On Three Types of Soft Rough Covering-Based Fuzzy Sets

Atef, Mohammed; Nada, S.I.; Gumaei, Abdu; Nawar, Ashraf S.

doi:10.1155/2021/6677298

Cited by 15 publications

(10 citation statements)

References 61 publications

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“…In soft sets parameterization by attributes provide them an advantage over the other contemporary theories which deal with uncertainty. The authors of Atef et al [2], Atef and Nada [3], Atef et al [4], A. Mukherjee and S. Debnath [37,38], successfully applied soft sets in the areas of decision-making problems and soft linear equations. Based on these work, we try to to use the concept of soft set theory to generalize the proposed study in future.…”

Section: Attribute Reductionmentioning

confidence: 99%

Fuzzy covering-based rough set on two different universes and its application

Bin

2022

Artif Intell Rev

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In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh's extension principle. We mainly address the following issues in this paper. First, we present the definition of fuzzy β-neighborhood, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe and study its properties. Then we define a new type of fuzzy covering-based rough set model on two different universes and investigate the properties of this model. Meanwhile, we give a necessary and sufficient condition under which two fuzzy β-coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Moreover, matrix representations of the fuzzy covering lower and fuzzy covering upper approximation operators are investigated. Finally, we propose a new approach to a kind of multiple criteria decision making problem based on fuzzy coveringbased rough set model over two universes. The proposed models not only enrich the theory of fuzzy covering-based rough set but also provide a new perspective for multiple criteria decision making with uncertainty.

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Section: Attribute Reductionmentioning

confidence: 99%

Fuzzy covering-based rough set on two different universes and its application

Bin

2022

Artif Intell Rev

View full text Add to dashboard Cite

show abstract

Section: Attribute Reductionmentioning

confidence: 99%

Fuzzy covering-based rough set on two different universes and its application

Bin

2021

Preprint

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In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh’s extension principle. We mainly address the following issues in this paper. First, we present the definition of fuzzy β-neighborhood, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe and study its properties. Then we define a new type of fuzzy covering-based rough set model on two different universes and investigate the properties of this model. Meanwhile, we give a necessary and sufficient condition under which two fuzzy β-coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Moreover, matrix representations of thefuzzy covering lower and fuzzy covering upper approximation operators are investigated. Finally, we propose a new approach to a kind of multiple criteria decision making problem based on fuzzy covering-based rough set model over two universes. The proposed models not onlyenrich the theory of fuzzy covering-based rough set but also provide a new perspective for multiple criteria decision making with uncertainty.

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“…Deng et al [29] proposed new model of fuzzy covering according to FRS. Atef et al and Li et al studied additional kinds of fuzzy rough covering (FRC) [30][31][32][33][34]. Also, Ma [35] discovered kinds of fuzzy covering rough set (FCRS) using the fuzzy β-neighborhood.…”

Section: Introductionmentioning

confidence: 99%

Cq-ROFRS: covering q-rung orthopair fuzzy rough sets and its application to multi-attribute decision-making process

Garg

Atef

2022

Complex Intell. Syst.

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Pythagorean fuzzy sets (briefly, PFSs) were created as an upgrade to intuitionistic fuzzy sets (briefly, IFSs) which helped to address some problems that IFSs couldn’t solve. The definition of q-rung orthopair fuzzy sets (briefly, q-ROFS) is then declared to generalize and solve PFS and IFS failures. Using the concept of PF $$\beta $$ β -neighborhood, Zhan et al. defined the description of the covering through the Pythagorean fuzzy rough set (briefly, CPFRS). Hussain et al. also developed the concept of q-ROF $$\beta $$ β -neighborhood to build the concept of covering through q-rung orthopair fuzzy rough sets (Cq-ROFRS). To enhance the results in Zhan et al.’s and Hussain et al.’s method and in a related context, the concept of PF complementary $$\beta $$ β -neighborhood is constructed. Hence, using PF $$\beta $$ β -neighborhood and PF complementary $$\beta $$ β -neighborhood, three novel kinds of CPFRS are investigated and the related characteristics are analyzed. The interrelationships between Zhan et al.’s approach and our approaches are also discussed. Besides, the concept of q-ROF complementary $$\beta $$ β -neighborhood is examined. Three new Cq-ROFRS models are differentiated using the principles of q-ROF $$\beta $$ β -neighborhood and q-ROF complementary $$\beta $$ β -neighborhood. As a result, the related properties and relationships between these various models and Hussain et al.’s model are established. Because of these correlations, we may consider our approach to be a generalization of Zhan et al.’s and Hussain et al’s approaches. Finally, we developed applications to solve MADM problems using CPFRS and Cq-ROFRS, as well as variances of the two methods using numerical examples are presented.

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On Three Types of Soft Rough Covering-Based Fuzzy Sets

Cited by 15 publications

References 61 publications

Fuzzy covering-based rough set on two different universes and its application

Fuzzy covering-based rough set on two different universes and its application

Fuzzy covering-based rough set on two different universes and its application

Cq-ROFRS: covering q-rung orthopair fuzzy rough sets and its application to multi-attribute decision-making process

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