Author
Ali Kandil
Bio: Ali Kandil is an academic researcher from Helwan University. The author has contributed to research in topics: Rough set & Fuzzy logic. The author has an hindex of 5, co-authored 14 publications receiving 42 citations.
Papers
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01 Sep 2020TL;DR: Two kinds of approximation operators via ideals which represent extensions of Pawlak’s approximation operator have been presented and the definitions of upper and lower approximations based on ideals have been given.
Abstract: The original model of rough sets was advanced by Pawlak, which was mainly involved with the approximation of things using an equivalence relation on the universal set of his approximation space. In this paper, two kinds of approximation operators via ideals which represent extensions of Pawlak’s approximation operator have been presented. In both kinds, the definitions of upper and lower approximations based on ideals have been given. Moreover, a new type of approximation spaces via two ideals which is called bi-ideal approximation spaces was introduced for the first time. This type of approximations was analyzed by two different methods, their properties are investigated, and the relationship between these methods is proposed. The importance of these methods was its dependent on ideals which were topological tools, and the two ideals represent two opinions instead of one opinion. At the end of the paper, an applied example had been introduced in the chemistry field by applying the current methods to illustrate the definitions in a friendly way.
17 citations
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TL;DR: In this paper, the authors explore the theoretical aspects of multiset by extending the notions of compact, proximity relation and proximal neighborhood to the multiiset context and present an integral example of multi-set proximity relations.
10 citations
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TL;DR: The fuzzy soft C5-connected component may be not exists and if it exists, it may not be fuzzy soft closed set and some very interesting properties for fuzzy soft connected components in discrete fuzzy soft topological spaces are investigated.
10 citations
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7 citations
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01 Jan 20166 citations
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TL;DR: The natural properties of these types of soft sets are studied and the validity of the exact versions of some known results in ordinary topological spaces regarding ω -open sets in soft topological Spaces is studied.
Abstract: In this paper, we define soft ω -open sets and strongly soft ω -open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of some known results in ordinary topological spaces regarding ω -open sets in soft topological spaces. Also, we study the relationships between the ω -open sets of a given indexed family of topological spaces and the soft ω -open sets (resp. strongly soft ω -open sets) of their generated soft topological space. These relationships form a biconditional logical connective which is a symmetry. As an application of strongly soft ω -open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces.
40 citations
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TL;DR: This paper generalizes three types of rough set models based on j-neighborhood space, and investigates some of their basic properties, and gives a comparison between the Yao’s approach and the authors' approach.
Abstract: In this paper, we generalize three types of rough set models based on j-neighborhood space (i.e, type 1 j-neighborhood rough set, type 2 j-neighborhood rough set, and type 3 j-neighborhood rough set), and investigate some of their basic properties. Also, we present another three types of rough set models based on j-adhesion neighborhood space (i.e, type 4 j-adhesion neighborhood rough set, type 5 j-adhesion neighborhood rough set, and type 6 j-adhesion neighborhood rough set). The fundamental properties of approximation operators based on j-adhesion neighborhood space are established. The relationship between the properties of these types is explained. Finally, according to j-adhesion neighborhood space, we give a comparison between the Yao’s approach and our approach.
38 citations
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TL;DR: To demonstrate the utility and effectiveness of the proposed entropy measures, an entropy-based approach of determining objective weights of attributes is developed to solve multiple-attribute decision-making problems in the context of linguistic term sets.
33 citations
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TL;DR: The main contribution of the present article is to introduce a modification and a generalization for Feng's approximations, namely, soft β -rough approxIMations, and some of their properties will be studied.
Abstract: Soft rough set theory has been presented as a basic mathematical model for decision-making for many real-life data However, soft rough sets are based on a possible fusion of rough sets and soft sets which were proposed by Feng et al [20] The main contribution of the present article is to introduce a modification and a generalization for Feng's approximations, namely, soft β -rough approximations, and some of their properties will be studied A comparison between the suggested approximations and the previous one [20] will be discussed Some examples are prepared to display the validness of these proposals Finally, we put an actual example of the infections of coronavirus (COVID-19) based on soft β -rough sets This application aims to know the persons most likely to be infected with COVID-19 via soft β -rough approximations and soft β -rough topologies [ABSTRACT FROM AUTHOR] Copyright of Turkish Journal of Mathematics is the property of Scientific and Technical Research Council of Turkey and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )
27 citations
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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