Explore the vast range of titles available.

In this paper, we propose a technique to solve LR -bipolar fuzzy linear system(BFLS), LR -complex bipolar fuzzy linear (CBFL) system with real coefficients and LR -complex bipolar fuzzy linear (CBFL) system with complex coefficients of equations. Initially, we solve the LR -BFLS of equations using a pair of positive ( ∗ ) and negative ( ∙ ) of two n × n LR -real linear systems by using mean values and left-right spread systems. We also provide the necessary and sufficient conditions for the solution of LR -BFLS of equations. We illustrate the method by using some numerical examples of symmetric and asymmetric LR -BFLS equations and obtain the strong and weak solutions to the systems. Further, we solve the LR -CBFL system of equations with real coefficients and LR -CBFL system of equations with complex coefficients by pair of positive ( ∗ ) and negative ( ∙ ) two n × n real and complex LR -bipolar fuzzy linear systems by using mean values and left-right spread systems. Finally, we show the usage of technique to solve the current flow circuit which is represented by LR -CBFL system with complex coefficients and obtain the unknown current in term of LR -bipolar fuzzy complex number.

Vendor selection is an established problem in supply chain management. It is regarded as a strategic resource by manufacturers, which must be managed efficiently. Any inappropriate selection of the vendors may lead to severe issues in the supply chain network. Hence, the desire to develop a model that minimizes the combination of transportation, deliveries, and ordering costs under uncertainty situation. In this paper, a multi-objective vendor selection problem under fuzzy environment is solved using a fuzzy goal programming approach. The vendor selection problem was modeled as a multi-objective problem, including three primary objectives of minimizing the transportation cost; the late deliveries; and the net ordering cost subject to constraints related to aggregate demand; vendor capacity; budget allocation; purchasing value; vendors’ quota; and quantity rejected. The proposed model input parameters are considered to be LR fuzzy numbers. The effectiveness of the model is illustrated with simulated data using R statistical package based on a real-life case study which was analyzed using LINGO 16.0 optimization software. The decision on the vendor’s quota allocation and selection under different degree of vagueness in the information was provided. The proposed model can address realistic vendor selection problem in the fuzzy environment and can serve as a useful tool for multi-criteria decision-making in supply chain management.

Over the last two decades, the panel data model has become a focus of applied research. While there are numerous proposals for soft regression models in the literature, only a few linear regression models have been proposed based on fuzzy panel data. However, these models have serious limitations. This study is an attempt to propose a kind of two-way fuzzy panel regression model with crossed effects, fuzzy responses and crisp predictors to overcome the shortcomings of these models in real applications. The corresponding parameter estimation is provided based on a three-step procedure. For this purpose, the conventional least absolute error technique is employed. Two real data sets are analyzed to investigate the fitting and predictive capabilities of the proposed fuzzy panel regression model. These real data applications demonstrate that our proposed model has good fitting accuracy and predictive performance.

The arithmetic operations on fuzzy numbers are the necessary tools for solving fuzzy equations. Unlike the addition, the procedure of multiplication of two fuzzy numbers is more demanding. In this paper, a new approximate multiplication formula for the LR fuzzy numbers is defined. Also, two simple applications of this new multiplication are presented. It is shown that, unlike the existing formulas, the proper fuzzy solution can be obtained by using the presented multiplication formula for some fuzzy algebraic equations.

Computer simulations are a powerful tool in many fields of research. This also applies to the broadly understood analysis of experimental data, which are frequently burdened with multiple imperfections. Often the underlying imprecision or vagueness can be suitably described in terms of fuzzy numbers which enable also the capture of subjectivity. On the other hand, due to the random nature of the experimental data, the tools for their description must take into account their statistical nature. In this way, we come to random fuzzy numbers that model fuzzy data and are also solidly formalized within the probabilistic setting. In this contribution, we introduce the so-called LR random fuzzy numbers that can be used in various Monte-Carlo simulations on fuzzy data. The proposed method of generating fuzzy numbers with membership functions given by probability densities is both simple and rich, well-grounded mathematically, and has a high application potential.

