Axioms

21 pages, 452 KiB

Open AccessArticle

A Numerical Method for a Heat Conduction Model in a Double-Pane Window

by Aníbal Coronel, Fernando Huancas, Esperanza Lozada and Alex Tello

Axioms 2022, 11(8), 422; https://doi.org/10.3390/axioms11080422 - 22 Aug 2022

Cited by 4 | Viewed by 1608

In this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction problem. The [...] Read more.

In this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction problem. The designed scheme is mainly based on approximations satisfying the facts that all inner grid points has second-order temporal and spatial truncation errors, while at the boundary points and at inter-facial points has second-order temporal truncation error and first-order spatial truncation error, respectively. We prove that the finite difference scheme introduced is unconditionally stable, convergent, and has a rate of convergence two in space and time for the

L_{\infty}

-norm. Moreover, we give a numerical example to confirm our theoretical results. Full article

(This article belongs to the Special Issue Advances in Applied Mathematical Modelling)

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16 pages, 599 KiB

Open AccessArticle

Stability Analysis of a Stage-Structure Predator–Prey Model with Holling III Functional Response and Cannibalism

by Yufen Wei and Yu Li

Axioms 2022, 11(8), 421; https://doi.org/10.3390/axioms11080421 - 21 Aug 2022

Viewed by 1638

Abstract

This paper considers the time taken for young predators to become adult predators as the delay and constructs a stage-structured predator–prey system with Holling III response and time delay. Using the persistence theory for infinite-dimensional systems and the Hurwitz criterion, the permanent persistence [...] Read more.

This paper considers the time taken for young predators to become adult predators as the delay and constructs a stage-structured predator–prey system with Holling III response and time delay. Using the persistence theory for infinite-dimensional systems and the Hurwitz criterion, the permanent persistence condition of this system and the local stability condition of the system’s coexistence equilibrium are given. Further, it is proven that the system undergoes a Hopf bifurcation at the coexistence equilibrium. By using Lyapunov functions and the LaSalle invariant principle, it is shown that the trivial equilibrium and the coexistence equilibrium are globally asymptotically stable, and sufficient conditions are derived for the global stability of the coexistence equilibrium. Some numerical simulations are carried out to illustrate the main results. Full article

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10 pages, 756 KiB

Open AccessArticle

Comparison of Overlap and Grouping Functions

by Songsong Dai

Axioms 2022, 11(8), 420; https://doi.org/10.3390/axioms11080420 - 20 Aug 2022

Cited by 1 | Viewed by 1377

Abstract

This paper investigates the pointwise comparability of overlap and grouping functions which obtained by Bustince et al.’s and Bedregal et al.’s generator pairs, respectively. Some necessary and sufficient conditions for the comparison of these functions are proved. We also introduce some compositions of [...] Read more.

This paper investigates the pointwise comparability of overlap and grouping functions which obtained by Bustince et al.’s and Bedregal et al.’s generator pairs, respectively. Some necessary and sufficient conditions for the comparison of these functions are proved. We also introduce some compositions of these functions and study the order preservation of these compositions. Full article

(This article belongs to the Special Issue Non-classical Logics and Related Algebra Systems)

13 pages, 856 KiB

Open AccessArticle

The Relationship between Fuzzy Reasoning Methods Based on Intuitionistic Fuzzy Sets and Interval-Valued Fuzzy Sets

by Minxia Luo, Wenling Li and Hongyan Shi

Axioms 2022, 11(8), 419; https://doi.org/10.3390/axioms11080419 - 20 Aug 2022

Cited by 4 | Viewed by 1691

Abstract

Two important basic inference models of fuzzy reasoning are Fuzzy Modus Ponens (FMP) and Fuzzy Modus Tollens (FMT). In order to solve FMP and FMT problems, the full implication triple I algorithm, the reverse triple I algorithm and the Subsethood Inference Subsethood (SIS [...] Read more.

Two important basic inference models of fuzzy reasoning are Fuzzy Modus Ponens (FMP) and Fuzzy Modus Tollens (FMT). In order to solve FMP and FMT problems, the full implication triple I algorithm, the reverse triple I algorithm and the Subsethood Inference Subsethood (SIS for short) algorithm are proposed, respectively. Furthermore, the existing reasoning algorithms are extended to intuitionistic fuzzy sets and interval-valued fuzzy sets according to different needs. The purpose of this paper is to study the relationship between intuitionistic fuzzy reasoning algorithms and interval-valued fuzzy reasoning algorithms. It is proven that there is a bijection between the solutions of intuitionistic fuzzy triple I algorithm and the interval-valued fuzzy triple I algorithm. Then, there is a bijection between the solutions of intuitionistic fuzzy reverse triple I algorithm and the interval-valued fuzzy reverse triple I algorithm. At the same time, it is shown that there is also a bijection between the solutions of intuitionistic fuzzy SIS algorithm and interval-valued fuzzy SIS algorithm. Full article

(This article belongs to the Special Issue Approximation Theory and Related Applications)

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23 pages, 366 KiB

Open AccessArticle

Incomplete Complex Intuitionistic Fuzzy System: Preference Relations, Expert Weight Determination, Group Decision-Making and Their Calculation Algorithms

by Fangdi Wang, Zengtai Gong and Yabin Shao

Axioms 2022, 11(8), 418; https://doi.org/10.3390/axioms11080418 - 19 Aug 2022

Cited by 5 | Viewed by 1692

Abstract

As is well known, complex intuitionistic fuzzy preference relation can describe the fuzzy characters of things in more detail and comprehensively and is very useful in dealing with decision-making problems that include periodic or recurring phenomena. However, sometimes, a decision-maker may provide incomplete [...] Read more.

