Asian Journal of Fuzzy and Applied Mathematics
Asian Journal of Fuzzy and Applied Mathematics (AJFAM) ISSN (Online): 2321-564X
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Algorithm to Solve Spherical Fuzzy Optimization Problems with Applications
In operation research, a specific area being analysed in great depth is the optimization problem. The primary objective of this issue is to determine the most economical costs for commodities in order to satisfy customer requirements at various destinations, while taking into account the resources available at their points of origin or deals with assigning tasks to locations. In this paper, the spherical fuzzy optimization problem (SFOP) determines the optimal cost of carrying items from origin to destination (or job to machine). While reliable data is frequently employed, these variables are actually ambiguous and inaccurate. Many generalizations and expansions of fuzzy sets have been proposed and investigated in the literature. The spherical fuzzy set (SFS) is one of the most recent developments in fuzzy sets. It is capable of identifying neutral degrees in addition to membership and non-membership degrees. In this study, a proposed approach is developed to find the solution for each of all three form of the SFOP. For a better understanding, the suggested article includes six solved situations together with screen grabs of the output summaries from the software used for the calculations. Additionally, the unique approach's advantages over the current work are mentioned. Finally, conclusion and future scope direction are also given.
Copyright (c) 2025 Sudhir Kumar, Anita Kumari https://creativecommons.org/licenses/by-nc/4.0
A Concise Formula for Determining the Order and Error Constant of Fourth-Order Linear Multistep Method
In this study, we develop a concise and efficient formula for determining the order and error constants of fourth-order linear multistep methods used in the numerical solution of ordinary differential equations. Traditional approaches to computing these parameters often involve tedious algebraic manipulations, which can be time-consuming and error prone. This new approach provides a streamlined and systematic method that simplifies the analysis while ensuring accuracy and reliability. By leveraging this new approach, researchers can more efficiently assess the accuracy and stability of fourth-order linear multistep method schemes.
Fourth-order, Linear Multistep Method (LMM), Order and Error Constant.
Copyright (c) 2025 Ahmed Olajuwon Subair, A. M. Badmus https://creativecommons.org/licenses/by-nc/4.0
Analytical Construction of Uniformly Convergent Method for Convection Diffusion Problem
In this paper, we study the uniformly convergent method on equidistant meshes for the convection-diffusion problem of type; where the formal adjoint operator of L. Lu=-εu''+bu'+c u=f(x), u(0)=0, u(1)=0 At the end of the this paper we will generate the scheme; -e^(ρ_i )/(e^(ρ_i )+1) U_(i-1)+U_i-1/(e^(ρ_i )+1) U_(i+1)=(f_i-c_i U_i ) h/b ((e^(ρ_i )-1)/(e^(ρ_i )+1))
Local Green’s function, convection-diffusion problem, boundary value problem, boundary layer, singular points.
Copyright (c) 2021 Ali Filiz https://creativecommons.org/licenses/by-nc/4.0
Compactly Completeness and Finitarily Completeness on Continuous Information System
The plane here, introduce and study the concepts of bounded completeness and finitely completeness on continuous information system. Further more compactly completeness, finitarily completeness and strongly compactly completeness for continuous information system. Some interactions between these concepts are investigated. Some corresponding results in posets and domains due to R.Hechmann [5] are generalized.
continuous information system , compactly completeness, finitarily completeness, poset
Copyright (c) 2021 Mohammed M. Khalaf, Mohammed M. Ali Al-Shamiri https://creativecommons.org/licenses/by-nc/4.0
Unknown Values Estimation in Incomplete Fuzzy Soft and Interval Valued Soft Matrices
In day-to-day problems, incomplete information due to unknown values in data is the cause of the loss of information which leads to uncertainly, ambiguity and vagueness. There are many reasons for unknown values in data, like errors in data collection, lack of data information, inappropriate technique, and illegibility of data which cause incompleteness in data. Thus, estimating the unknown values in data of various information systems is an important area of research. In this communication, the definitions of incomplete Fuzzy soft and interval-valued fuzzy soft matrices are given with application in numerical problems. An algorithm is proposed for unknown values estimation in an incomplete fuzzy soft matrix and applied in solving a numerical problem. An application of an incomplete fuzzy soft matrix after inserting the unknown values in dimension reduction is studied. The unknown values in the incomplete interval-valued fuzzy soft matrix are also estimated and applied in the multi-criteria decision-making method.
