Fuzzy Sense Research Articles

Impact of the Prey Refuge Parameter in the Presence of Fear Effect on the Fuzzy Two-Prey–One Predator Model with Switching Effect

It has been thought of as a class of models where a generalist predator feeds on two distinct prey species. We wish to examine how prey refuge factors affect prey–predator models when fear effects are present. In order to achieve this, a two-prey–one predator model with prey refuge has been taken into consideration in the presence of the predator’s fear effect on two prey species. Both prey species engage in intra-specific competition. We enhance our model by including a switching mechanism in predation. In order to account for the inherent imperfection of environmental conditions, some parameters have been taken as fuzzy numbers. Analytical and numerical results on the system have been examined in fuzzy sense. The system’s positivity, boundedness, and permanence are examined. The system’s local and global stability analyses have been investigated. Hopf bifurcation analysis around the positive interior equilibrium point has been explored. The stability of the limit cycle of our suggested fuzzy system has been discussed. The system’s numerical simulations have been investigated with pertinent tables and graphical illustrations. When the prey refuge parameter and fear parameter exceed the critical value, the system experiences Hopf bifurcation at the positive interior equilibrium point.

On Covering Properties in Intuitionistic Fuzzy Topological Spaces: A survey

We show here some results on covering properties in intuitionistic fuzzy topological spaces. In 1983, K.T. Atanassov proposed a generalization of the notion of fuzzy set: the concept of intuitionistic fuzzy set. D. Çoker constructed the fundamental theory on intuitionistic fuzzy topological spaces, and D. Çoker and other mathematicians studied compactness, connectedness, continuity, separation, convergence and paracompactness in intuitionistic fuzzy topological spaces. Finally, G.-J Wang and Y.Y. He showed that every intuitionistic fuzzy set may be regarded as an L-fuzzy set for some appropriate lattice L. Nevertheless, the results obtained by above authors are not redundant with other for ordinary fuzzy sense.

An Approach to Solve Gas Dynamic Equation by Fuzzy Hilfer Fractional Differential Equation

In this work, Adomian decomposition method (ADM) based on Hilfer derivative is proposed to solve nonlinear fuzzy fractional gas dynamic equation. We reform the provided fractional gas dynamic equation into fuzzy Hilfer fractional differential equation. Subsequently with description of Hilfer fractional derivative and suitable initial conditions under fuzzy sense, we obtain approximate solution to the given problem. This method provides an analytical solution in the form of infinite power series. The behavior of the solution is illustrated using graphical representation.

A Legitimate Productive Repertoire Replica Betwixt Envirotech Outlay Towards Fragile Commodities Using Trapezoidal Neutrosophic Fuzzy Number

This present contemplate confers a productive repertoire replica in which ultimatum is appraised as a basis of medical utilization of fragile commodities by the juvenile diabetes. Abundant embalming mechanisms are drawn on to preserve the Confectionary from putrefaction over time. It is consequential to ascertain that greenhouse gas emissions by virtue of transportation, production and storage of Confectionary is susceptible to putrefaction that has to be steered up. This contemplate recommends an optimal productive repertoire replica considering the production and inventory components for commodities contingent to decline in fuzzy sense using trapezoidal neutrosophic fuzzy number. To determine the minimal overall cost, a comparative study of different cases is authenticated by working out numerical examples using models.

Picture Fuzzy Subgroup

Picture fuzzy subgroup of a crisp group is established here and some properties connected to it are investigated. Also, normalized restricted picture fuzzy set, conjugate picture fuzzy subgroup, picture fuzzy coset, picture fuzzy normal subgroup and the order of picture fuzzy subgroup are defined. The order of picture fuzzy subgroup is defined using the cardinality of a special type of crisp subgroup. Some corresponding properties are established in this regard. Significant Statement. Subgroup is an important algebraic structure in the field of Pure Mathematics. Study of different properties of subgroup in fuzzy sense is an interesting fact to the readers because fuzzy sense is the extension of classical sense. Readers can easily observe how the properties of subgroup hold in fuzzy sense like classical sense. Picture fuzzy sense is the generalization of fuzzy sense. In other words, picture fuzzy sense can be treated as advanced fuzzy sense. Readers will be interested to study how the properties of subgroup hold when the number of components increases in fuzzy environment. Our study is actually the study of an important type of advanced fuzzy algebraic structure.

