Journal Description
Axioms
Axioms
is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published monthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT), International Fuzzy Systems Association (IFSA) and Union of Slovak Mathematicians and Physicists (JSMF) are affiliated with Axioms and their members receive discounts on the article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High visibility: indexed within SCIE (Web of Science), dblp, and other databases.
- Journal Rank: JCR - Q2 (Mathematics, Applied)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 21.8 days after submission; acceptance to publication is undertaken in 2.8 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Companion journal: Logics.
Impact Factor:
2.0 (2022);
5-Year Impact Factor:
1.9 (2022)
Latest Articles
Terracini Loci, Linear Projections, and the Maximal Defect
Axioms 2024, 13(4), 271; https://doi.org/10.3390/axioms13040271 - 18 Apr 2024
Abstract
We continue the study of Terracini loci formed by x points of a variety embedded in a projective space. Our main results are a refined study of Terracini loci arising from linear projections, the description of the maximal x with a non-empty Terracini
[...] Read more.
We continue the study of Terracini loci formed by x points of a variety embedded in a projective space. Our main results are a refined study of Terracini loci arising from linear projections, the description of the maximal x with a non-empty Terracini locus for Hirzebruch surfaces, and the maximal “weight”, “corank”, or “defect” in several cases. For low x, we even show which defects can occur.
Full article
(This article belongs to the Special Issue Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima)
Open AccessArticle
A Novel View of Closed Graph Function in Nano Topological Space
by
Kiruthika Kittusamy, Nagaveni Narayanan, Sheeba Devaraj and Sathya Priya Sankar
Axioms 2024, 13(4), 270; https://doi.org/10.3390/axioms13040270 - 18 Apr 2024
Abstract
►▼
Show Figures
The objective of this research is to describe and investigate a novel class of separation axioms and discuss some of their fundamental characteristics using a nano weakly generalized closed set. In nano topological space, -closed graph and strongly
[...] Read more.
The objective of this research is to describe and investigate a novel class of separation axioms and discuss some of their fundamental characteristics using a nano weakly generalized closed set. In nano topological space, -closed graph and strongly -closed graph functions are introduced and explored. We also analyse some of the characterizations of closed graph functions with the separation axioms via a nano weakly generalized closed set.
Full article
Figure 1
Open AccessArticle
The Vertex Gutman Index and Gutman Index of the Union of Two Cycles
by
Yinzhen Mei and Hongli Miao
Axioms 2024, 13(4), 269; https://doi.org/10.3390/axioms13040269 - 18 Apr 2024
Abstract
The Wiener index is one of the most classic and widely used indicators in topology. It reflects the average distance of any node pair in the graph. It not only makes the boundaries of given graphs clearer but also continuously generates topological indices
[...] Read more.
The Wiener index is one of the most classic and widely used indicators in topology. It reflects the average distance of any node pair in the graph. It not only makes the boundaries of given graphs clearer but also continuously generates topological indices that are more suitable for new fields, such as the Gutman index. The Wiener index and Gutman index are two important topological indices, which are commonly used to describe the characteristics of molecular structure. They are closely related to the physical and chemical properties of molecular compounds. And they are widely used to predict the physical and chemical properties and biological activity of molecular compounds. In this paper, we study the vertex Gutman index and Gutman index and describe the structural characteristics of all cases of two simple cycles intersecting. We comprehensively analyze the Gutman index and vertex Gutman index in these cases in detail by means of classification discussion and analogical reasoning and characterize their maximum and minimum accordingly.
Full article
(This article belongs to the Special Issue Advances in Convex Geometry and Analysis)
Open AccessArticle
Bergman Space Properties of Fractional Derivatives of the Cauchy Transform of a Certain Self-Similar Measure
by
Songran Wang and Zhimin Wang
Axioms 2024, 13(4), 268; https://doi.org/10.3390/axioms13040268 - 18 Apr 2024
Abstract
►▼
Show Figures
Let be a self-similar measure with compact support K. The Hausdorff dimension of K is . The Cauchy transform of is denoted by . For we define the function
[...] Read more.
Let be a self-similar measure with compact support K. The Hausdorff dimension of K is . The Cauchy transform of is denoted by . For we define the function which compares with the fractional derivative of F of order Let . In this paper, we prove that belongs to for , and belongs to for , where is the Bergman space. At the same time, we give a value distribution property of F, which is similar to the big Picard theorem.