Fuzzy soft set, Interval-valued Fuzzy soft set, Estimation, Fuzzy Soft Matrices and Dimension Reduction.
Application of Estimation Methods have been illustrated with numerical problems.
Copyright (c) 2021 D. S. Hooda, Seema Singh, S. C. Malik https://creativecommons.org/licenses/by-nc/4.0
A Sustainable Approach for Smart Supply Chain with Quality Humiliation and Carbon Emission Cost
Most decisive principles affecting customers’ ordering decision is quality of the products. The intention of the work is to provide the sustainable decisions such as order lot-size and total number of lot-size to create a smart SC in view of minimum carbon emissions and joint total cost. This research considers an imperfect production vendor-buyer inventory system involving quality degradation of raw material and carbon emission cost. The vendor’s production process produces some imperfect products, even manufactured products inspect twice, which are examined by buyer and those are return back to vendor in the subsequent shipment. We incorporate the emissions throughout the production processes, transport and storage. Mathematical based inventory model is developed to attain the sustainable decisions which are illustrated numerically.
Copyright (c) 2021 S. Priyan https://creativecommons.org/licenses/by-nc/4.0
Non-Convex Penalized Estimation of Count Data Responses via Generalized Linear Model (GLM)
This study provided a non-convex penalized estimation procedure via Smoothed Clipped Absolute Deviation (SCAD) and Minimax Concave Penalty (MCP) for count data responses to checkmate the problem of covariates exceeding the sample size . The Generalized Linear Model (GLM) approach was adopted in obtaining the penalized functions needed by the MCP and SCAD non-convex penalizations of Binomial, Poisson and Negative-Binomial related count responses regression. A case study of the colorectal cancer with six (6) covariates against sample size of five (5) was subjected to the non-convex penalized estimation of the three distributions. It was revealed that the non-convex penalization of Binomial regression via MCP and SCAD best explained four un-penalized covariates needed in determining whether surgical or therapy ideal for treating the turmoil.
Copyright (c) 2020 Rasaki Olawale Olanrewaju, Johnson Funminiyi Ojo https://creativecommons.org/licenses/by-nc/4.0
An Applied Component Modeling to the Irreversibility from a New Configurationally Perspective of the Statistical Physics
From the perspective of statistical physics (Boltzmann equation), configurational entropy can be calculated using the study of the microstates of the system. When a physical process is performed, identifying the entropy production can be used to investigate the irreversibility, but from the perspective of the Boltzmann equation, to study entropy production, both all microstates and macrostates must be studied. Therefore, a very large volume of calculations will be needed. In this report, using a new innovative energy structure equation, a new macroscopic component modeling is extracted to investigate the configurational irreversibility. To investigate the irreversibility in physical systems, the energy structure equation of the system can be studied in different paths. During performing a physical process, some activated energy components related to the reversible process and remain will be related to the irreversible process. In this report, also using a quasi-statistical approach, the structure of irreversible components is studied. When macroscopic energy components are the base of the equations, a very large volume of the needed calculations will be less than Boltzmann equation and in fact, studying all particles isn’t needed, but it is enough that a few macroscopic components to be investigated. Also, considering the theories of dissipated energy, the extracted equations have the same base as the different formulations of the second law of thermodynamics.
Statistical Physics; Irreversibility Structure; Irreversibility components; Energy Structure; Energy components
Copyright (c) 2020 Saeed Shahsavari, Mehran Moradi https://creativecommons.org/licenses/by-nc/4.0
A Mathematical Study on a Diseased Prey-Predator Model with Predator Harvesting
In this paper, we present a mathematical model for a prey-predator system with infectious disease in the prey population. We assumed that there is harvesting from the predator and a defensive property against predation. This model is constituted by a system of nonlinear decoupled ordinary first order differential equations, which describe the interaction among the healthy prey, infected prey and predator. The existence, uniqueness and boundedness of the system solutions are investigated. Local stability of the system at equilibrium points is discussed.