Impact of Fear and Prey Refuge Parameters in a Fuzzy Prey–Predator Model with Group Defense

Prey–predator interactions are perhaps the most ordinarily noticed phenomena in the environment. In this article, we have proposed a three-species prey–predator model incorporating three important factors, namely, prey refuge, group defense, and the growth rate of two prey species which is reduced for the amount of fear of the predator species. All the biological parameters of our system have been presented as fuzzy numbers to make them more realistic. The system has been studied analytically and numerically in the fuzzy sense. Model analyses such as positivity, boundedness, and permanence of the system are investigated. Stability analysis at all equilibrium points of the system has been studied. Hopf bifurcation analysis around the positive interior equilibrium point has been discussed. All the numerical simulations of the system are presented with suitable tables and graphical diagrams by using MATHEMATICA and MATLAB. Numerically, we have seen that the fear effect and prey refuge parameter can stabilize the system from chaos to a stable region. The effect of fear and prey refuge on stability has been analyzed in the numerical section. Stable focus and limit cycle analysis are investigated in crisp as well as fuzzy environment. The system undergoes Hopf bifurcation at the positive equilibrium point when the fear parameter [Formula: see text] and refuge parameter [Formula: see text] cross the threshold value in crisp as well as fuzzy environment.

On the notion of fuzzy dispersion measure and its application to triangular fuzzy numbers

In this paper, based on the analysis of the most widely used dispersion measure in the real context (namely, the variance), we introduce the notion of fuzzy dispersion measure associated to a finite set of data given by fuzzy numbers. This measure is implemented as a fuzzy number, so there is no loss of information caused by any defuzzification. The proposed concept satisfies the usual properties in a genuinely fuzzy sense and it avoids limitations in terms of its geometric shape or its analytical properties: under this conception, it could have a piece of its support in the negative part of the real line. This novel notion can be interpreted as a way of fusing the information included in a fuzzy data set in order to make a decision based on its dispersion. To illustrate the main characteristics of this approach, we present an example of a fuzzy dispersion measure that allows to conclude that this new way to deal this problem is coherent, at least, from the point of view of human intuition.

Pareto Optimal Solution of a Fuzzy Newsboy Problem

In this paper, a multi-item classical newsboy problem is formulated, occurring both fuzziness and randomness with floor space constraint. Here, the demand is considered as a random variable in fuzzy sense and also the purchase cost, salvage value, and selling price are fuzzy numbers. Initially, a method is explained for solving such a problem by using the minimization of a FN by Buckley [Buckley, JJ (2003). Fuzzy probabilities: New approach and applications]. Then the fuzzy programming technique, [Formula: see text]-constraint, and the weighted sum methods are applied to handle the multiobjective programming problem. The basic idea for transforming the fuzzy stochastic programming problem into a deterministic equivalent has been discussed. Finally, the deterministic model is solved by the LINGO package and is illustrated numerically.

Fuzzy Inventory Model for Imperfect Items with Price Discount and Penalty Maintenance Cost

The present paper considers the fuzzy economic manufacturing model (FEMM) for an inventory model with an imperfect production process that has been studied along with rework. During the pandemic, it is evident that the products accumulated without a sale, which has increased the maintenance cost of the products. This research paper compares a special sale of products with discount and without discount prices both in the fuzzy environment and in the crisp case. New computing methods based on fuzzy logic are being utilized to enhance identification, decision making, and optimization. A triangular fuzzy number is applied in the economic production quantity to emphasize the importance of optimal manufacturing. The EPQ model’s optimal total cost is obtained in the crisp version. It is to be noted that this model is developed in the fuzzy sense by using the deterioration as a triangular fuzzy number. The applications of this model in the fields are constructing customized industrial machinery or heavy‐duty construction equipment, specific chemicals, and processed food. By using MATLAB R2021, a numerical example of the optimal solution is provided. Finally, the present research discusses how changing several parameters affects the optimum total cost.

Fuzzy EPQ Model for Green Quality Products of Three Step Production Processes

Abstract: Most commercial industries now encourage environmentally friendly or green products since they are safe for the environment in their creation, use, and disposal. Eco-friendly items serve an important role in decreasing pollution both during production and recycling. To ensure client happiness, most branded products are developed in an environmentally friendly manner. This research proposes a cost-effective manufacturing quantity model that promotes high-quality green products. To solve the model in a fuzzy sense, an extension of the lagrangian method is applied. The parameters are expressed as a fuzzy pentagonal number. Defuzzification is accomplished using the graded mean integration approach. To demonstrate the model, a numerical example is provided.

