Attribute reduction is an important topic in the research of rough set theory, and it has been widely used in many aspects. Reduction based on an identifiable matrix is a common method, but a lot of space is occupied by repetitive and redundant ident...
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...
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...
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 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...
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...
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
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 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...
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...
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...
Due to their importance for studies oi wireless networks, recent years have seen a surge of activity on the design of local algorithms for the solution of a variety of network tasks. We study the behaviour of algorithms with very low localities. Desp...
This study evaluates whether fractional-order shaping provides a meaningful performance advantage for robust current control of a frequency-controlled parallel-resonant inverter when compared under identical conditions with strongly tuned integer-ord...
For the application of unmanned aerial vehicle (UAV)-based passive target localization, the positions of the UAVs play an important role because different UAV configurations provide distinct TDOA measurement geometries. In addition, the uncertainty o...
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 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...
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...
We present a novel information-theoretic framework, termed as TURBO, designed to systematically analyse and generalise auto-encoding methods. We start by examining the principles of information bottleneck and bottleneck-based networks in the auto-enc...
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...
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
After the 2007 financial crisis, many central banks adopted policies to lower their interest rates; the dynamics of these rates cannot be captured using classical models. Recently, Meucci and Loregian proposed an approach to estimate nonnegative inte...
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 numerical approximation of the
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 takes the commercial JG4246A cast Ni3Al-based superalloy as the research object, under the conditions of preheating the mold shell at 1020 °C and a pouring temperature of 1520 °C, characteristic simulation castings were poured. The...
The relationship between the inverse Langevin function and the proposed r0-r1-Lambert W function is defined. The derived relationship leads to new approximations for the inverse Langevin function with lower relative error bounds than comparable publi...
Fuzzy rough set theory has been successfully applied to many attribute reduction methods, in which the lower approximation set plays a pivotal role. However, the definition of lower approximation used has ignored the information conveyed by the upper...
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...
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 article, a new mixed finite element (MFE) algorithm is presented and developed to find the numerical solution of a two-dimensional nonlinear fourth-order Riemann–Liouville fractional diffusion-wave equation. By introducing two auxiliary...
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...
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...
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...
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...
We develop an approximation method for the differential entropy
In the pursuit of energy efficiency in next-generation communication systems, approximate computing is emerging as a promising technique. In the proposed work, efforts are made to address the challenge of bridging the gap between the level of approxi...
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...
Approximate transport maps can facilitate exploration of a Bayesian target distribution, but the resulting samples generally do not follow that distribution. To address this problem, we develop residual-slice correction, a sampling framework that com...
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...
The expected utility principle is often used to compute the insurance premium through a second-order approximation of the expected value of the utility of losses. We investigate the impact of using a more accurate approximation based on the fourth-or...
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...
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