Pre-predator model, Equilibrium points, Stability Analysis, Non-linear differential equations
Copyright (c) 2020 https://creativecommons.org/licenses/by-nc/4.0
Use of Fuzzy Matrices for the Diagnosis of Diabetes, Anaemia and Hypertension
The mathematical model presented here aims to enhance the precision in diagnostic process of diabetes, anaemia and hypertension by means of fuzzy interface. In real life, the imprecise nature of medical documentation and uncertain information provided by patients often do not give the desired degree of confidence to the diagnosis. To that end using the capability of fuzzy logic in representing, interpreting and utilizing data and information that are vague and lack certainty, a new algorithm based on different fuzzy matrices and fuzzy relations is developed. In the process a medical knowledge base is developed with the help of 51 doctors. The model achieved 94.44% accuracy in the diagnosis, which shows its usefulness. To implement this model-based diagnosis procedure a user-friendly Excel program is designed.
Fuzzy logic, fuzzy matrices, max-min product, Chi-square test.
Copyright (c) 2020 Rajeev Gajanan Sapre, Muktai Milind Desai, Mugdha Mahesh Pokharanakar https://creativecommons.org/licenses/by-nc/4.0
Some Results on Fuzzy Topological Modules and Fuzzy Topological Submodules
In this paper, we bring together the structure of fuzzy topological space ,fuzzy module and that of fuzzy ring to form a combined structure, that of a fuzzy topological R-module. Properties of fuzzy topological R-module ,topological R-submodule and its Properties are also briefly examined. we proved many theorems and corollaries as results shown in this paper.
A New Generalized Entropy Measure and its Properties
Â In this research article, a new two parametric measure of Entropy Â and its corresponding code word length Â has been developed. The developed measures are the generalizations to some well known existing measures. Besides, some noiseless coding theorems for discrete noiseless channel have been developed, and the results thus obtained have been verified with the support of an numerical example. Also, at the end of this research article, a comparative study in terms of Â monotonic behavior Â among the proposed entropy Â , Matahi’s entropy Â and Tsallis entropy Â together Â with their respective average code word length measures have been made and graphically displayed.
Shannon Fanno Codes and Noiseless Coding theorem.
Fuzzy Equivalence Relation, Fuzzy Congrunce Relation and Fuzzy Normal Subgroups on Group G Over T-Norms
In this study, by using t-norms, fuzzy equivalence relation, fuzzy congrunce relation on group G, fuzzy relation of subgroup H of group G, fuzzy normal subgroups of fuzzy subgroups, direct product of fuzzy subgroups(normal fuzzy subgroups) are introduced and some the their properties will be discussed. Next by using group homomorphisms, the image and pree image of them will be investigated.
Probability Functions of Order Statistics from Discrete Uniform Distribution
In this paper, we firstly give basic definitions and theorems for order statistics. Later, we show that r. probability function of order statistics from discrete uniform distribution can be obtained in another form.
Scalar Singularly Perturbed Cauchy Problem for a Differential Equation of Fractional Order
In this paper we consider initial problem for an ordinary differential equation of fractional order with a small parameter for the derivative. S.A. Lomov regularization method is used to construct an asymptotic approximate solution of the problem with accuracy up to any power of a small parameter. Using the computer mathematics system (CMS) Maple, a symbolic solution of the original problem is obtained, and solution schedules are constructed, depending on the initial data and various values of the small parameter. It is shown that the asymptotic solution presented in the form of a specific convergent series and the solution represented by the CMS Maple coincides with the exact solution of the original problem. Â
About Solution of the Nonlinear Generalized Abel Integral Equation
As is known, many problems of electronics, nuclear physics, optics and astrophysics, etc. are described by the Abel integral equation of the first kind. In this paper we consider the nonlinear generalized Abel equation and show that its solution can be represented as an integral of a power function. It is shown that the constructed analytical solution and the symbolic solution obtained by means of the computer mathematics system Maple coincides, and their planar and spatial graphs are presented.