As is well known, complex intuitionistic fuzzy preference relation can describe the fuzzy characters of things in more detail and comprehensively and is very useful in dealing with decision-making problems that include periodic or recurring phenomena. However, sometimes, a decision-maker may provide incomplete judgments in a complex intuitionistic fuzzy preference relation because of a lack of knowledge, time pressure, and the decision-makers’ limited expertise related to the problem domain. In such cases, it would be sensible not to force the expert to express “false” preferences over these objects. Consequently, how to define incomplete complex intuitionistic fuzzy preference relations and to estimate their missing elements in an incomplete complex intuitionistic fuzzy preference relation becomes a necessary step in a decision-making process. In this paper, the concept of incomplete complex intuitionistic fuzzy preference relation is introduced and its properties are discussed. Meanwhile, the multiplicative consistent incomplete complex intuitionistic fuzzy preference relations are defined. Secondly, estimating algorithms are developed to estimate the missing elements in the acceptable incomplete complex intuitionistic fuzzy preference relations. Finally, an expert weight determination algorithm and the group decision-making algorithms based on incomplete complex intuitionistic fuzzy preference relations are established. The solving process of the algorithms is illustrated by an example, the practicability of the algorithms is verified, the advantages and disadvantages of two group decision-making algorithms are compared and analyzed, and the simulation verification of incomplete complex intuitionistic fuzzy system is carried out by MATLAB software. The framework proposed in this paper effectively generalizes and enriches the previous works and has a good application prospect. Full article

(This article belongs to the Special Issue Multiple-Criteria Decision-Making and Computational Intelligence: Recent Applications)

14 pages, 335 KiB

Open AccessArticle

The Independence Number Conditions for 2-Factors of a Claw-Free Graph

by Wanpeng Lei, Liming Xiong and Jun Yin

Axioms 2022, 11(8), 417; https://doi.org/10.3390/axioms11080417 - 19 Aug 2022

Viewed by 1463

Abstract

In 2014, some scholars showed that every 2-connected claw-free graph G with independence number

α (G) \leq 3

is Hamiltonian with one exception of family of graphs. If a nontrivial path contains only internal vertices of degree two and end vertices [...] Read more.

In 2014, some scholars showed that every 2-connected claw-free graph G with independence number

α (G) \leq 3

is Hamiltonian with one exception of family of graphs. If a nontrivial path contains only internal vertices of degree two and end vertices of degree not two, then we call it a branch. A set S of branches of a graph G is called a branch cut if we delete all edges and internal vertices of branches of S leading to more components than G. We use a branch bond to denote a minimal branch cut. If a branch-bond has an odd number of branches, then it is called odd. In this paper, we shall characterize all 2-connected claw-free graphs G such that every odd branch-bond of G has an edge branch and such that

α (G) \leq 5

but has no 2-factor. We also consider the same problem for those 2-edge-connected claw-free graphs with

α (G) \leq 4

. Full article

(This article belongs to the Special Issue Graph Theory with Applications)

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7 pages, 3139 KiB

Open AccessArticle

Modulation Transfer between Microwave Beams: A Hypothesized Case of a Classically-Forbidden Stochastic Process

by Anedio Ranfagni and Ilaria Cacciari

Axioms 2022, 11(8), 416; https://doi.org/10.3390/axioms11080416 - 19 Aug 2022

Cited by 3 | Viewed by 1437

Abstract

Measurements of delay time in the transfer of modulation between a modulated to an unmodulated one, both of them derived by the same microwave source, are reported and interpreted. In the light of these results, the transfer of modulation can be hypothesized as [...] Read more.

Measurements of delay time in the transfer of modulation between a modulated to an unmodulated one, both of them derived by the same microwave source, are reported and interpreted. In the light of these results, the transfer of modulation can be hypothesized as due to a stochastic, classically-forbidden process, assisted by a photon–photon scattering mechanism. Full article

(This article belongs to the Special Issue Advances in Stochastic Modelling)

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17 pages, 1731 KiB

Open AccessArticle

Bitcoin as a Safe-Haven Asset and a Medium of Exchange

by Yu Yan, Yiming Lei and Yiming Wang

Axioms 2022, 11(8), 415; https://doi.org/10.3390/axioms11080415 - 18 Aug 2022

Cited by 4 | Viewed by 3280

Abstract

A monetary model is established to introduce that bitcoin does have the characteristics of a price rise when the economic situation is terrible under high risk aversion. At this time, Bitcoin has the property of a safe-haven asset, and when economic conditions are [...] Read more.

A monetary model is established to introduce that bitcoin does have the characteristics of a price rise when the economic situation is terrible under high risk aversion. At this time, Bitcoin has the property of a safe-haven asset, and when economic conditions are good and risk aversion is low, Bitcoin has a pro-cyclical nature. At this time, Bitcoin has a stronger property as a medium of exchange. To show the movement law of the bitcoin price, we make a logarithmic linearization of the model and simulation, and the result is consistent with the theoretical analysis. To better understand the role of bitcoin in the real economy, several standard portfolio models are used to measure the similarities and differences between gold and bitcoin in an investment portfolio. After the outbreak of COVID-19, bitcoin has shown stronger safe-haven asset properties. Full article

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17 pages, 321 KiB

Open AccessArticle

A Fuzzy Random Boundary Value Problem

by Hari M. Srivastava, Reza Chaharpashlou, Reza Saadati and Chenkuan Li

Axioms 2022, 11(8), 414; https://doi.org/10.3390/axioms11080414 - 18 Aug 2022

Cited by 1 | Viewed by 1386

Abstract

A system of generalized fuzzy random differential equations with boundary conditions is investigated, which is a fuzzy version of a system of general random differential equations. We first present random fixed point (RFP) theorems in fuzzy metric space (FM). In the sequel, we [...] Read more.

