In the first part of our paper, we construct a cyclic hypergroup of matrices using the Ends Lemma. Its properties are then, in the second part of the paper, used to describe the symmetry of lower and upper approximations in certain rough sets with re...
18 November 2022
The grade-added rough set (GRS) approach is an extension of the rough set theory proposed by Pawlak to deal with numerical data. However, the GRS has problems with overtraining, unclassified and unnatural results. In this study, we propose a new appr...
Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In...
Based on the geometry of a radial function, a sequence of approximations for arcsine, arccosine and arctangent are detailed. The approximations for arcsine and arccosine are sharp at the points zero and one. Convergence of the approximations is prove...
In this study, we investigate the upper- and lower-bound approximations of numerical eigenvalues derived by weak Galerkin spectral element methods on arbitrary convex quadrilateral meshes for the Laplace eigenvalue problem. Firstly, the Piola transfo...
In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of Jordan&rs...
In order to approximate an undefinable set of objects by using the extensions in OE-concept lattices, this study combines three-way concept analysis with covering-based rough set and introduces an innovative approach for managing uncertain informatio...
We consider the initial-boundary value problem of reaction-diffusion-advection that has a solution of a front form. The statement comes from the theory of wave physics. We study the question of the solution stabilizing to the stationary one. Proof of...
In this paper, we introduce the concepts of Alexandrov L-fuzzy pre-proximities on complete residuated lattices. Moreover, we investigate their relations among Alexandrov L-fuzzy pre-proximities, Alexandrov L-fuzzy topologies, L-fuzzy upper approximat...
Rough set theory is a methodology that defines the definite or probable membership of an element for exploring data with uncertainty and incompleteness. It classifies data sets using lower and upper approximations to model uncertainty and missing inf...
Many of the new fuzzy structures with complete
This paper proposes a theoretical framework for studying rough intuitionistic fuzzy filters within the structure of BE-algebras. Building on rough set theory and intuitionistic fuzzy set theory, we introduce rough intuitionistic fuzzy filters via low...
This paper focuses on constructing four novel multiquadric (MQ) quasi-interpolation operators. We conduct a comprehensive analysis of the essential properties of the proposed operators and further derive rigorous optimal upper and lower bounds for th...
An algorithm is presented for the construction of an asymptotic approximation of a stable stationary solution to a diffusion equation system in a two-dimensional domain with a smooth boundary and a source function that is discontinuous along some smo...
This paper investigates a class of nonlinear fractional differential equations with boundary value problems involving Caputo–Hadamard-type derivatives. By relaxing the monotonicity constraints on the nonlinear terms and considering more general...
In rough set theory, the multiplicity of methods of calculating neighborhood systems is very useful to calculate the measures of accuracy and roughness. In line with this research direction, in this article we present novel kinds of rough neighborhoo...
This paper presents the novel concept of rough intuitionistic fuzzy ideals within the realm of BCK-algebras and investigates their fundamental properties. Furthermore, we introduce a set-valued homomorphism over a BCK-algebra, laying the foundation f...
In this thesis, we consider the existence of extreme solutions to a class of coupled causal differential equations. By utilizing two comparison theorems and a monotone iterative technique, we have obtained sufficient conditions under which the equati...
Intuitionistic Fuzzy Sets (
The challenging issues of computer networks and databases are not only the intrusion detection but also the reduction of false positives and increase of detection rate. In any intrusion detection system, anomaly detection mainly focuses on modeling t...
An important mathematical way to deal with ambiguity and uncertainty in knowledge is rough set (RS) theory. It is believed that a grill is a necessary addition to this idea. Since it expands the approximate of RSs, it is a helpful technique for remov...
Given an ideal topological space
In this work, the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions, we focus on the fourth-order sin...
Variational inference provides a way to approximate probability densities through optimization. It does so by optimizing an upper or a lower bound of the likelihood of the observed data (the evidence). The classic variational inference approach sugge...
A multigranulation rough set (MGRS) model is an expansion of the Pawlak rough set, in which the uncertain concept is characterized by optimistic and pessimistic upper/lower approximate boundaries, respectively. However, there is a lack of approximate...
