Graded rough set model based on two universes and its properties

Liu, Caihui; Miao, Duoqian; Zhang, Nan

doi:10.1016/j.knosys.2012.02.012

Cited by 66 publications

(29 citation statements)

References 36 publications

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“…Ma and Sun [217] investigated the decisiontheoretic rough set theory over two universes, based on the idea of classical DTRS theory. Liu et al [218] studied the GRS approach based on two universes and discussed its properties. Chen et al [102] used fuzzy-rough sets to present a matrix of fuzzy discernibility.…”

Section: Related Workmentioning

confidence: 99%

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

et al. 2017

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Rough set theory has been used extensively in fields of complexity, cognitive sciences, and artificial intelligence, especially in numerous fields such as expert systems, knowledge discovery, information system, inductive reasoning, intelligent systems, data mining, pattern recognition, decision-making, and machine learning. Rough sets models, which have been recently proposed, are developed applying the different fuzzy generalisations. Currently, there is not a systematic literature review and classification of these new generalisations about rough set models. Therefore, in this review study, the attempt is made to provide a comprehensive systematic review of methodologies and applications of recent generalisations discussed in the area of fuzzy-rough set theory. On this subject, the Web of Science database has been chosen to select the relevant papers. Accordingly, the systematic and metaanalysis approach, which is called "PRISMA," has been proposed and the selected articles were classified based on the author and year of publication, author nationalities, application field, type of study, study category, study contribution, and journal in which the articles have appeared. Based on the results of this review, we found that there are many challenging issues related to the different application area of fuzzy-rough set theory which can motivate future research studies.

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Section: Related Workmentioning

confidence: 99%

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

et al. 2017

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“…Sun et al [26] defined the fuzzy compatible relation and presented the fuzzy rough set model on the different universes. Liu et al proposed the graded rough set model on two distinct, but related universes in [27]. Ma et al [28] presented the properties of the probabilistic rough set over two universes and discussed the uncertainty measure of the knowledge granularity and rough entropy for a probabilistic rough set over two universes.…”

Section: Introductionmentioning

confidence: 99%

Granular Structure of Type-2 Fuzzy Rough Sets over Two Universes

Lü

Zhai

et al. 2017

Symmetry

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Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic granules. In the theory of fuzzy rough set, granular fuzzy sets can be used to describe the lower and upper approximations of a fuzzy set. This paper discusses the granular structure of type-2 fuzzy rough sets over two universes. Definitions of type-2 fuzzy rough sets over two universes are given based on a wavy-slice representation of type-2 fuzzy sets. Two granular type-2 fuzzy sets are deduced and then proven to be basic granules of type-2 fuzzy rough sets over two universes. Then, the properties of lower and upper approximation operators and these two granular type-2 fuzzy sets are investigated. At last, several examples are given to show the applications of type-2 fuzzy rough sets over two universes.

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“…Liu et al . () studied the graded rough set model over two universes. Based on the prior research, Sun and Ma () presented a rough fuzzy set model by a fuzzy compatibility relation between two different universes.…”

Section: Introductionmentioning

confidence: 99%

“…Also, an algorithm for obtaining the lower and upper approximations of any object set over a dual universe was established. Liu et al (2012) studied the graded rough set model over two universes. Based on the prior research, Sun and Ma (2011) presented a rough fuzzy set model by a fuzzy compatibility relation between two different universes.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision‐making

Sun

Chen

2015

Expert Systems

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Probabilistic approaches to rough sets are still an important issue in rough set theory. Although many studies have been written on this topic, they focus on approximating a crisp concept in the universe of discourse, with less effort on approximating a fuzzy concept in the universe of discourse. This article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space over two universes. We first present the definition of a lower and upper approximation of a fuzzy set with respect to a probabilistic approximation space over two universes by defining the conditional probability of a fuzzy event. That is, we define the rough fuzzy set on a probabilistic approximation space over two universes. We then define the fuzzy probabilistic approximation over two universes by introducing a probability measure to the approximation space over two universes. Then, we establish the fuzzy rough set model on the probabilistic approximation space over two universes. Meanwhile, we study some properties of both rough fuzzy sets and fuzzy rough sets on the probabilistic approximation space over two universes. Also, we compare the proposed model with the existing models to show the superiority of the model given in this paper. Furthermore, we apply the fuzzy rough set on the probabilistic approximation over two universes to emergency decision‐making in unconventional emergency management. We establish an approach to online emergency decision‐making by using the fuzzy rough set model on the probabilistic approximation over two universes. Finally, we apply our approach to a numerical example of emergency decision‐making in order to illustrate the validity of the proposed method.

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Graded rough set model based on two universes and its properties

Cited by 66 publications

References 36 publications

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

Granular Structure of Type-2 Fuzzy Rough Sets over Two Universes

Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision‐making

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