Application of Mathematical Modeling in Multi Criteria Decision Making Process: Intuitionistic Fuzzy PROMETHEE

In this paper, the intuitionistic fuzzy PROMETHEE method is explained in detail and an original application has been made. The aim of the paper is to bring innovation to the evaluation system in the field of education by using the intuitionistic fuzzy PROMETHEE method. The advantages of using the PROMETHEE method, which is one of the many methods used in multi-criteria decision-making problems, in the intuitionistic fuzzy sense are explained in detail. Intuitionistic fuzzy PROMETHEE is a method that attracts our attention thanks to its benefits such as allowing the researcher to observe the positive and negative rankings simultaneously, expressing the degree of hesitation, changing the significance weights of the criteria, and using different methods when identifying the significance levels for each criterion, putting the degree of hesitation of significance weights into action, and enabling decision-makers, who are given the opportunity to use different criteria types and different criteria types for alternatives and criteria, to establish a unique system; moreover, the method also provides us numerous advantages while using it in our application area. It is of great importance for decision-makers to determine the specific importance level for each criterion. In this paper, controlled sets are used to express the importance of the criteria in the form of intuitionistic fuzzy values. The intuitionistic fuzzy-based PROMETHEE algorithm, aiming to contribute to the education system by examining the factors affecting the students' achievement, is a unique algorithm, and it is the first to shed light on various researchers.

A cost analysis on Multi-item Inventory model for Factory Outlets with investment constraint under ranking Asteroid Fuzzy Set

Purpose of the study: A multi-item inventory model for factory outlets in crisp and fuzzy sense are formulated in the fuzzy environment with investment under one constraint has been considered. In this model, demand is constant and is related to the price per unit item. The asteroid fuzzy set is defined and is properties are given.
 Methodology: The parameters involved in this model represented by asteroid fuzzy set. The average total cost is defuzzify by ranking method.
 Main Findings: The analytical expressions for maximum inventory level and average total cost are derived for the proposed model by using nonlinear programming technique. A numerical example is presented to illustrate the results.
 Applications of this study: Ranking Asteroid fuzzy set is considered profitable in small businesses. Here we considered the factory outlet .Also its use is considered to help the small scale entrepreneurs during festival period and pandemic situation.
 Novelty/Originality of this study: In this paper, a novel approach to handle the asteroid fuzzy set is proposed. It uses ranking the cost parameters of the asteroid fuzzy set with the best approximation level. The parameters involved are asteroid fuzzy set and are all ill-defined in nature.

A dynamical study of a fuzzy epidemic model of Mosquito-Borne Disease

Numerical models help us to understand the transmission dynamics of infectious diseases. Since vectors transmit many diseases, vector host models are very important. The transmission dynamics of Dengue fever with an incubation period of the virus with fuzzy parameters have been analyzed in this article. Sometimes it is very difficult and almost impossible to collect numerical data as a fixed value. Due to the lack of precise numerical data for the parameters, the fuzzy model is considered here. Fuzzy theory is a very powerful mathematical tool for dealing with imprecision and uncertainties. In this article, the chance of the occurrence of dengue infection βh(a), the recovery rate r(a) and the mortality rate of the human population μh(a) due to dengue fever are considered fuzzy numbers. The stability of equilibrium points of the model has been determined and a reproduction number has been derived respectively in a fuzzy sense. A numerical model is designed for the studied model having fuzzy parameters and some numerical experiments are performed which indicate that the proposed method shows positivity, stability, and convergence at each time step size. Hence the method preserves the essential features of the dynamic epidemic models.

An Efficient Method for Solving Second-Order Fuzzy Order Fuzzy Initial Value Problems

In this paper, we present an accurate numerical approach based on the reproducing kernel method (RKM) for solving second-order fuzzy initial value problems (FIVP) with symmetry coefficients such as symmetric triangles and symmetric trapezoids. Finding the exact solution of FIVP is not an easy task since the definition will produce a complicated optimization problem. To overcome this difficulty, a numerical method is developed to solve this type of problems. We start by introducing the necessary definitions and theorems about the fuzzy logic. Then, we derived the kernels for two Hilbert spaces. The RKM is derived for the second-order IVP in the Boolean sense, and then we generalize it for the fuzzy sense. Numerical and theoretical results will be given to obtain the accuracy of the developed technique. We solved four linear and non-linear fuzzy IVPs numerically using the proposed method, and we compute the error in each case to show the efficiency of the method. The absolute error was very small in the four examples.