In the literature, several numerical methods are proposed for solving nth-order fuzzy linear diff?erential equations. However, till now there are only two analytical methods for the same. In this paper, the fuzzy Kolmogorov's di?fferential equations, obtained with the help of fuzzy Markov model of piston manufacturing system, are solved by one of these analytical methods and illustrated that the obtained solution does not represent a fuzzy number. To resolve the drawback of existing method, a new analytical method is proposed for solving nth-order fuzzy linear di?fferential equations. Furthermore, the advantage of proposed method over existing method is also discussed.

In a world where supply chains are increasingly complex and unpredictable, finding the optimal way to move goods through transshipment networks is more important and challenging than ever. In addition to addressing the complexity of transportation costs and demand, this study presents a novel method that offers flexible routing alternatives to manage these complexities. When real-world variables such as fluctuating costs, variable capacity, and unpredictable demand are considered, traditional transshipment models often prove inadequate. To overcome these challenges, we propose an innovative fully fuzzy-based framework using LR flat fuzzy numbers. This framework allows for more adaptable and flexible decision-making in multi-objective transshipment situations by effectively capturing uncertain parameters. To overcome these challenges, we develop an innovative, fully fuzzy-based framework using LR flat fuzzy numbers to effectively capture uncertainty in key parameters, offering more flexible and adaptive decision-making in multi-objective transshipment problems. The proposed model also presents alternative route options, giving decision-makers a range of choices to satisfy multiple requirements, including reducing costs, improving service quality, and expediting delivery. Through extensive numerical experiments, we demonstrate that the model can achieve greater adaptability, efficiency, and flexibility than standard approaches. This multi-path structure provides additional flexibility to adapt to dynamic network conditions. Using ranking strategies, we compared our multi-objective transshipment model with existing methods. The results indicate that, while traditional methods such as goal and fuzzy programming generate results close to the anti-ideal value, thus reducing their efficiency, our model produces solutions close to the ideal value, thereby facilitating better decision making. By combining dynamic routing alternatives with a fully fuzzy-based approach, this study offers an effective tool to improve decision-making and optimize complex networks under real-world conditions in practical settings. In this paper, we utilize LINGO 18 software to solve the provided numerical example, demonstrating the effectiveness of the proposed method.

A mediator variable is a variable that causes mediation in the dependent and the independent variables. The mediator variables play important roles in data analysis which involve several variables, especially when the dependent and independent variables are affected by other variables. Thus, mediation analysis is needed in almost all areas that need regression analysis especially in psychology, business, education, science, engineering area, etc. Mediation analysis has been proposed in many studies. However, sometimes it is much more reasonable to express the data using fuzzy theory when the variables are not clearly defined. For example, it is better to express the mood of a person “bad”, “moderate”, “good” using fuzzy numbers than using real numbers (crisp numbers). In this paper, several fuzzy mediation analysis models have been proposed. And confidence intervals and hypothesis tests are also provided. Several psychological data have been applied to find the total, direct and indirect effect when the mediator and confounding variable exist.

As a crucial concept of characterizing uncertainty, entropy has been widely used in fuzzy programming problems, while involving complicated calculations. To simplify the operations so as to broaden its applicable areas, this paper investigates the entropy within the framework of credibility theory and derives the formulas for calculating the entropy of regular LR fuzzy numbers by virtue of the inverse credibility distribution. By verifying the favorable property of this operator, a calculation formula of a linear function’s entropy is also proposed. Furthermore, considering the strength of semi-entropy in measuring one-side uncertainty, the lower and upper semi-entropies, as well as the corresponding formulas are suggested to handle return-oriented and cost-oriented problems, respectively. Finally, utilizing entropy and semi-entropies as risk measures, two types of entropy optimization models and their equivalent formulations derived from the proposed formulas are given according to different decision criteria, providing an effective modeling method for fuzzy programming from the perspective of entropy. The numerical examples demonstrate the high efficiency and good performance of the proposed methods in decision making.

A novel approach to the problem of regression modeling for fuzzy input-output data is introduced. In order to estimate the parameters of the model, a distance on the space of interval-valued quantities is employed. By minimizing the sum of squared errors, a class of regression models is derived based on the interval-valued data obtained from the $\\alpha$-level sets of fuzzy input-output data. Then, by integrating the obtained parameters of the interval-valued regression models, the optimal values of parameters for the main fuzzy regression model are estimated. Numerical examples and comparison studies are given to clarify the proposed procedure, and to show the performance of the proposed procedure with respect to some common methods.