Fuzzy topological structures via fuzzy graphs and their applications

Atef, Mohammed; Atik, Abd El Fattah El; Nawar, Ashraf S.

doi:10.1007/s00500-021-05594-8

Cited by 22 publications

(12 citation statements)

References 41 publications

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“…There are close connections between the MOGS and the orthogonal arrays [12]. New types of topological structures can be constructed based on the new graphs constructed in this paper, see [1,5].…”

Section: Introductionmentioning

confidence: 84%

Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares

El-Mesady

Shaaban

2021

AKCE International Journal of Graphs and Combinatorics

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The subject of mutually orthogonal Latin squares (MOLSs) has fascinated researchers for many years. Although there is a number of intriguing results in this area, many open problems remain to which the answers seem as elusive as ever. Mutually orthogonal graph squares (MOGSs) are considered a generalization to MOLS. MOLS are considered an area of combinatorial design theory which has many applications in optical communications, cryptography, storage system design, wireless communications, communication protocols, and algorithm design and analysis, to mention just a few areas. In this paper, we introduce a technique for constructing the mutually orthogonal disjoint union of graphs squares and the generalization of the Kronecker product of MOGS as a generalization to the MacNeish's Kronecker product of MOLS. These are useful for constructing many new results concerned with the MOGS.

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Section: Introductionmentioning

confidence: 84%

Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares

El-Mesady

Shaaban

2021

AKCE International Journal of Graphs and Combinatorics

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“…As shown in Figure . 1, Yang and Hu put forward some types of fuzzy coverings-based rough set model based on the concepts of fuzzy β-neighborhood in [67,69]. Based on these work, some research focus on fuzzy neighborhood operators are addressed, such as [5,6,34]. Furthermore, a fuzzy covering-based rough set model was proposed in [66] by using fuzzy β-minimal description.…”

Section: The Motivation Of Our Researchmentioning

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: The Motivation Of Our Researchmentioning

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.

show abstract

Fuzzy topological structures via fuzzy graphs and their applications

Cited by 22 publications

References 41 publications

Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares

Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares

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

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

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