Full article
Figure 1
Open AccessArticle
Some Applications of Fuzzy Sets in Residuated Lattices
by
Cristina Flaut, Dana Piciu and Bianca Liana Bercea
Axioms 2024, 13(4), 267; https://doi.org/10.3390/axioms13040267 - 18 Apr 2024
Abstract
Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices
[...] Read more.
Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices are presented. Since ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic, first, we investigate the lattice of fuzzy ideals in residuated lattices and study some connections between fuzzy sets associated to ideals and Hadamard codes. Finally, we present applications of fuzzy sets in coding theory.
Full article
(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics)
Open AccessEditorial
Advance in Topology and Functional Analysis in Honour of María Jesús Chasco’s 65th Birthday
by
Xabier Domínguez, Elena Martín-Peinador, T. Christine Stevens and Mikhail Tkachenko
Axioms 2024, 13(4), 266; https://doi.org/10.3390/axioms13040266 - 18 Apr 2024
Abstract
We are honoured to present this Special Issue of Axioms with the title “Topology and Functional Analysis” to showcase recent work on this and related topics and to provide an opportunity for María Jesús Chasco’s friends and colleagues to pay tribute to her
[...] Read more.
We are honoured to present this Special Issue of Axioms with the title “Topology and Functional Analysis” to showcase recent work on this and related topics and to provide an opportunity for María Jesús Chasco’s friends and colleagues to pay tribute to her mathematical career on the occasion of her 65th birthday [...]
Full article
(This article belongs to the Special Issue Advance in Topology and Functional Analysis——In Honour of María Jesús Chasco's 65th Birthday)
Open AccessArticle
An Extended Thermodynamics Study for Second-Grade Adiabatic Fluids
by
Elvira Barbera and Claudia Fazio
Axioms 2024, 13(4), 265; https://doi.org/10.3390/axioms13040265 - 17 Apr 2024
Abstract
A 10-field theory for second-grade viscoelastic fluids is developed in the framework of Rational Extended Thermodynamics. The field variables are the density, the velocity, the temperature and the stress tensor. The particular case of an adiabatic fluid is considered. The field equations are
[...] Read more.
A 10-field theory for second-grade viscoelastic fluids is developed in the framework of Rational Extended Thermodynamics. The field variables are the density, the velocity, the temperature and the stress tensor. The particular case of an adiabatic fluid is considered. The field equations are determined by use of physical universal principles such as the Galileian and the Entropy Principles. As already proved, Rational Extended Thermodynamics is able to eliminate some inconsistencies with experiments that arise in Classical Thermodynamics. Moreover, the paper shows that, if the quadratic terms are taken into account, the classical constitutive relations for a second-grade fluid can be obtained as a limit case of the field equations of the present theory.
Full article
(This article belongs to the Section Mathematical Physics)
Open AccessArticle
A Singular Tempered Sub-Diffusion Fractional Equation with Changing-Sign Perturbation
by
Xinguang Zhang, Jingsong Chen, Lishuang Li and Yonghong Wu
Axioms 2024, 13(4), 264; https://doi.org/10.3390/axioms13040264 - 16 Apr 2024
Abstract
In this paper, we establish some new results on the existence of positive solutions for a singular tempered sub-diffusion fractional equation involving a changing-sign perturbation and a lower-order sub-diffusion term of the unknown function. By employing multiple transformations, we transform the changing-sign singular
[...] Read more.
In this paper, we establish some new results on the existence of positive solutions for a singular tempered sub-diffusion fractional equation involving a changing-sign perturbation and a lower-order sub-diffusion term of the unknown function. By employing multiple transformations, we transform the changing-sign singular perturbation problem to a positive problem, then establish some sufficient conditions for the existence of positive solutions of the problem. The asymptotic properties of solutions are also derived. In deriving the results, we only require that the singular perturbation term satisfies the Carathéodory condition, which means that the disturbance influence is significant and may even achieve negative infinity near some time singular points.
Full article
(This article belongs to the Section Mathematical Analysis)
Open AccessArticle
Strict Vector Equilibrium Problems of Multi-Product Supply–Demand Networks with Capacity Constraints and Uncertain Demands
by
Ru Li and Guolin Yu
Axioms 2024, 13(4), 263; https://doi.org/10.3390/axioms13040263 - 16 Apr 2024
Abstract
This paper considers a multi-product, multi-criteria supply–demand network equilibrium model with capacity constraints and uncertain demands. Strict network equilibrium principles are proposed both in the case of a single criterion and multi-criteria, respectively. Based on a single criterion, it proves that strict network
[...] Read more.