A system of generalized fuzzy random differential equations with boundary conditions is investigated, which is a fuzzy version of a system of general random differential equations. We first present random fixed point (RFP) theorems in fuzzy metric space (FM). In the sequel, we define the operators that are of integral type. Furthermore, these operators are related to a part of random differential equations (RDE). For the desired system with boundary conditions, we study the suitable integral operators associated with a large family of random differential equations. Finally, we prove the existence of a unique random solution (EURS). Full article

(This article belongs to the Special Issue Mathematical Analysis and Applications III)

11 pages, 286 KiB

Open AccessArticle

Fixed Point of Modified F-Contraction with an Application

by Min Wang, Naeem Saleem, Shahid Bashir and Mi Zhou

Axioms 2022, 11(8), 413; https://doi.org/10.3390/axioms11080413 - 18 Aug 2022

Cited by 2 | Viewed by 1516

Abstract

In this paper, we prove the existence of fixed points for every 2-rotative continuous mapping in Banach spaces to answer an open question raised by Goebel and Koter. Further, we modify F-contraction by developing F-rotative mapping and establish some fixed-point theorems. [...] Read more.

In this paper, we prove the existence of fixed points for every 2-rotative continuous mapping in Banach spaces to answer an open question raised by Goebel and Koter. Further, we modify F-contraction by developing F-rotative mapping and establish some fixed-point theorems. Finally, we apply our results to prove the existence of a solution of a non-linear fractional differential equation. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics III)

21 pages, 4326 KiB

Open AccessArticle

The Performance of Topic Evolution Based on a Feature Maximization Measurement for the Linguistics Domain

by Junchao Feng, Jianjun Miao, Yue Tang, Yuechen Li and Jundong Feng

Axioms 2022, 11(8), 412; https://doi.org/10.3390/axioms11080412 - 18 Aug 2022

Cited by 1 | Viewed by 1518

Abstract

Understanding the performance of the data mining approach and topic evolution in a certain scientific domain is imperative to capturing key domain developments and facilitating knowledge transfer within and across domains. Our research selects linguistics as an exploratory domain and exploits the feature [...] Read more.

Understanding the performance of the data mining approach and topic evolution in a certain scientific domain is imperative to capturing key domain developments and facilitating knowledge transfer within and across domains. Our research selects linguistics as an exploratory domain and exploits the feature maximization (FM) measurement for feature selection, combined with the contrast ratio to conduct the diachronic analysis for the linguistics domain’s topics. To accurately mine the linguistics domain’s topics and obtain the optimal clustering model selection, we exploit an integrated method associated with the deep embedding for clustering (DEC) algorithm based on the keywords-based Text Representation Matrix (KTRM) and Lamirel’s EC index and test the performance of this method. The results show that the FM measurement is applicable in the linguistics domain for topic mining, and the combinatory method has the advantage of an unbiased clustering optimization model and applies to the design of non-parameter clustering and algorithms from the low dimension to the high dimension of datasets. The findings suggest that this approach could be suitable for a diachronic analysis of topic evolution and facilitate the performance of topic detection. In addition, these findings of text detection can rise to knowledge fusion cognition with the factor of language as an available research objective in interdisciplinary research. Full article

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9 pages, 778 KiB

Open AccessArticle

An Improved Clustering Algorithm for Multi-Density Data

by Abdulwahab Ali Almazroi and Walid Atwa

Axioms 2022, 11(8), 411; https://doi.org/10.3390/axioms11080411 - 18 Aug 2022

Cited by 1 | Viewed by 1575

Abstract

The clustering method divides a dataset into groups with similar data using similarity metrics. However, discovering clusters in different densities, shapes and distinct sizes is still a challenging task. In this regard, experts and researchers opt to use the DBSCAN algorithm as it [...] Read more.

The clustering method divides a dataset into groups with similar data using similarity metrics. However, discovering clusters in different densities, shapes and distinct sizes is still a challenging task. In this regard, experts and researchers opt to use the DBSCAN algorithm as it uses density-based clustering techniques that define clusters of different sizes and shapes. However, it is misapplied to clusters of different densities due to its global attributes that generate a single density. Furthermore, most existing algorithms are unsupervised methods, where available prior knowledge is useless. To address these problems, this research suggests the use of a clustering algorithm that is semi-supervised. This allows the algorithm to use existing knowledge to generate pairwise constraints for clustering multi-density data. The proposed algorithm consists of two stages: first, it divides the dataset into different sets based on their density level and then applies the semi-supervised DBSCAN algorithm to each partition. Evaluation of the results shows the algorithm performing effectively and efficiently in comparison to unsupervised clustering algorithms. Full article

(This article belongs to the Special Issue Computational Intelligence and Software Engineering)

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29 pages, 8785 KiB

Open AccessEditor’s ChoiceArticle

Design of Type-3 Fuzzy Systems and Ensemble Neural Networks for COVID-19 Time Series Prediction Using a Firefly Algorithm

by Patricia Melin, Daniela Sánchez, Juan R. Castro and Oscar Castillo

Axioms 2022, 11(8), 410; https://doi.org/10.3390/axioms11080410 - 17 Aug 2022

Cited by 29 | Viewed by 2538

Abstract

In this work, information on COVID-19 confirmed cases is utilized as a dataset to perform time series predictions. We propose the design of ensemble neural networks (ENNs) and type-3 fuzzy inference systems (FISs) for predicting COVID-19 data. The answers for each ENN module [...] Read more.

