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Fuzzy rough sets in Sostak sense

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Applied mathematics(A Journal of Chinese Universities) 2022年第4期37卷 563-582页

作者： Ismail Ibedou S.E.Abbas Department of mathematics Faculty of ScienceBenha UniversityBenhaEgypt Department of mathematics Faculty of ScienceSohag UniversitySohagEgypt

In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.

关键词： fuzzy rough set fuzzy approximation space fuzzy ideal approximation space r-fuzzy separation axioms r-fuzzy connectedness r-fuzzy compactness

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Cube attacks on round-reduced MORUS and GimLi

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Science China(Information Sciences) 2022年第1期65卷 265-267页

作者： Siwei CHEN Zejun XIANG Xiangyong ZENG Shasha ZHANG Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied MathematicsHubei University

Dear editor,Cube attack is a chosen plaintext/initial value(IV) keyrecovery attack, which was proposed by Dinur and Shamir at EUROCRYPT 2009 [1]. As an important cryptanalysis technique, it is widely used in symmetric ciphers. The main ideal of cube attack is to look for cubes to acquire several linear polynomials(superpolys) with respect to secret variables. The secret variables can be recovered by solving these linear equations. However, thus far, no general method has been established to search for cubes.

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On the bit-based division property of S-boxes

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Science China(Information Sciences) 2022年第4期65卷 261-263页

作者： Zejun XIANG Xiangyong ZENG Shasha ZHANG Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied MathematicsHubei University

Dear editor,The S-box, which is one of the most popular cipher components, has been extensively applied in modern symmetrickey primitives. Moreover, it is often the case that S-boxes are the only nonlinear components ... 详细信息

关键词： division property Sbox ANF divisional optimal divisional suboptimal

Approximations by Ideal Minimal Structure with Chemical Application

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Intelligent Automation & Soft Computing 2023年第6期36卷 3073-3085页

作者： Rodyna A.Hosny Radwan Abu-Gdairi Mostafa K.El-Bably Department of mathematics Faculty of ScienceZagazig UniversityZagazig44519Egypt Department of mathematics Faculty of ScienceZarqa UniversityZarqa13132Jordan Department of mathematics Faculty of ScienceTanta UniversityTanta31527Egypt

The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset.This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J.The novel approach(indicated by JMSAS)modifies the approximation space to diminish the bound-ary region and enhance the measure of accuracy.The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques.Via illustrated examples,several remarkable results using these notions are obtained and some of their properties are established.Several sorts of near open(resp.closed)sets based on JMSAS are studied.Furthermore,the connections between these assorted kinds of near-open sets in JMSAS are deduced.The advantages and disadvan-tages of the proposed approach compared to previous ones are examined.An algorithm using MATLAB and a framework for decision-making problems are verified.Finally,the chemical application for the classification of amino acids(AAs)is treated to highlight the significance of applying the suggested approximation.

关键词： Ideal minimal structure spaces rough set theory approximation spaces

On the partial stability of nonlinear impulsive Caputo fractional systems

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Applied mathematics(A Journal of Chinese Universities) 2023年第2期38卷 166-179页

作者： Boulbaba Ghanmi Saifeddine Ghnimi Department of mathematics Faculty of SciencesUniversity of GafsaTunisia

In this work,stability with respect to part of the variables of nonlinear impulsive Caputo fractional differential equations is investigated.Some effective sufficient conditions of stability,uniform stability,asymptotic uniform stability and Mittag Leffler stability.The approach presented is based on the specially introduced piecewise continuous Lyapunov functions.Furthermore,some numerical examples are given to show the effectiveness of our obtained theoretical results.

关键词： impulsive fractional differential equations Mittag-Leffler function partial stability Caputo derivative

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On Multi-Granulation Rough Sets with Its Applications

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Computers, Materials & Continua 2024年第4期79卷 1025-1038页

作者： Radwan Abu-Gdairi R.Mareay M.Badr Department of mathematics Faculty of ScienceZarqa UniversityZarqa13132Jordan Department of mathematics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh33516Egypt Department of mathematics Faculty of ScienceNew Valley UniversityEl Kharga72713Egypt

Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.

关键词： Multi-granulation rough sets data classifications information systems interior operators closure operators approximation structures

Morrey smoothness spaces:A new approach

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Science China mathematics 2023年第6期66卷 1301-1358页

作者： Dorothee D.Haroske Hans Triebel Institute of mathematics Faculty of Mathematics and Computer ScienceFriedrich Schiller University JenaJena 07743Germany

In the recent years,the so-called Morrey smoothness spaces attracted a lot of interest.They can(also)be understood as generalisations of the classical spaces A_(p,q)^(s)(R^(n))with A∈{B,F}in R^(n),where the parameter... 详细信息

关键词： Morrey space smoothness space of Morrey type Besov-Morrey space Triebel-Lizorkin-Morrey space Besov-type space Triebel-Lizorkin-type space

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Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

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Computer Modeling in Engineering & Sciences 2024年第8期140卷 1619-1645页

作者： Nasser Sweilam Seham Al-Mekhlafi Aya Ahmed Ahoud Alsheri Emad Abo-Eldahab mathematics Department Faculty of ScienceCairo UniversityGiza12613Egypt mathematics Department Faculty of EducationSana’a UniversitySana’a1247Yemen mathematics Department Faculty of ScienceHelwan UniversityCairo11795Egypt Department of mathematics College of ScienceUniversity of BishaAl Namas67398-5644Saudi Arabia

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

关键词： Cancer diseases hybrid variable-order fractional derivatives adams bashfourth fifth step generalized fifth order Runge-Kutta method

Complete Monotonicity of Functions Related to Trigamma and Tetragamma Functions

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Computer Modeling in Engineering & Sciences 2022年第4期131卷 263-275页

作者： Mona Anis Hanan Almuashi Mansour Mahmoud faculty of Science Mathematics DepartmentMansoura UniversityMansoura35516Egypt faculty of Science Mathematics DepartmentJeddah UniversityJeddah21589Saudi Arabia faculty of Science Mathematics DepartmentKing Abdulaziz UniversityJeddah21589Saudi Arabia

In this paper,we study the completely monotonic property of two functions involving the functionΔ(x)=[ψ′(x)]2+ψ″(x)and deduce the double inequality x^(2)+3x+3/3x^(4)(2x+1)^(2)0which improve some recent results,whereψ(x)is the logarithmic derivative of the Gamma function.Also,we deduce the completely monotonic degree of a function involvingψ′(x).

关键词： Trigamma function tetragamma function completely monotonic function completely monotonic degree inequality