This paper considers a multi-product, multi-criteria supply–demand network equilibrium model with capacity constraints and uncertain demands. Strict network equilibrium principles are proposed both in the case of a single criterion and multi-criteria, respectively. Based on a single criterion, it proves that strict network equilibrium flows are equivalent to vector variational inequalities, and the existence of strict network equilibrium flows is derived by virtue of the Fan–Browder fixed point theorem. Based on multi-criteria, the scalarization of strict network equilibrium flows is given by using Gerstewitz’s function without any convexity assumptions. Meanwhile, the necessary and sufficient conditions of strict network equilibrium flows are derived in terms of vector variational inequalities. Finally, an example is given to illustrate the application of the derived theoretical results.
Full article
(This article belongs to the Special Issue Numerical Analysis and Optimization)
►▼
Show Figures
Figure 1
Open AccessFeature PaperArticle
Jordan-Type Inequalities and Stratification
by
Miloš Mićović and Branko Malešević
Axioms 2024, 13(4), 262; https://doi.org/10.3390/axioms13040262 - 14 Apr 2024
Abstract
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’s inequality is enabled by considering the corresponding
[...] Read more.
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’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions. Based on this approach, some optimal approximations of the sinc function are derived by determining the corresponding minimax approximants.
Full article
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications II)
►▼
Show Figures
Figure 1
Open AccessArticle
Existence of Solutions: Investigating Fredholm Integral Equations via a Fixed-Point Theorem
by
Faruk Özger, Merve Temizer Ersoy and Zeynep Ödemiş Özger
Axioms 2024, 13(4), 261; https://doi.org/10.3390/axioms13040261 - 14 Apr 2024
Abstract
Integral equations, which are defined as “the equation containing an unknown function under the integral sign”, have many applications of real-world problems. The second type of Fredholm integral equations is generally used in radiation transfer theory, kinetic theory of gases, and neutron transfer
[...] Read more.
Integral equations, which are defined as “the equation containing an unknown function under the integral sign”, have many applications of real-world problems. The second type of Fredholm integral equations is generally used in radiation transfer theory, kinetic theory of gases, and neutron transfer theory. A special case of these equations, known as the quadratic Chandrasekhar integral equation, given by can be very often encountered in many applications, where x is the function to be determined, is a parameter, and . In this paper, using a fixed-point theorem, the existence conditions for the solution of Fredholm integral equations of the form are investigated in the space where is the unknown function to be determined, V is a given operator, and are two given functions. Moreover, certain important applications demonstrating the applicability of the existence theorem presented in this paper are provided.
Full article
(This article belongs to the Special Issue New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization)
Open AccessArticle
Randomness Test of Thinning Parameters for the NBRCINAR(1) Process
by
Shuanghong Zhang
Axioms 2024, 13(4), 260; https://doi.org/10.3390/axioms13040260 - 14 Apr 2024
Abstract
Non-negative integer-valued time series are usually encountered in practice, and a variety of integer-valued autoregressive processes based on various thinning operators are commonly used to model these count data with temporal dependence. In this paper, we consider a first-order integer-valued autoregressive process constructed
[...] Read more.
Non-negative integer-valued time series are usually encountered in practice, and a variety of integer-valued autoregressive processes based on various thinning operators are commonly used to model these count data with temporal dependence. In this paper, we consider a first-order integer-valued autoregressive process constructed by the negative binomial thinning operator with random coefficients, to address the problem of constant thinning parameters which might not always accurately represent real-world settings because of numerous external and internal causes. We estimate the model parameters of interest by the two-step conditional least squares method, obtain the asymptotic behaviors of the estimators, and furthermore devise a technique to test the constancy of the thinning parameters, which is essential for determining whether or not the proposed model should consider the parameters’ randomness. The effectiveness and dependability of the suggested approach are illustrated by a series of thorough simulation studies. Finally, two real-world data analysis examples reveal that the suggested approach is very useful and flexible for applications.