In this work, information on COVID-19 confirmed cases is utilized as a dataset to perform time series predictions. We propose the design of ensemble neural networks (ENNs) and type-3 fuzzy inference systems (FISs) for predicting COVID-19 data. The answers for each ENN module are combined using weights provided by the type-3 FIS, in which the ENN is also designed using the firefly algorithm (FA) optimization technique. The proposed method, called ENNT3FL-FA, is applied to the COVID-19 data for confirmed cases from 12 countries. The COVID-19 data have shown to be a complex time series due to unstable behavior in certain periods of time. For example, it is unknown when a new wave will exist and how it will affect each country due to the increase in cases due to many factors. The proposed method seeks mainly to find the number of modules of the ENN and the best possible parameters, such as lower scale and lower lag of the type-3 FIS. Each module of the ENN produces an individual prediction. Each prediction error is an input for the type-3 FIS; moreover, outputs provide a weight for each prediction, and then the final prediction can be calculated. The type-3 fuzzy weighted average (FWA) integration method is compared with the type-2 FWA to verify its ability to predict future confirmed cases by using two data periods. The achieved results show how the proposed method allows better results for the real prediction of 20 future days for most of the countries used in this study, especially when the number of data points increases. In countries such as Germany, India, Italy, Mexico, Poland, Spain, the United Kingdom, and the United States of America, on average, the proposed ENNT3FL-FA achieves a better performance for the prediction of future days for both data points. The proposed method proves to be more stable with complex time series to predict future information such as the one utilized in this study. Intelligence techniques and their combination in the proposed method are recommended for time series with many data points. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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10 pages, 434 KiB

Open AccessReview

Near-Field Seismic Motion: Waves, Deformations and Seismic Moment

by Bogdan Felix Apostol

Axioms 2022, 11(8), 409; https://doi.org/10.3390/axioms11080409 - 17 Aug 2022

Cited by 1 | Viewed by 1831

Abstract

The tensorial force acting in a localized seismic focus is introduced and the corresponding seismic waves are derived, as solutions of the elastic wave equation in a homogeneous and isotropic body. The deconvolution of the solution for a structured focal region is briefly [...] Read more.

The tensorial force acting in a localized seismic focus is introduced and the corresponding seismic waves are derived, as solutions of the elastic wave equation in a homogeneous and isotropic body. The deconvolution of the solution for a structured focal region is briefly discussed. The far-field waves are identified as P and S seismic waves. These are spherical-shell waves, with a scissor-like shape, and an amplitude decreasing with the inverse of the distance. The near-field seismic waves are spherical-shell waves, decreasing with the inverse of the squared distance. The amplitudes and the polarizations of the near-field seismic waves are given. The determination of the seismic-moment tensor and the earthquake parameters from measurements of the P and S seismic waves at Earth’s’ surface is briefly discussed. Similarly, the mainshock generated by secondary waves on Earth’s surface is reviewed. The near-field static deformations of a homogeneous and isotropic half-space are discussed and a method of determining the seismic-moment tensor from epicentral near-field (quasi-) static deformations in seismogenic regions is presented. Full article

(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Physics)

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20 pages, 442 KiB

Open AccessArticle

A Priori Estimates for the Solution of an Initial Boundary Value Problem of Fluid Flow through Fractured Porous Media

by Nurlana Alimbekova, Abdumauvlen Berdyshev and Dossan Baigereyev

Axioms 2022, 11(8), 408; https://doi.org/10.3390/axioms11080408 - 17 Aug 2022

Cited by 1 | Viewed by 1421

Abstract

The paper studies a model of fluid flow in a fractured porous medium in which fractures are distributed uniformly over the volume. This model includes a nonlinear equation containing several terms with fractional derivatives in the sense of Caputo of order belonging to [...] Read more.

The paper studies a model of fluid flow in a fractured porous medium in which fractures are distributed uniformly over the volume. This model includes a nonlinear equation containing several terms with fractional derivatives in the sense of Caputo of order belonging to the interval

(1, 2)

. The relevance of studying this problem is determined by its practical significance in the oil industry, since most of the world’s oil reserves are in these types of reservoirs. The uniqueness of the solution to the problem in a differential form and its dependence on the initial data and the right-hand side of the equation is proved. A numerical method is proposed based on the use of the finite difference approximation for integer and fractional time derivatives and the finite element method in the spatial direction. A change of variables is introduced to reduce the order of the fractional derivatives. Furthermore, the fractional derivative is approximated by using the L1-method. The stability and convergence of the proposed numerical method are rigorously proved. The theoretical order of convergence is confirmed by the results of numerical tests for a problem of fluid flow in fractured porous media with a known exact solution. Full article

(This article belongs to the Special Issue Recent Advancements in Computational Fluid Mechanics and Heat Transfer)

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18 pages, 2572 KiB

Open AccessArticle

Power Consumption Forecast of Three Major Industries in China Based on Fractional Grey Model

by Yuhan Xie, Yunfei Yang and Lifeng Wu

Axioms 2022, 11(8), 407; https://doi.org/10.3390/axioms11080407 - 16 Aug 2022

Cited by 7 | Viewed by 1711

Abstract

As one of the most significant carbon emission departments in China, the power industry will gradually become the core hub of reducing carbon emissions in the process of undertaking carbon emissions transferred from other industries. Therefore, it is of vital importance to predict [...] Read more.