On the Question of Asymptotic Integration of Singularly Perturbed Fractional-Order Problems
In this paper we consider an initial problem for systems of differential equations of fractional order with a small parameter for the derivative. Regularization problem is produced, and algorithm for normal and unique solubility of general iterative systems of differential equations with partial derivatives is given. Â
differential equation of fractional order
Regularization Method for Nonlinear Singularly Perturbed Systems of Fractional Order
The paper is devoted to construction of an asymptotic solution of a weakly nonlinear singularly perturbed differential system of fractional order. To construct the asymptotic solution we use ideas of normal differential forms method of V.F. Safonov. In the environment of the computer mathematical system Maple, approximate solutions are calculated, and corresponding solution schedules for various values of a small parameter are constructed.
Nonlinear differential equation of fractional order
On a New Modification of Homotopy Analysis Method for Solving Nonlinear Nonhomogeneous Differential Equations
In this paper, new powerful modification of homotopy analysis technique (NMHAM) was submitted to create an approximate solution of nonhomogeneous nonlinear ordinary and partial differential equations. The NMHAM is a combination of the new technique of homotopy analysis method(NHAM) [4] and the new technique of homotopy analysis method(nHAM) [7].Three illustrative examples are employed to illustrate the accuracy and computational proficiency of this approach. The outcomes uncover that the NMHAM is more accurate than the NHAM and nHAM.
On Recent Modifications of Extended Weibull Families Distributions and Its Applications
Â The paper discusses an extended form of family of Weibull distributions and some important cases of this distributions. The family of Weibull distributions and its derivate models finds many applications. The author proposes a new six parameters extended Weibull model, which generalizes the family of weibull distributions. The applicability of the new models is well justified by means of two real data sets. Several methods are used to estimate the Weibull parameters which are (MLE) and (ME). Various properties of this new family are investigated and then exploited to derive several related results, especially characterizations, in probability. As a motivation, the statistical applications of the results based on health related data are included which investigates reliability properties of a flexible extended weibull family of distributions. The findings of this work will be useful for the practitioners in various fields of theoretical and applied sciences.
On the Globally Asymptotically Stability of Periodic Solutions of a Certain Class of Non-Linear Delay Differential Equations
The objective of this paper is to investigate and give sufficient conditions that will guarantee globally asymptotically stable periodic solutions of the non-linear differential equations with delay of the form (1.1). the Razumikhin’s technique was improve upon, to enhance better results equation (1.2) was studied along side with equation (1.1). Equation (1.2) is an integro-differential equations with delay kernel. The coefficients of (1.2) are periodic, and the equation can be rewritten as in form of (3.1), where a,b and c ≥ 0 and -periodic continuous function on R.G ≥ 0, is a normalized kernel from equation (1.2). Equation (1.2) enable Â us to defined equation (3.1) as a fixed point. Since the defined operator “Bâ€ for equation (3.1) are not empty, claim ( 1-iv) enable us to use the fixed point theorem to investigate and established our defined properties. (Theorem 3.1 Lemma 3.1 and Theorem 3.2) was used to prove for periodic and asymptotically stability and the Liapunovis direct (second) method was used to prove our main result. See, (Theorem 3.3, 3.4 and 3.5) Â which Â established the objective of this study.
Strict Fuzzy Triangular and Trigonometric Exponential Truncated Distributions
In this paper, based on the definition of strict fuzzy probability introduced by Abed, et. al. (2016) we will show how we can construct strict fuzzy membership function from classical fuzzy membership function introduced by Zadeh (1965). This technique will be applied to triangular and trigonometric fuzzy memberships. Once we reach that result we will introduce strict fuzzy exponential triangular and trigonometric distributions and some of their properties.
Nonstructural Flood Control using Multi-reservoir Operation
Nonstructural flood damage minimization through optimizing a short term multi-reservoir system operation is considered in this paper using a simulation-based optimization model. The well known evolutionary computation technique of particle swarm optimization (PSO) has been combined with a simulation model of river flood routing. The hydraulic routing model includes numerical solution of unsteady gradually varied flow equations by Preissmann method. The developed model has been used in a three-reservoir system as a real case study southwest of Iran. The results show applicability and efficiency of the proposed simulation-optimization model in determining optimal reservoir releases.
