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This research addresses the Inventory-Routing Problem (IRP) with priority customers under conditions of uncertainty. The problem involves devising a plan to supply a set of customers from a facility, establishing precedence rules, and making transportation and inventory management decisions while considering uncertainty in customer demand. Priority in deliveries is assigned to customers in the health sector in accordance with government regulations. Companies must uphold product quality for health sector customers while simultaneously aiming to minimize total costs. We propose a fuzzy mixed-integer linear programming model to solve the IRP with priority customers and uncertainty in demand rates, modeled using triangular fuzzy numbers. To convert the fuzzy linear programming model into a deterministic one, an ordering method for fuzzy numbers is applied. The model is implemented using CPLEX, and a set of benchmark instances is solved. The primary results indicate that prioritizing customers leads to an increase in total costs due to visiting these customers first on each route created. Additionally, routes without priority customers exhibit higher average vehicle capacity utilization. In most cases, the solutions obtained maintain quality within the specified time limits. [ABSTRACT FROM AUTHOR]

An alternative new method for solving an epistemic uncertainty such as fuzzy-based linear programming problem with equality constraints has been proposed here. In this approach, the optimal solution of the considered fuzzy problem has been achieved by solving a related crisp problem. Moreover, the objective function of the crisp problem has been obtained by taking the linear combination of the fuzzified version of the original uncertain objective function. The coefficients of the linear combination are considered as strictly positive real numbers. And the constraints of the crisp problem are obtained equivalently from the equality constraints of the fuzzy problem. Triangular fuzzy numbers are considered for this analysis. Comparisons have been made with the results of Kumar et al. (Appl Math Model 35:817–823, 2011), Najafi and Edalatpanah (Appl Math Model 37:7865–7867, 2013), Ezzati et al. (Appl Math Model 39:3183-3193, 2015) and Ghoushchi et al. (Mathematics 9:2937, 2021. https://doi.org/10.3390/math9222937). [ABSTRACT FROM AUTHOR]

The necessarily optimal solution is known as the most reasonable solution to linear programming problems with interval/fuzzy objective function coefficients. As it remains optimal against the certain fluctuations of objective function coefficients, the necessarily optimal solution can be seen as a robust optimal solution. In this paper, we demonstrate that the necessary optimality degree of a non-degenerate basic feasible solution can be obtained easily by utilizing the tolerance approach. The necessary optimality degree evaluates to what extent the solution remains optimal against the fluctuations of objective function coefficients. Several types of fuzzy subsets showing the possible range of the objective function coefficient vector are considered. For each type of fuzzy subset, an efficient calculation method of necessary optimality degree is proposed. Numerical examples are given to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Nowadays, the intensification of a competitive environment in markets in conjunction with sustainability issues has forced organizations to concentrate on designing sustainable closed-loop supply chains. In this study, a sustainable closed-loop supply chain network is configured under uncertain conditions based on fuzzy theory. The proposed network is a multi-product multi-period problem which is formulated by a bi-objective mixed-integer linear programming model with fuzzy demand and return rate. The objectives are to maximize the supply chain profit and customer satisfaction at the same time. Moreover, the carbon footprint is included in the first objective function in terms of cost (tax) to affect the total profit and treat the environmental aspect. Fuzzy linear programming and Lp-metric method are then applied to deal with the uncertainty and bi-objectiveness of the model, respectively. In order to validate the methodology, a case study problem in the dairy industry is investigated where the proposed Lp-metric is also compared to goal attainment method. The obtained results demonstrate the superiority of Lp-metric against goal attainment method as well as the applicability and efficiency of the proposed methodology to treat a real case study problem. Furthermore, from the management perspective, outsourcing the production during high-demand periods is highly recommended as an efficient solution. [ABSTRACT FROM AUTHOR]

In this study, we first show that the existing arithmetic operations of trapezoidal fuzzy numbers do not satisfy the basic properties. Then, for trapezoidal fuzzy numbers, we define new arithmetic operations. Furthermore, we demonstrate that the existing Simplex method for addressing fully fuzzy linear programming problems has some drawbacks. Finally, we provide a new strategy for solving fully fuzzy linear programming problems and compare our results with the existing methods. [ABSTRACT FROM AUTHOR]