As one of the most significant carbon emission departments in China, the power industry will gradually become the core hub of reducing carbon emissions in the process of undertaking carbon emissions transferred from other industries. Therefore, it is of vital importance to predict the power consumption in China’s end energy consumption to achieve the carbon peak goal on time. This paper firstly uses the gray relational analysis model to study the relationship between power consumption indicators of the three major industries and some social and economic indicators and obtains the influencing factors with the greatest correlation with the power consumption of the three industries. Then, based on the analysis of socio-economic factors, considering different growth rates, the GMCN(1,N) model of electricity consumption in China’s three major industries is established. Forecast data under different scenarios have important practical significance for formulating active and effective energy policies. The data indicate that the secondary and tertiary industries consume the greatest amount of electricity. It is estimated that the power consumption of China’s three major industries will reach 10.15 trillion kWh (kilowatt hours) by 2030. Full article

(This article belongs to the Special Issue Fractional-Order Grey Models and Their Applications)

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23 pages, 385 KiB

Open AccessArticle

Neighborhood Structures and Continuities via Cubic Sets

by Jeong-Gon Lee, Güzide Şenel, Jong-Il Baek, Sang Hyeon Han and Kul Hur

Axioms 2022, 11(8), 406; https://doi.org/10.3390/axioms11080406 - 16 Aug 2022

Cited by 4 | Viewed by 1227

Abstract

Cubic sets are a very useful generalization of fuzzy sets where one is allowed to extend the output through a subinterval of [0, 1] and a number from [0, 1]. In this article, we first highlight some of the claims made in the [...] Read more.

Cubic sets are a very useful generalization of fuzzy sets where one is allowed to extend the output through a subinterval of [0, 1] and a number from [0, 1]. In this article, we first highlight some of the claims made in the previous article about cubic sets. Then, the concept of semi-coincidence in cubic sets, cubic neighborhood system according to cubic topology, and cubic bases and subbases are introduced. This article deals with a cubic closure and a cubic interior and how to obtain their various properties. In addition, cubic compact spaces and their properties are defined and a useful example is given. We mainly focus on the concept of cubic continuities and deepen our research by finding its characterization. One of the most important discoveries of this paper is determining that there is a cubic product topology induced by the projection mappings, and discovering sufficient conditions for the projection mappings to be cubic open. Full article

(This article belongs to the Special Issue Cubic Set Structure and Its Applications)

12 pages, 282 KiB

Open AccessArticle

A New Contraction-Type Mapping on a Vectorial Dislocated Metric Space over Topological Modules

by Ion Marian Olaru

Axioms 2022, 11(8), 405; https://doi.org/10.3390/axioms11080405 - 15 Aug 2022

Viewed by 1184

Abstract

One recent and prolific direction in the development of fixed point theory is to consider an operator

T : X \to X

defined on a metric space

(X, d)

which is an F—contraction, i.e., T verifies a condition of [...] Read more.

One recent and prolific direction in the development of fixed point theory is to consider an operator

T : X \to X

defined on a metric space

(X, d)

which is an F—contraction, i.e., T verifies a condition of type

τ + F (d (T (x), T (y)) \leq F (d (x, y))

, for all

x, y \in X

,

T (x) \neq T (y)

, where

τ > 0

and

F : (0, \infty) \to R

satisfies some suitable conditions which ensure the existence and uniqueness for the fixed point of operator T. Moreover, the notion of F-contraction over a metric space

(X, d)

was generalized by considering the notion of

(G, H)

—contraction, i.e., a condition of type

G (d (T x, T y)) \leq H (d (x, y))

, for all

x, y \in X

,

T x \neq T y

for some appropriate

G, H : (0, \infty) \to R

functions. Recently, the abovementioned F-contraction theory was extended to the setup of cone metric space over the topological left modules. The principal objective of this paper is to introduce the concept of vectorial dislocated metric space over a topological left module and the notion of A-Cauchy sequence, as a generalization of the classical Cauchy sequence concept. Furthermore, based on the introduced concept, a fixed point result is provided for an operator

T : X \to X

, which satisfies the condition

(G, H)

—contraction, where

G, H

are defined on the interior of a solid cone. Full article

(This article belongs to the Section Mathematical Analysis)

22 pages, 1059 KiB

Open AccessArticle

Evaluation of Cryptocurrencies for Investment Decisions in the Era of Industry 4.0: A Borda Count-Based Intuitionistic Fuzzy Set Extensions EDAS-MAIRCA-MARCOS Multi-Criteria Methodology

by Fatih Ecer, Adem Böyükaslan and Sarfaraz Hashemkhani Zolfani

Axioms 2022, 11(8), 404; https://doi.org/10.3390/axioms11080404 - 15 Aug 2022

Cited by 19 | Viewed by 5282

Abstract

Blockchain technologies, which form the basis of Industry 4.0, paved the way for cryptocurrencies to emerge as technological innovation in the technology age. Recently, investors worldwide have been interested in cryptocurrencies with increasing acceleration due to high earning expectations though they have no [...] Read more.