Searching Web Documents Using a Fuzzy-Based Method
Web searching could be more fruitful if a user could easily find documents which satisfy his/her needs in terms of structure, format and contents. Herein a solution through a fuzzy linguistic description of the document is proposed, a linguistic variant of standard metadata types. Linguistic expressions are used to qualitatively represent both meta-information and user needs and a matching system is developed to select the most compatible documents with the user profile. The documents retrieved by a web search engine are organized in clusters and ordered in each cluster.
A Hybrid Modified Approach for Solving Fuzzy Differential Equations
In this paper, a hybrid method is presented by combining Laplace transformation and variational iteration method for solving fuzzy differential equations with fuzzy initial and boundaries values. A defuzzification technique had been implemented to convert the fuzzy parameters into crisp values by building an extended ranking method. Then the method is implemented on the new problem in which two approaches has been built according to the formula of Lagrange multiplier obtaining the lower, upper and center solutions.
On The Formal–Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics
Random Fixed Point Result of Weak Contraction
We define Cone random metric space and find some fixed point results for weak contraction condition.
Buoyancy Driven Convection in a Liquid Layer with Insulating Permeable Boundaries
In this paper, we investigate the onset of buoyancy driven thermal convection in a horizontal layer of fluid with thermally insulating permeable boundaries, using the classical linear stability analysis. It is proved that the principle of exchange of stabilities is valid. The eigenvalue problem is solved by using the Galerkin method. Results are obtained and discussed for a wide range of values of the boundary parameters characterizing the permeable nature of boundaries. Attention is focused on a situation where the value of the critical Rayleigh number is less than that for the case when one of the boundaries is rigid while the other one is free and the convection is not maintained in general. In the case, when permeability parameter of either one of the two boundaries varies inversely to that of the other, we discover that the critical Rayleigh number decreases and goes through a lowest minimum at a certain value of the permeability parameter and this situation pertains when the critical wave number is zero. In addition, existing results for various combinations of the boundary conditions namely, when both the bounding surfaces are either dynamically free or rigid and when either one of them is dynamically free while the other one is rigid, are obtained as limiting cases of the boundary parameters.
Effect of Magnetic Field on Rayleigh Bénard Marangoni Convection in a Relatively Hotter or Cooler Layer of Liquid with Insulating Boundaries
The effect of the uniform vertical magnetic field acting opposite to gravity on the onset of steady Rayleigh-Bénard-Marangoni convection in horizontal layer of an electrically conducting liquid is investigated, using the modified linear stability theory. The upper surface of liquid layer is free where surface tension gradients arise on account of variation of temperature and the lower boundary surface is rigid, each subject to the constant heat flux condition. Both mechanisms namely, surface tension and buoyancy causing instability are taken into account. The Galerkin method is used to obtain the eigenvalue equation which is then computed numerically. Results of this analysis indicate that the critical eigenvalues in the presence of a uniform magnetic field are greater in a relatively hotter layer of liquid than a cooler one under identical conditions otherwise. The asymptotic behaviour of both the Rayleigh and Marangoni numbers for large values of the Chandrasekhar number is also obtained. During the course of this analysis, we also correct the inaccuracies in the work of earlier authors.
Fuzzy Nonparametric Predictive Inference for the Reliability of Series Systems
This paper presents fuzzy lower and upper probabilities for the reliability of series systems. Attention is restricted to series systems with exchangeable components. In this paper, we consider the problem of the evaluation of system reliability based on the nonparametric predictive inferential (NPI) approach, in which the defining the parameters of reliability function as crisp values is not possible and parameters of reliability function are described using a triangular fuzzy number. The formula of a fuzzy reliability function and its α-cut set are present. The fuzzy reliability of structures defined based on a fuzzy number. Furthermore, the fuzzy reliability functions of series systems discussed. Finally, some numerical examples are present to illustrate how to calculate the fuzzy reliability function and its α-cut set. In other words, the aim of this paper is present a new method titled fuzzy nonparametric predictive inference for the reliability of series systems.