Full article
(This article belongs to the Special Issue Time Series Analysis: Research on Data Modeling Methods)
►▼
Show Figures
Figure 1
Open AccessArticle
Distributed Charging Strategy of PEVs in SCS with Feeder Constraints Based on Generalized Nash Equilibria
by
Jialong Tang, Huaqing Li, Menggang Chen, Yawei Shi, Lifeng Zheng and Huiwei Wang
Axioms 2024, 13(4), 259; https://doi.org/10.3390/axioms13040259 - 14 Apr 2024
Abstract
►▼
Show Figures
In this article, a distributed charging strategy problem for plug-in electric vehicles (PEVs) with feeder constraints based on generalized Nash equilibria (GNE) in a novel smart charging station (SCS) is investigated. The purpose is to coordinate the charging strategies of all PEVs in
[...] Read more.
In this article, a distributed charging strategy problem for plug-in electric vehicles (PEVs) with feeder constraints based on generalized Nash equilibria (GNE) in a novel smart charging station (SCS) is investigated. The purpose is to coordinate the charging strategies of all PEVs in SCS to minimize the energy cost of SCS. Therefore, we build a non-cooperative game framework and propose a new price-driven charging control game by considering the overload constraint of the assigned feeder, where each PEV minimizes the fees it pays to satisfy its optimal charging strategy. On this basis, the existence of GNE is given. Furthermore, we employ a distributed algorithm based on forward–backward operator splitting methods to find the GNE. The effectiveness of the employed algorithm is verified by the final simulation results.
Full article
Figure 1
Open AccessArticle
The Application of the Bidiagonal Factorization of Totally Positive Matrices in Numerical Linear Algebra
by
José-Javier Martínez
Axioms 2024, 13(4), 258; https://doi.org/10.3390/axioms13040258 - 14 Apr 2024
Abstract
The approach to solving linear systems with structured matrices by means of the bidiagonal factorization of the inverse of the coefficient matrix is first considered in this review article, the starting point being the classical Björck–Pereyra algorithms for Vandermonde systems, published in 1970
[...] Read more.
The approach to solving linear systems with structured matrices by means of the bidiagonal factorization of the inverse of the coefficient matrix is first considered in this review article, the starting point being the classical Björck–Pereyra algorithms for Vandermonde systems, published in 1970 and carefully analyzed by Higham in 1987. The work of Higham briefly considered the role of total positivity in obtaining accurate results, which led to the generalization of this approach to totally positive Cauchy, Cauchy–Vandermonde and generalized Vandermonde matrices. Then, the solution of other linear algebra problems (eigenvalue and singular value computation, least squares problems) is addressed, a fundamental tool being the bidiagonal decomposition of the corresponding matrices. This bidiagonal decomposition is related to the theory of Neville elimination, although for achieving high relative accuracy the algorithm of Neville elimination is not used. Numerical experiments showing the good behavior of these algorithms when compared with algorithms that ignore the matrix structure are also included.
Full article
(This article belongs to the Special Issue Advances in Linear Algebra with Applications)
Open AccessArticle
Research on the Optimization of Pricing and the Replenishment Decision-Making Problem Based on LightGBM and Dynamic Programming
by
Wenyue Tao, Chaoran Wu, Ting Wu and Fuyuan Chen
Axioms 2024, 13(4), 257; https://doi.org/10.3390/axioms13040257 - 13 Apr 2024
Abstract
Vegetables have a short period of freshness, and therefore, the purchase of vegetables has to be carefully matched with sales, especially in the “small production and big market” setting prevalent in China. Therefore, it is worthwhile to develop a systematic and comprehensive mathematical
[...] Read more.
Vegetables have a short period of freshness, and therefore, the purchase of vegetables has to be carefully matched with sales, especially in the “small production and big market” setting prevalent in China. Therefore, it is worthwhile to develop a systematic and comprehensive mathematical model of replenishment plans and pricing strategies for each category of vegetables and individual products. In this paper, we analyze the following three questions: Question One: What is the distribution law and relationship between the sales volume of vegetable categories and single products? Question Two: What is the relationship between total sales volume and cost-plus pricing of vegetable categories? And is it possible to provide the daily total replenishment and pricing strategy of each vegetable category for the following week to maximize supermarket profit? Question Three: How can we incorporate the market demand for single vegetable products into a profit-maximizing program for supermarkets? Is it possible to further formulate the replenishment plan requirements for single products? To answer the first question, we created pivot tables to analyze occupancy. We found that mosaic leaves, peppers, and edible mushrooms accounted for a larger proportion of occupacy, while cauliflowers, aquatic rhizomes, and eggplants accounted for a smaller proportion. For the single items, lettuce, cabbage, green pepper, screw pepper, enoki mushroom, and shiitake mushroom accounted for a large proportion of their respective categories. We used the Pearson correlation coefficient and the Mfuzz package based on fuzzy c-means (FCM) algorithm to analyze the correlation between vegetable categories and single products. We found that there was a strong correlation between vegetable categories. Moreover, the sale of vegetable items belonging to the same category exhibited the same patterns of change over time. In order to address the second question, we established the LightGBM sales forecasting model. Combined with previous sales data, we forecasted and planned an efficient daily replenishment volume for each vegetable category in the coming week. In addition, we developed a pricing strategy for vegetable categories to maximize supermarket profits. For the third question, we built a dynamic programming model combining an optimal replenishment volume with a product pricing strategy for single items, which let the supermarket maximize its expected profits.