Blockchain technologies, which form the basis of Industry 4.0, paved the way for cryptocurrencies to emerge as technological innovation in the technology age. Recently, investors worldwide have been interested in cryptocurrencies with increasing acceleration due to high earning expectations though they have no backing and intrinsic value. As such, this paper seeks to identify the most proper cryptocurrencies from an investment standpoint in our technological era. Fifteen well-known cryptocurrencies with the highest market capitalization are evaluated as per sixteen factors. An intuitionistic fuzzy set-driven methodology incorporating Evaluation Based on Distance from Average Solution (EDAS), Multi-Attributive Ideal Real Comparative Analysis (MAIRCA, and Measurement of Alternatives and Ranking according to COmpromise Solution (MARCOS), which is the study’s prominent novelty, has been applied to provide a strong group decision vehicle for cryptocurrency selection. Notwithstanding, although the results obtained with the three approaches are highly consistent, investors would not like to doubt the instrument they will invest in. The Borda count is then applied to obtain a compromise for the rankings obtained from each approach. As per our findings, Ethereum, Tether, and Bitcoin are the most suitable cryptocurrencies, whereas reliable software, ease of inclusion in the wallet, and stability are the foremost factors to consider when investing in cryptocurrencies. The findings are further discussed in detail from a financial perspective. The proposed approach could be employed to select different investment instruments in future studies. Full article

(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)

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17 pages, 359 KiB

Open AccessArticle

On (k,ψ)-Hilfer Fractional Differential Equations and Inclusions with Mixed (k,ψ)-Derivative and Integral Boundary Conditions

by Sotiris K. Ntouyas, Bashir Ahmad, Cholticha Nuchpong and Jessada Tariboon

Axioms 2022, 11(8), 403; https://doi.org/10.3390/axioms11080403 - 15 Aug 2022

Cited by 9 | Viewed by 1720

Abstract

In this paper we study single-valued and multi-valued (k,ψ)-Hilfer-type boundary value problems of fractional order in (1,2], subject to nonlocal boundary conditions involving (k,ψ)-Hilfer-type derivative and integral operators. The results for single-valued case are established [...] Read more.

In this paper we study single-valued and multi-valued (k,ψ)-Hilfer-type boundary value problems of fractional order in (1,2], subject to nonlocal boundary conditions involving (k,ψ)-Hilfer-type derivative and integral operators. The results for single-valued case are established by using Banach and Krasnosel’skiĭ fixed point theorems as well as Leray–Schauder nonlinear alternative. In the multi-valued case, we establish an existence result for the convex valued right-hand side of the inclusion via Leray–Schauder nonlinear alternative for multi-valued maps, while the second one when the right-hand side has non-convex values is obtained by applying Covitz–Nadler fixed point theorem for multi-valued contractions. Numerical examples illustrating the obtained theoretical results are also presented. Full article

(This article belongs to the Special Issue Impulsive, Delay and Fractional Order Systems)

21 pages, 2113 KiB

Open AccessArticle

Periodic Waves and Ligaments on the Surface of a Viscous Exponentially Stratified Fluid in a Uniform Gravity Field

by Yuli D. Chashechkin and Artem A. Ochirov

Axioms 2022, 11(8), 402; https://doi.org/10.3390/axioms11080402 - 15 Aug 2022

Cited by 17 | Viewed by 1873

Abstract

The theory of singular perturbations in a unified formulation is used, for the first time, to study the propagation of two-dimensional periodic perturbations, including capillary and gravitational surface waves and accompanying ligaments in the [...] Read more.

The theory of singular perturbations in a unified formulation is used, for the first time, to study the propagation of two-dimensional periodic perturbations, including capillary and gravitational surface waves and accompanying ligaments in the

10^{- 4} < ω < 10^{3} s^{- 1}

frequency range, in a viscous continuously stratified fluid. Dispersion relations for flow constituents are given, as well as expressions for phase and group velocities for surface waves and ligaments in physically observable variables. When the wave-length reaches values of the order of the stratification scale, the liquid behaves as homogeneous. As the wave frequency approaches the buoyancy frequency, the energy transfer rate decreases: the group velocity of surface waves tends to zero, while the phase velocity tends to infinity. In limiting cases, the expressions obtained are transformed into known wave dispersion expressions for an ideal stratified or actually homogeneous fluid. Full article

(This article belongs to the Special Issue Singularly Perturbed Problems: Asymptotic Analysis and Approximate Solution)

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14 pages, 3864 KiB

Open AccessArticle

Spatial Fuzzy C-Means Clustering Analysis of U.S. Presidential Election and COVID-19 Related Factors in the Rustbelt States in 2020

by Shianghau Wu

Axioms 2022, 11(8), 401; https://doi.org/10.3390/axioms11080401 - 15 Aug 2022

Viewed by 1954

Abstract

The rustbelt states play a key role in determining the vote turnout in the U.S. elections. The current study attempts to utilize the spatial fuzzy C-means method to analyze the U.S. presidential election in the rustbelt states in 2020. We intend to explore [...] Read more.

The rustbelt states play a key role in determining the vote turnout in the U.S. elections. The current study attempts to utilize the spatial fuzzy C-means method to analyze the U.S. presidential election in the rustbelt states in 2020. We intend to explore that the U.S. presidential election had related factors, including COVID-19-related factors, such as the mask-wearing percentage and the COVID-19 death tolls in each county of the rust belt states. Contrary to the related literature, the study uses education level, number of house units, unemployment rate, household income, COVID-19-related factors and the share of Republican’s votes in the presidential election. The results indicate that spatial generalized fuzzy C-means analysis has better clustering results than the C-means clustering method. Moreover, the COVID-19 death toll in each county did not affect the Republican’s vote share in the rustbelt states, while the mask-wearing behavior in some regions had a negative impact on the Republican’s vote share. Full article

(This article belongs to the Special Issue 10th Anniversary of Axioms: Logic)

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21 pages, 1188 KiB

Open AccessArticle

Stability Analysis of Delayed COVID-19 Models

by Mohamed A. Zaitri, Cristiana J. Silva and Delfim F. M. Torres

Axioms 2022, 11(8), 400; https://doi.org/10.3390/axioms11080400 - 13 Aug 2022

Cited by 5 | Viewed by 1931

Abstract

We analyze mathematical models for COVID-19 with discrete time delays and vaccination. Sufficient conditions for the local stability of the endemic and disease-free equilibrium points are proved for any positive time delay. The stability results are illustrated through numerical simulations performed in MATLAB. [...] Read more.

