On Fuzzy Rough Sets and Their Topological Structures

Tang, Weidong; Wu, Jinzhao; Zheng, Dingwei

doi:10.1155/2014/546372

Cited by 16 publications

(4 citation statements)

References 35 publications

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“…It is possible by means of visual information describing different gradations of gray or brightness. Such information allows representing GETS structure in the form of the fuzzy rough soft set [19]. The fuzzy rough soft set of cells, which subdivides the set of cells into phases at each time moment t is represented as the set of three elements consisting of upper and lower approximation of the rough set ( Fig.4), as well as the boundary area of the rough set in the form of the fuzzy set:…”

Section: Representing the Gets Structure Using Fuzzy Rough Soft Setsmentioning

confidence: 99%

A model of destructive processes based on interval fuzzy rough soft sets

Zharikova

Sherstjuk

Wójcik

et al. 2019

ELECTROTECHNICAL REVIEW

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This work presents a spatial model of destructive processes for the real-time GIS-based decision support systems. A dynamic fuzzy rough soft topology represents a structure of a geoecotechnogenic system that contains a multitude of interacting processes, which evolve in space and time. In disaster conditions, some of the interacting processes can be destructive. Their dynamics are modeled using the spread model. The area of interest is represented as an approximation by a grid of cubic cells. This allows taking into account the peculiarities of the initial information obtained from drones using remote sensing techniques and having a significant uncertainty. The proposed model reduces the computational complexity and provides the acceptable performance of real-time DSS. Streszczenie. W niniejszej pracy przedstawiono przestrzenny model destrukcyjnych procesów dla systemów wspomagania decyzji opartych na GIS w czasie rzeczywistym. Dynamicznie rozmyta topologia przybliżona reprezentuje strukturę geo-eko-techno-gennego systemu, który zawiera wiele interakcji procesów, które ewoluują w przestrzeni i czasie. W warunkach katastrofy niektóre z oddziałujących procesów mogą być destrukcyjne. Ich dynamika jest modelowana przy użyciu modelu spreadu. Obszar zainteresowania jest reprezentowany jako przybliżenie przez siatkę komórek sześciennych. Pozwala to na uwzględnienie specyfiki początkowej informacji uzyskanej z dronów za pomocą technik teledetekcji i posiadającej znaczną niepewność. Proponowany model zmniejsza złożoność obliczeniową i zapewnia akceptowalną wydajność DSS w czasie rzeczywistym. (Model procesów destrukcyjnych opartych na interwałowych rozmytych zbiorach przybliżonych).

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Section: Representing the Gets Structure Using Fuzzy Rough Soft Setsmentioning

confidence: 99%

A model of destructive processes based on interval fuzzy rough soft sets

Zharikova

Sherstjuk

Wójcik

et al. 2019

ELECTROTECHNICAL REVIEW

View full text Add to dashboard Cite

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“…As is known that fuzzy topology represents a robust mathematical instrument for processing uncertainty in real-world applications; especially, those related to the selection of the best alternative(s). This provides different applications of fuzzy topology in practical issues and prompts the fast development of the fuzzy topology in a short measure of time, see, [10,11].…”

Section: Introductionmentioning

confidence: 99%

Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology

Saleh,

Al-shami,

Azzam

et al. 2023

Mathematics

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It is common knowledge that fuzzy topology contributes to developing techniques to address real-life applications in various areas like information systems and optimal choices. The building blocks of fuzzy topology are fuzzy open sets, but other extended families of fuzzy open sets, like fuzzy pre-open sets, can contribute to the growth of fuzzy topology. In the present work, we create some classifications of fuzzy topologies which enable us to obtain several desirable features and relationships. At first, we introduce and analyze stronger forms of fuzzy pre-separation and regularity properties in fuzzy topology called fuzzy pre-Ti,i=0,12,1,2,3,4, fuzzy pre-symmetric, and fuzzy pre-Ri,i=0,1,2,3 by utilizing the concepts of fuzzy pre-open sets and quasi-coincident relation. We investigate more novel properties of these classes and uncover their unique characteristics. By presenting a wide array of related theorems and interconnections, we structure a comprehensive framework for understanding these classes and interrelationships with other separation axioms in this setting. Moreover, the relations between these classes and those in some induced topological structures are examined. Additionally, we explore the hereditary and harmonic properties of these classes.

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“…Recently, some studies were investigated on the relationship between topology structure and rough set [4-7, 21, 48], fuzzy topology structure with fuzzy rough set [16,17], and IFT structure with IFS rough set [18,19]. These studies show that it is possible to build topology from RST and vice versa.…”

Section: Introductionmentioning

confidence: 99%

A New Approach for Attribute Reduction from Decision Table based on Intuitionistic Fuzzy Topology

Dai¹,

Giang

Thi

et al. 2022

Preprint

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Most of the current attribute reduction methods use the measure to define the reduct, such as positive region of rough set theory (RST), granular information entropy, and granular distance measures. However, the reducts defined based on the measures are still limited in sizes because of the information conservation property of the reduct compared to the original dataset. Dealing with this matter, this paper proposes a new approach using the intuitionistic fuzzy topology (IFT) to develop an attribute reduction method to find the reduct with the optimal size through topology. Specifically, the IFT base and IFT sub-base structures are proposed based on the pre-order relation. Secondly, we propose a new measure to evaluate the significance of the attribute based on the IFT sub-base. Lastly, we propose a new definition of the reduct based on the IFT base and design two new algorithms based on Heuristic approaches. The theoretical and experimental results show that the proposed method is efficient in size and accuracy of the reduct

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On Fuzzy Rough Sets and Their Topological Structures

Cited by 16 publications

References 35 publications

A model of destructive processes based on interval fuzzy rough soft sets

A model of destructive processes based on interval fuzzy rough soft sets

Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology

A New Approach for Attribute Reduction from Decision Table based on Intuitionistic Fuzzy Topology

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