Different kinds of generalized rough sets based on neighborhoods with a medical application
26 Aug 2021-International Journal of Biomathematics (World Scientific Publishing Company)-Vol. 14, Iss: 08
TL;DR: New approximations are proposed representing an extension of Pawlak’s rough sets and some of their generalizations, where the precision of these approximation is substantially improved and a medical application of lung cancer disease is given.
Abstract: Approximation space can be said to play a critical role in the accuracy of the set’s approximations. The idea of “approximation space” was introduced by Pawlak in 1982 as a core to describe informa...
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TL;DR: In this article , a subset neighborhood is defined under an arbitrary binary relation using the inclusion relations between Nρ-neighborhoods, and Sρ-accuracy and roughness measures are derived.
Abstract: We present a novel kind of neighborhood, named subset neighborhood and denoted as Sρ-neighborhood. It is defined under an arbitrary binary relation using the inclusion relations between Nρ-neighborhoods. We study its relationships with some kinds of neighborhood systems given in the literature. Then, we formulate the concepts of Sρ-lower and Sρ-upper approximations, and Sρ-accuracy and roughness measures based on Sρ-neighborhoods. We show in which cases the Sρ-accuracy measure is the highest among related approximations and investigate under which conditions the Sρ-accuracy and Sρ-roughness measures are monotonic. Moreover, we compare our approach with two existing ones and elucidate the advantages of our technique to obtain accuracy measures under some specific relations. To support the obtained results, we provide two medical examples.
28 citations
15 Oct 2021
TL;DR: In this paper, the authors apply a topological concept called "somewhere dense sets" to improve the accuracy of rough set theory, which is a non-statistical approach to handle uncertainty and uncertain knowledge.
Abstract: Rough set theory is a non-statistical approach to handle uncertainty and uncertain knowledge. It is characterized by two methods called classification (lower and upper approximations) and accuracy measure. The closeness of notions and results in topology and rough set theory motivates researchers to explore the topological aspects and their applications in rough set theory. To contribute to this area, this paper applies a topological concept called “somewhere dense sets” to improve the approximations and accuracy measure in rough set theory. We firstly discuss further topological properties of somewhere dense and cs-dense sets and give explicitly formulations to calculate S-interior and S-closure operators. Then, we utilize these two sets to define new concepts in rough set context such as SD-lower and SD-upper approximations, SD-boundary region, and SD-accuracy measure of a subset. We establish the fundamental properties of these concepts as well as show their relationships with the previous ones. In the end, we compare the current method of approximations with the previous ones and provide two examples to elucidate that the current method is more accurate.
28 citations
TL;DR: In this paper , the authors introduce a topological method to produce new rough set models based on the idea of "somewhat open sets" which is one of the celebrated generalizations of open sets.
Abstract: Abstract In this paper, we introduce a topological method to produce new rough set models. This method is based on the idea of “somewhat open sets” which is one of the celebrated generalizations of open sets. We first generate some topologies from the different types of $$N_\rho $$ N ρ -neighborhoods. Then, we define new types of rough approximations and accuracy measures with respect to somewhat open and somewhat closed sets. We study their main properties and prove that the accuracy and roughness measures preserve the monotonic property. One of the unique properties of these approximations is the possibility of comparing between them. We also compare our approach with the previous ones, and show that it is more accurate than those induced from open, $$\alpha $$ α -open, and semi-open sets. Moreover, we examine the effectiveness of the followed method in a problem of Dengue fever. Finally, we discuss the strengths and limitations of our approach and propose some future work.
23 citations
TL;DR: New topological approaches are presented as a generalization of Pawlak’s theory by using j-adhesion neighborhoods and the relationship between them and some other types of approximations with the aid of examples are elucidated.
Abstract: The rough set principle was proposed as a methodology to cope with vagueness or uncertainty of data in the information systems. Day by day, this theory has proven its efficiency in handling and modeling many real-life problems. To contribute to this area, we present new topological approaches as a generalization of Pawlak’s theory by using j-adhesion neighborhoods and elucidate the relationship between them and some other types of approximations with the aid of examples. Topologically, we give another generalized rough approximation using near open sets. Also, we generate generalized approximations created from the topological models of j-adhesion approximations. Eventually, we compare the approaches given herein with previous ones to obtain a more affirmative solution for decision-making problems.