Full article
(This article belongs to the Special Issue Multi-Criteria Decision Making (MCDM) with Preference Modeling)
►▼
Show Figures
Figure 1
Open AccessArticle
Remark on Intuitionistic Fuzzy Temporal Modal Topological Structures
by
Krassimir Atanassov
Axioms 2024, 13(4), 256; https://doi.org/10.3390/axioms13040256 - 11 Apr 2024
Abstract
In a series of papers, we have discussed the concept of a modal topological structure modified, extended and illustrated by examples from intuitionistic fuzzy sets. Here, the concept of a temporal modal topological structure is introduced and illustrated with four different intuitionistic fuzzy
[...] Read more.
In a series of papers, we have discussed the concept of a modal topological structure modified, extended and illustrated by examples from intuitionistic fuzzy sets. Here, the concept of a temporal modal topological structure is introduced and illustrated with four different intuitionistic fuzzy temporal modal topological structures. These structures are based on intuitionistic fuzzy topological, temporal and modal operators. They are extensions of the temporal topological structures as well as of the modal topological structures.
Full article
(This article belongs to the Section Logic)
►▼
Show Figures
Figure 1
Open AccessArticle
Simpson’s Variational Integrator for Systems with Quadratic Lagrangians
by
Juan Antonio Rojas-Quintero, François Dubois and José Guadalupe Cabrera-Díaz
Axioms 2024, 13(4), 255; https://doi.org/10.3390/axioms13040255 - 11 Apr 2024
Abstract
This contribution proposes a variational symplectic integrator aimed at linear systems issued from the least action principle. An internal quadratic finite-element interpolation of the state is performed at each time step. Then, the action is approximated by Simpson’s quadrature formula. The implemented scheme
[...] Read more.
This contribution proposes a variational symplectic integrator aimed at linear systems issued from the least action principle. An internal quadratic finite-element interpolation of the state is performed at each time step. Then, the action is approximated by Simpson’s quadrature formula. The implemented scheme is implicit, symplectic, and conditionally stable. It is applied to the time integration of systems with quadratic Lagrangians. The example of the linearized double pendulum is treated. Our method is compared with Newmark’s variational integrator. The exact solution of the linearized double pendulum example is used for benchmarking. Simulation results illustrate the precision and convergence of the proposed integrator.
Full article
(This article belongs to the Special Issue Advances in Dynamical Systems and Control)
►▼
Show Figures
Figure 1
Open AccessArticle
Federated Learning Incentive Mechanism with Supervised Fuzzy Shapley Value
by
Xun Yang, Shuwen Xiang, Changgen Peng, Weijie Tan, Yue Wang, Hai Liu and Hongfa Ding
Axioms 2024, 13(4), 254; https://doi.org/10.3390/axioms13040254 - 11 Apr 2024
Abstract
The distributed training of federated machine learning, referred to as federated learning (FL), is discussed in models by multiple participants using local data without compromising data privacy and violating laws. In this paper, we consider the training of federated machine models with uncertain
[...] Read more.
The distributed training of federated machine learning, referred to as federated learning (FL), is discussed in models by multiple participants using local data without compromising data privacy and violating laws. In this paper, we consider the training of federated machine models with uncertain participation attitudes and uncertain benefits of each federated participant, and to encourage all participants to train the desired FL models, we design a fuzzy Shapley value incentive mechanism with supervision. In this incentive mechanism, if the supervision of the supervised mechanism detects that the payoffs of a federated participant reach a value that satisfies the Pareto optimality condition, the federated participant receives a distribution of federated payoffs. The results of numerical experiments demonstrate that the mechanism successfully achieves a fair and Pareto optimal distribution of payoffs. The contradiction between fairness and Pareto-efficient optimization is solved by introducing a supervised mechanism.
