms of a numerical evaluation of the dependency properties generated by these attributes. In this paper we re-interpret the classical γ in terms of a classic measure based on sets, the Marczewski–Steinhaus metric, and also in terms of “proportional reduction of errors” (PRE) measures. We also exhibit infinitely many possibilities to define γ-like statistics which are meaningful in situations different from the classical one, and provide tools to ascertain the statistical significance of the proposed measures, which are valid for any kind of sample

    A Comparative Analysis of Rough Sets for Incomplete Information System in Student Dataset

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    Rough set theory is a mathematical model for dealing with the vague, imprecise, and uncertain knowledge that has been successfully used to handle incomplete information system. Since we know that in fact, in the real-world problems, it is regular to find conditions where the user is not able to provide all the necessary preference values. In this paper, we compare the performance accuracy of the extension of rough set theory, i.e. Tolerance Relation, Limited Tolerance Relation, Non-Symmetric Similarity Relation and New Limited Tolerance Relation of Rough Sets for handling incomplete information system in real-world student dataset. Based on the results, it is shown that New Limited Tolerance Relation of Rough Sets has outperformed the previous techniques.
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