We analyze mathematical models for COVID-19 with discrete time delays and vaccination. Sufficient conditions for the local stability of the endemic and disease-free equilibrium points are proved for any positive time delay. The stability results are illustrated through numerical simulations performed in MATLAB. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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22 pages, 3889 KiB

Open AccessArticle

Arctan-Based Family of Distributions: Properties, Survival Regression, Bayesian Analysis and Applications

by Omid Kharazmi, Morad Alizadeh, Javier E. Contreras-Reyes and Hossein Haghbin

Axioms 2022, 11(8), 399; https://doi.org/10.3390/axioms11080399 - 12 Aug 2022

Cited by 5 | Viewed by 2163

Abstract

In this paper, a new class of the continuous distributions is established via compounding the arctangent function with a generalized log-logistic class of distributions. Some structural properties of the suggested model such as distribution function, hazard function, quantile function, asymptotics and a useful [...] Read more.

In this paper, a new class of the continuous distributions is established via compounding the arctangent function with a generalized log-logistic class of distributions. Some structural properties of the suggested model such as distribution function, hazard function, quantile function, asymptotics and a useful expansion for the new class are given in a general setting. Two special cases of this new class are considered by employing Weibull and normal distributions as the parent distribution. Further, we derive a survival regression model based on a sub-model with Weibull parent distribution and then estimate the parameters of the proposed regression model making use of Bayesian and frequentist approaches. We consider seven loss functions, namely the squared error, modified squared error, weighted squared error, K-loss, linear exponential, general entropy, and precautionary loss functions for Bayesian discussion. Bayesian numerical results include a Bayes estimator, associated posterior risk, credible and highest posterior density intervals are provided. In order to explore the consistency property of the maximum likelihood estimators, a simulation study is presented via Monte Carlo procedure. The parameters of two sub-models are estimated with maximum likelihood and the usefulness of these sub-models and a proposed survival regression model is examined by means of three real datasets. Full article

(This article belongs to the Special Issue Mathematical Tools and Techniques Applicable to Probability Theory and Statistics)

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15 pages, 526 KiB

Open AccessArticle

Solving a Generalized Fractional Nonlinear Integro-Differential Equations via Modified Sumudu Decomposition Transform

by Kamel Al-Khaled

Axioms 2022, 11(8), 398; https://doi.org/10.3390/axioms11080398 - 11 Aug 2022

Cited by 2 | Viewed by 1634

Abstract

The Sumudu decomposition method was used and developed in this paper to find approximate solutions for a general form of fractional integro-differential equation of Volterra and Fredholm types. The Caputo definition was used to deal with fractional derivatives. As the method under consideration [...] Read more.

The Sumudu decomposition method was used and developed in this paper to find approximate solutions for a general form of fractional integro-differential equation of Volterra and Fredholm types. The Caputo definition was used to deal with fractional derivatives. As the method under consideration depends mainly on writing non-linear terms, which are often found inside the kernel of the integral equation, writing it in the form of Adomian’s polynomials in the well-known way. After applying the Sumudu transformation to both sides of the integral equation, the solution was written in the form of a convergent infinite series whose terms can be alternately calculated. The method was applied to three examples of non-linear integral equations with fractional derivatives. The results that were presented in the form of tables and graphs showed that the method is accurate, effective and highly efficient. Full article

(This article belongs to the Special Issue Nonlinear Problems in Mathematical Physics)

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15 pages, 801 KiB

Open AccessArticle

Learning and Applying Cooperative Solutions: A Classroom Experiment on Transportation Games

by Nikolaos Georgantzis, Carlos Gutiérrez-Hita and Joaquín Sánchez-Soriano

Axioms 2022, 11(8), 397; https://doi.org/10.3390/axioms11080397 - 11 Aug 2022

Viewed by 1446

Abstract

In a trade experiment, groups of students were taught how to bargain over a pie generated in a transportation game. Data collection and detailed group reports of the bargaining process allowed us to identify the type of bargaining followed and its correspondence with [...] Read more.

In a trade experiment, groups of students were taught how to bargain over a pie generated in a transportation game. Data collection and detailed group reports of the bargaining process allowed us to identify the type of bargaining followed and its correspondence with cooperative game theory concepts. Explicit coalitions were rather scarce (17%), although coalition stability was implied by 47.8% of the agreements. Efficiency was achieved in the vast majority (82%) of cases, whereas in 34.8% of the agreements, students used a lexicographic ordering of multiple solutions before choosing among them. Regarding the bargaining procedure, in 40% of the agreements, quantities traded were decided before profit sharing rules were negotiated, whereas in 16% of the cases they were simultaneously agreed upon. Our findings suggest that bargaining procedures often do not imply explicit coalitions. Moreover, efficiency can be achieved even in the absence of bargaining processes. Full article

(This article belongs to the Special Issue Strategic Decision Models and Applications)

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29 pages, 7349 KiB

Open AccessArticle

A Novel Algorithmic Forex Trade and Trend Analysis Framework Based on Deep Predictive Coding Network Optimized with Reptile Search Algorithm

by Swaty Dash, Pradip Kumar Sahu, Debahuti Mishra, Pradeep Kumar Mallick, Bharti Sharma, Mikhail Zymbler and Sachin Kumar

Axioms 2022, 11(8), 396; https://doi.org/10.3390/axioms11080396 - 11 Aug 2022

Cited by 4 | Viewed by 3528

Abstract

This paper proposed a short-term two-stage hybrid algorithmic framework for trade and trend analysis of the Forex market by augmenting the currency pair datasets with transformed attributes using a few technical indicators and statistical measures. In the first phase, an optimized deep predictive [...] Read more.