Full article
(This article belongs to the Special Issue Advances in Logic and Game Theory)
►▼
Show Figures
Figure 1
Open AccessArticle
An Extension of the Fréchet Distribution and Applications
by
Yolanda M. Gómez, Inmaculada Barranco-Chamorro, Jaime S. Castillo and Héctor W. Gómez
Axioms 2024, 13(4), 253; https://doi.org/10.3390/axioms13040253 - 11 Apr 2024
Abstract
This paper presents the Slash-Exponential-Fréchet distribution, which is an expanded version of the Fréchet distribution. Through its stochastic representation, probability distribution function, moments and other relevant features are obtained. Evidence supports that the updated model displays a lighter right tail than the Fréchet
[...] Read more.
This paper presents the Slash-Exponential-Fréchet distribution, which is an expanded version of the Fréchet distribution. Through its stochastic representation, probability distribution function, moments and other relevant features are obtained. Evidence supports that the updated model displays a lighter right tail than the Fréchet model and is more flexible as for skewness and kurtosis. Results on maximum likelihood estimators are given. Our proposition’s applicability is demonstrated through a simulation study and the evaluation of two real-world datasets.
Full article
(This article belongs to the Special Issue Probability, Statistics and Estimation)
►▼
Show Figures
Figure 1
Open AccessArticle
Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
by
Satish Shukla, Nikita Dubey and Juan-José Miñana
Axioms 2024, 13(4), 252; https://doi.org/10.3390/axioms13040252 - 10 Apr 2024
Abstract
The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval , but in an ordered interval of a Banach
[...] Read more.
The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval , but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy metric space which generalizes, extends and unifies the notion of classical fuzzy metric space and complex-valued fuzzy metric space and permits us to consider the fuzzy sets and metrics in a larger domain. Some topological properties of such spaces are discussed and some fixed point results in this new setting are proved. Multifarious examples are presented which clarify and justify our claims and results.
Full article
(This article belongs to the Special Issue General Topology and Fuzzy Topology)
Journal Menu
► ▼ Journal Menu-
- Axioms Home
- Aims & Scope
- Editorial Board
- Reviewer Board
- Topical Advisory Panel
- Instructions for Authors
- Special Issues
- Topics
- Sections & Collections
- Article Processing Charge
- Indexing & Archiving
- Editor’s Choice Articles
- Most Cited & Viewed
- Journal Statistics
- Journal History
- Journal Awards
- Society Collaborations
- Editorial Office
Journal Browser
► ▼ Journal BrowserHighly Accessed Articles
Latest Books
E-Mail Alert
News
Topics
Topic in
Axioms, Computation, MCA, Mathematics, Symmetry
Mathematical Modeling
Topic Editors: Babak Shiri, Zahra AlijaniDeadline: 31 May 2024
Topic in
Algorithms, Axioms, Fractal Fract, Mathematics, Symmetry
Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems
Topic Editors: Xiaofeng Wang, Fazlollah SoleymaniDeadline: 30 June 2024
Topic in
Crystals, Mathematics, Symmetry, Fractal Fract, Axioms
Mathematical Applications of Nonlinear Wave Properties in Crystalline and Dispersive Media
Topic Editors: Mahmoud A.E. Abdelrahman, Emad El-ShewyDeadline: 31 August 2024
Topic in
Entropy, Fractal Fract, Dynamics, Mathematics, Computation, Axioms
Advances in Nonlinear Dynamics: Methods and Applications
Topic Editors: Ravi P. Agarwal, Maria Alessandra RagusaDeadline: 20 October 2024
Conferences
Special Issues
Special Issue in
Axioms
Advances in Differential Geometry and Mathematical Physics
Guest Editor: David D. McNuttDeadline: 20 April 2024
Special Issue in
Axioms
Computational and Experimental Fluid Dynamics
Guest Editors: Yuli Chashechkin, Sergey E. YakushDeadline: 29 April 2024
Special Issue in
Axioms
Advances in Mathematical Methods and Applications for High-Performance Computing
Guest Editor: Jin SunDeadline: 20 May 2024
Special Issue in
Axioms
Discrete Curvatures and Laplacians
Guest Editors: Emil Saucan, David Xianfeng GuDeadline: 31 May 2024
Topical Collections
Topical Collection in
Axioms
Mathematical Analysis and Applications
Collection Editor: Hari Mohan Srivastava
Topical Collection in
Axioms
Differential Equations and Dynamical Systems
Collection Editor: Feliz Manuel Minhós