Schröder based series for the principal and negative one branches of the Lambert W function are defined; the series are generic and are in terms of an initial, arbitrary, approximating function. Upper and lower bounds for the initial approximati...
The generalized roughness in LA-semigroups is introduced, and several properties of lower and upper approximations are discussed. We provide examples to show that the lower approximation of a subset of an LA-semigroup may not be an LA-subsemigroup/id...
This study investigates extremal solutions for fractional-order delayed difference equations, utilizing the Caputo nabla operator to establish mild lower and upper approximations via discrete fractional calculus. A new approach is employed to demonst...
In this paper an algorithm for approximate solving of a boundary value problem for a nonlinear differential equation with a special type of fractional derivative is suggested. This derivative is called a generalized proportional Caputo fractional der...
For L a complete co-residuated lattice and R an L-fuzzy relation, an L-fuzzy upper approximation operator based on co-implication adjoint with L is constructed and discussed. It is proved that, when L is regular, the new approximation operator is the...
The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary re...
Mixture models are in high demand for machine-learning analysis due to their computational tractability, and because they serve as a good approximation for continuous densities. Predominantly, entropy applications have been developed in the context o...
A critical step for gene selection algorithms using rough set theory is the establishment of a gene evaluation function to assess the classification ability of candidate gene subsets. The concept of dependency in a classic neighborhood rough set mode...
The main aim of the paper is to present an algorithm to solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional fractional derivative on a finite interval. The main condition i...
10 January 2023
Although the older population has been rapidly growing, the availability of formal caregivers remains limited. Assistance provided by care robots has helped lower this burden; however, whether using a care robot while providing excretion care (EC) is...
The numerical approximation of the
Background/Objectives: The physiological ventilation–perfusion ratio (V/Q) in the upper pulmonary field is >3 and in the lower pulmonary field it is <1 due to the effect of gravity when the body is in an upright position. Pneumonectomy le...
Decision-making problems often involve simultaneous sources of uncertainty: interval-valued hesitation in expert judgments, positive–neutral–negative assessments, parameter-dependent evaluations, and boundary-region indiscernibility. To a...
Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning. This paper discusses the graded modal logic and puts forward the graded many-valued modal logic G(S5). Secondly, by emplo...
The paper contributes to stabilization problems of linear systems subject to time-varying delays. Drawing upon small gain criteria and robust analysis techniques, upper and lower bounds on the largest allowable time-varying delay are developed by usi...
Asymmetry in the upper and lower tails is an important feature in modeling bivariate distributions. This article focuses on the log ratio between the tail probabilities at upper and lower corners as a measure of tail asymmetry. Asymptotic behavior of...
Gastric MALToma is an extra-nodal marginal-type B-cell lymphoma. MALToma may occur secondary to chronic inflammation and autoimmunity. The most common gastrointestinal (GI) site of MALToma is the stomach, with approximately 50% of lesions occurring t...
This paper introduces an upper bound on the absolute difference between:
This study establishes a transient numerical model for the gas–solid two-phase flow of ultrafine dry powder fire extinguishing agents released in the confined space based on the Fluent software platform. The model investigates the spatial flow...
In this paper, we propose a new hybrid model, multi Q-hesitant fuzzy soft multi-granulation rough set model, by combining a multi Q-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi Q-hesita...
The relationship between Rough Set (RS) and algebraic systems has been long studied by mathematicians. RS is a growing research area that encourages studies into both real-world applications and the theory itself. In RS, a universe subset is characte...
Covering granular reduction is an important issue in multi-covering information systems. The main methods to solve this problem are set operators. How to solve this problem by quantitative analysis is an interesting topic. Furthermore, as a type of n...
As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximati...
After hydraulic fracturing of C shale formation, it is difficult to get stable production, and the flowback efficiency of fracturing fluid is low. In order to reveal the law of fracturing fluid invasion and flowback behavior and to investigate the mi...
In this paper, we introduce and investigate a hybrid type of nonlinear Riemann Liouville fractional integro-differential equations. We develop and extend previous work on such non-fractional equations, using operator theoretical techniques, and find...
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