This paper proposed a short-term two-stage hybrid algorithmic framework for trade and trend analysis of the Forex market by augmenting the currency pair datasets with transformed attributes using a few technical indicators and statistical measures. In the first phase, an optimized deep predictive coding network (DPCN) based on a meta-heuristic reptile search algorithm (RSA) inspired by the intelligent hunting activities of the crocodiles is exploited to develop this RSA-DPCN predictive model. The proposed model has been compared with optimized versions of extreme learning machine (ELM) and functional link artificial neural network (FLANN) with genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE) along with the RSA optimizers. The performance of this model has been evaluated and validated through several statistical tests. In the second phase, the up and down trends are analyzed using the Higher Highs Higher Lows, and Lower Highs Lower Lows (HHs/HLs and LHs/LLs) trend analysis tool. Further, the observed trends are compared with the actual trends observed on the exchange price of real datasets. This study shows that the proposed RSA-DPCN model accurately predicts the exchange price. At the same time, it provides a well-structured platform to discern the directions of the market trends and thereby guides in finding the entry and exit points of the Forex market. Full article

(This article belongs to the Special Issue Machine Learning: Theory, Algorithms and Applications)

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16 pages, 342 KiB

Open AccessArticle

General Pseudo Quasi-Overlap Functions on Lattices

by Rui Eduardo Brasileiro Paiva and Benjamín René Callejas Bedregal

Axioms 2022, 11(8), 395; https://doi.org/10.3390/axioms11080395 - 11 Aug 2022

Cited by 3 | Viewed by 1616

Abstract

The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, [...] Read more.

The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, this time focusing on another generalization, called general pseudo-overlap functions on lattices, which in a given classification system measures the degree of overlapping of several classes and for any given object where symmetry is an unnecessarily restrictive condition. Moreover, we also provide some methods of constructing these functions, as well as a characterization theorem for them. Also, the notions of pseudo-t-norms and pseudo-t-conorms are used to generalize the concepts of additive and multiplicative generators for the context of general pseudo-quasi-overlap functions on lattices and we explore some related properties. Full article

(This article belongs to the Section Logic)

7 pages, 302 KiB

Open AccessArticle

Non-Resonant Non-Hyperbolic Singularly Perturbed Neumann Problem

by Robert Vrabel

Axioms 2022, 11(8), 394; https://doi.org/10.3390/axioms11080394 - 11 Aug 2022

Cited by 1 | Viewed by 1348

Abstract

In this brief note, we study the problem of asymptotic behavior of the solutions for non-resonant, singularly perturbed linear Neumann boundary value problems

ε y^{″} + k y = f (t)

,

y^{'} (a) = 0

, [...] Read more.

In this brief note, we study the problem of asymptotic behavior of the solutions for non-resonant, singularly perturbed linear Neumann boundary value problems

ε y^{″} + k y = f (t)

,

y^{'} (a) = 0

,

y^{'} (b) = 0

,

k > 0,

with an indication of possible extension to more complex cases. Our approach is based on the analysis of an integral equation associated with this problem. Full article

(This article belongs to the Special Issue Singularly Perturbed Problems: Asymptotic Analysis and Approximate Solution)

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12 pages, 748 KiB

Open AccessArticle

On the Chromatic Index of the Signed Generalized Petersen Graph GP(n,2)

by Shanshan Zheng, Hongyan Cai, Yuanpei Wang and Qiang Sun

Axioms 2022, 11(8), 393; https://doi.org/10.3390/axioms11080393 - 10 Aug 2022

Viewed by 1774

Abstract

Let G be a graph and

σ : E (G) \to {+ 1, - 1}

be a mapping. The pair

(G, σ)

, denoted by

G_{σ}

, is called a signed graph. A (proper) [...] Read more.

Let G be a graph and

σ : E (G) \to {+ 1, - 1}

be a mapping. The pair

(G, σ)

, denoted by

G_{σ}

, is called a signed graph. A (proper) l-edge coloring

γ

of

G_{σ}

is a mapping from each vertex–edge incidence of

G_{σ}

to

M_{q}

such that

γ (v, e) = - σ (e) γ (w, e)

for each edge

e = v w

, and no two vertex–edge incidences have the same color; that is,

γ (v, e) \neq γ (v, f)

. The chromatic index is the minimal number q such that

G_{σ}

has a proper q-edge coloring, denoted by

χ^{'} (G_{σ})

. In 2020, Behr proved that the chromatic index of a signed graph is its maximum degree or maximum plus one. In this paper, we considered the chromatic index of the signed generalized Petersen graph

G P (n, 2)

and show that its chromatic index is its maximum degree for most cases. In detail, we proved that (1)

χ^{'} (G P_{σ} (n, 2)) = 3

if

n \equiv 3

mod 6

(n \geq 9)

; (2)

χ^{'} (G P_{σ} (n, 2)) = 3

if

n = 2 p (p \geq 4)

. Full article

(This article belongs to the Special Issue Graph Theory with Applications)

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