16 citations
TL;DR: In this article , the authors focus on the main concepts of rough set theory induced from the idea of neighborhoods, and apply Mσ-neighborhoods to define Mσ -lower and Mσ −upper approximations and elucidate which one of Pawlak's properties are preserved (evaporated) by these approximate neighborhoods.
Abstract: In this paper, we focus on the main concepts of rough set theory induced from the idea of neighborhoods. First, we put forward new types of maximal neighborhoods (briefly, Mσ -neighborhoods) and explore master properties. We also reveal their relationships with foregoing neighborhoods and specify the sufficient conditions to obtain some equivalences. Then, we apply Mσ -neighborhoods to define Mσ -lower and Mσ -upper approximations and elucidate which one of Pawlak's properties are preserved (evaporated) by these approximations. Moreover, we research AMσ -accuracy measures and prove that they keep the monotonic property under any arbitrary relation. We provide some comparisons that illustrate the best approximations and accuracy measures are obtained when σ=⟨i⟩ . To show the importance of Mσ -neighborhoods, we present a medical application of them in classifying individuals of a specific facility in terms of their infection with COVID-19. Finally, we scrutinize the strengths and limitations of the followed technique in this manuscript compared with the previous ones.
15 citations
References
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TL;DR: New definitions of lower and upper approximations are proposed, which are basic concepts of the rough set theory and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.
Abstract: This paper proposes new definitions of lower and upper approximations, which are basic concepts of the rough set theory. These definitions follow naturally from the concept of ambiguity introduced in this paper. The new definitions are compared to the classical definitions and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.
963 citations
TL;DR: This paper explores the topological properties of covering-based rough sets, studies the interdependency between the lower and the upper approximation operations, and establishes the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation.
588 citations
TL;DR: This paper presents and compares two views of the theory of rough sets: the operator-oriented and set-oriented views, which interprets rough set theory as an extension of set theory with two additional unary operators.
562 citations
TL;DR: This paper investigates a novel approach based on fuzzy-rough sets, fuzzy rough feature selection (FRFS), that addresses problems and retains dataset semantics and is applied to two challenging domains where a feature reducing step is important; namely, web content classification and complex systems monitoring.
Abstract: Attribute selection (AS) refers to the problem of selecting those input attributes or features that are most predictive of a given outcome; a problem encountered in many areas such as machine learning, pattern recognition and signal processing. Unlike other dimensionality reduction methods, attribute selectors preserve the original meaning of the attributes after reduction. This has found application in tasks that involve datasets containing huge numbers of attributes (in the order of tens of thousands) which, for some learning algorithms, might be impossible to process further. Recent examples include text processing and web content classification. AS techniques have also been applied to small and medium-sized datasets in order to locate the most informative attributes for later use. One of the many successful applications of rough set theory has been to this area. The rough set ideology of using only the supplied data and no other information has many benefits in AS, where most other methods require supplementary knowledge. However, the main limitation of rough set-based attribute selection in the literature is the restrictive requirement that all data is discrete. In classical rough set theory, it is not possible to consider real-valued or noisy data. This paper investigates a novel approach based on fuzzy-rough sets, fuzzy rough feature selection (FRFS), that addresses these problems and retains dataset semantics. FRFS is applied to two challenging domains where a feature reducing step is important; namely, web content classification and complex systems monitoring. The utility of this approach is demonstrated and is compared empirically with several dimensionality reducers. In the experimental studies, FRFS is shown to equal or improve classification accuracy when compared to the results from unreduced data. Classifiers that use a lower dimensional set of attributes which are retained by fuzzy-rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method. In addition, it is shown that FRFS is more powerful than the other AS techniques in the comparative study
408 citations
TL;DR: It is proved that for some special thresholds, β lower distribution reduct is equivalent to the maximum distribution reduction reduct, whereas β upper distribution reduCT is equivalents to the possible reduct.
388 citations