Multivariate fuzzy neural network interpolation operators and applications to image processing

In this paper, we introduce a novel family of multivariate fuzzy neural network interpolation operators activated by sigmoidal functions belonging to the new class of multivariate sigmoidal functions. To present an alternative way to the well-known shortcomings of the Hukuhara difference, we use a proper function defined on a set of fuzzy n-cell numbers. Moreover, we construct the Kantorovich variant of fuzzy NN interpolation operators, and also achieve approximation properties via Lp-type metric with respect to both modulus of continuity and Lp-modulus of continuity in fuzzy sense. Various special examples for the class of multivariate sigmoidal functions are presented. Also, we give some illustrative examples to demonstrate the approximation performances of all the above operators. Finally, we give a novel interpolation algorithm involving a multidimensional fuzzy inference system with applications in color image resizing and inpainting.

On the concept of solutions for fuzzy fractional initial value problem

It is evident that fuzzy arithmetic is different than that of normal arithmetic due to the different classes of functions and symbols. This article is concerned with an appropriate definition of the fractional derivative and integral in a fuzzy sense and a new concept of solutions for a fuzzy Caputo fractional initial value problem (IVP) is presented. Further, under some sufficient conditions on IVP, the existence, uniqueness, and stability results of the solution are established by applying the iterate methods. For the validation of established results, a particular fuzzy fractional Riccati differential equation is presented.

Fuzzy fractional mathematical model of COVID-19 epidemic

In this paper, we develop a mathematical model with a Caputo fractional derivative under fuzzy sense for the prediction of COVID-19. We present numerical results of the mathematical model for COVID-19 of most three infected countries such as the USA, India and Italy. Using the proposed model, we estimate predicting future outbreaks, the effectiveness of preventive measures and potential control strategies of the infection. We provide a comparative study of the proposed model with Ahmadian’s fuzzy fractional mathematical model. The results demonstrate that our proposed fuzzy fractional model gives a nearer forecast to the actual data. The present study can confirm the efficiency and applicability of the fractional derivative under uncertainty conditions to mathematical epidemiology.

Fuzzy Soc-Semi-Prime Sub-Modules

In this paper, we study a new concept of fuzzy sub-module, called fuzzy socle semi-prime sub-module that is a generalization the concept of semi-prime fuzzy sub-module and fuzzy of approximately semi-prime sub-module in the ordinary sense. This leads us to introduce level property which studies the relation between the ordinary and fuzzy sense of approximately semi-prime sub-module. Also, some of its characteristics and notions such as the intersection, image and external direct sum of fuzzy socle semi-prime sub-modules are introduced. Furthermore, the relation between the fuzzy socle semi-prime sub-module and other types of fuzzy sub-module presented.

On fuzzy numerical model dealing with the control of glucose in insulin therapies for diabetes via nonsingular kernel in the fuzzy sense

<abstract><p>Very recently, several novel conceptions of fractional derivatives have been proposed and employed to develop numerical simulations for a wide range of real-world configurations with memory, background, or non-local effects via an uncertainty parameter $ [0, 1] $ as a confidence degree of belief. Under the complexities of the uncertainty parameter, the major goal of this paper is to develop and examine the Atangana-Baleanu derivative in the Caputo sense for a convoluted glucose-insulin regulating mechanism that possesses a memory and enables one to recall all foreknowledge. However, as compared to other existing derivatives, this is a vitally important point, and the convenience of employing this derivative lessens the intricacy of numerical findings. The Atangana-Baleanu derivative in the Caputo sense of fuzzy valued functions (FVF) in parameterized interval representation is established initially in this study. Then, it is leveraged to demonstrate that the existence and uniqueness of solutions were verified using the theorem suggesting the Banach fixed point and Lipschitz conditions under generalized Hukuhara differentiability. In order to explore the regulation of plasma glucose in diabetic patients with impulsive insulin injections and by monitoring the glucose level that returns to normal in a finite amount of time, we propose an impulsive differential equation model. It is a deterministic mathematical framework that is connected to diabetes mellitus and fractional derivatives. The framework for this research and simulations was numerically solved using a numerical approach based on the Adams-Bashforth-Moulton technique. The findings of this case study indicate that the fractional-order model's plasma glucose management is a suitable choice.</p></abstract>

Construction and numerical analysis of a fuzzy non-standard computational method for the solution of an SEIQR model of COVID-19 dynamics

<abstract> <p>This current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.</p> </abstract>