Network planning is an important design-step wherein various network resources are provisioned at different network locations. Traffic demand for all node pairs in the network is an important determining factor for network planning, and typically, a static traffic demand matrix consisting of long-term average traffic values for all node pairs is employed. However, assessment of traffic demand matrix may not be accurate (precise). In this paper, we propose an optimization framework to minimize traffic congestion in a wavelength-routed wavelength-division multiplexing WDM optical backbone network using such approximate traffic demands. Modeling such a network is constrained by limited network resources, and can be formulated in general as a fuzzy optimization problem. Moreover, decision maker might want to relax traffic congestion goal by a small margin in presence of approximate traffic demand matrix, so as to reach some aspiration level, rather missing the crisp target by a very small amount. We use the network planning model to minimize traffic congestion so as to achieve an aspiration level of traffic congestion. We use Zimmermann's fuzzy programming technique to explore mixed integer linear programing based optimization model incorporating fuzzified constraints and objective function. All related constraints, such as traffic and lightpath routing, wavelength selection, restriction due to average propagation delay, lightpath degree and maximum hop count constraints are taken into consideration. Following the proposed model, under fuzzy environment, we implement reliable and efficient network planning and traffic provisioning, and estimate traffic congestion more accurately. [ABSTRACT FROM AUTHOR]

Environmental concerns are on the rise around the world, as carbon emissions are increasing rapidly and which is one of the leading causes of global warming. These emissions come from different sectors but the biggest contribution comes from the transport sector. As countermeasures, countries are shifting toward electric vehicles, which are much greener modes of transportation. Currently, different types of electric vehicles are available in the market. The selection of a viable type of electric vehicle for a developing country like Pakistan needs proper evaluation. In this study, two techniques are used. Firstly, fuzzy Strength, Weaknesses, Opportunities, and Threats (SWOT) approach is used for the selection of a suitable vehicle for the future market of Pakistan. Secondly, fuzzy linear programming is used to check the viability of electric vehicles in the current market scenario. Using these techniques, hydrogen fuel cell vehicle is selected as the most advantageous vehicle for Pakistan's future market and the hybrid electric vehicle comes out as the best alternative for the current market. The techniques and the case study of Pakistan are the main novelty of this study, as no literature exists on electric vehicles with these methods on Pakistan's perspective. Based on the results, different recommendations are given to the policymakers of Pakistan. The recommended policies could make electric vehicles a prime competitor to the combustion vehicles in the current and future markets. [ABSTRACT FROM AUTHOR]

Recently, Ghanbari et al. (IEEE Transactions on Fuzzy Systems 27:1286–1294, 2019) have proposed modified Kerre's method for comparison of LR fuzzy numbers. Here, we make use of the modified Kerre's method to solve fuzzy linear programming problems with LR coefficients. In an approach to solve a fuzzy linear program with fuzzy LR coefficients, a bi-objective optimization problem is formulated. For the associated bi-objective optimization problem, we present a time variant multi-objective particle swarm optimization (TV-MOPSO) algorithm to compute the Pareto front, a set containing a large number of solutions. Contrary to methods that change the fuzzy optimization problem to a crisp problem by use of a ranking function, using modified Kerre's method, the fuzzy optimization problem is solved directly, with no need for changing it to a crisp program. A comparative investigation using illustrative examples with triangular fuzzy coefficients show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Minimum-cost capacitated fuzzy network is formulated as a fuzzy linear programming problem. A novel fuzzy linear programming formulation for minimum-cost capacitated fuzzy network where the total resource constraints are fuzzy is proposed. The proposed model is then implemented to minimize the operations cost of American Airlines. The research is helpful to identify the most profitable destinations for the American Airlines. Twelve origin/destination pairs are taken into considerations namely Atlantic (A), Latin American (L), Pacific (P) and Domestic (D). Flight operations capacity, Available Seat Miles ASM, is taken as a measure of capacity. The goal is to minimize the flight operations cost while ensuring maximum flight operations capacities to all destinations. This is followed by perspective data analytics for "What American Airline should do to be more profitable?" Perspective analytics suggest the airline to extend flight operations capacity in certain origin/destination pairs, whereas to maintain the previous approximate average capacity for those having high operations costs. The solution of the proposed fuzzy model suggests that flight operations capacity ASM can be significantly increased by 22345148 (000) with relatively small increase 1539356 (000) USD in operations cost. The fuzzy model is superior for it emphasizes to increase flight operations capacity ASM for the origin/destination pairs with minimum flight operations costs. [ABSTRACT FROM AUTHOR]

In this study, a multi-element wind turbine blade that consists of NACA 6411 and NACA 4412 leading-edge slat design is investigated computationally. Optimum design parameters of the slatted wind turbine blade leading to maximum value of CL/CD related to the turbine power are obtained. In the optimization process, a new fuzzy logic linear programming methodology integrating with fuzzy linear regression and 2D CFD analysis is proposed. The aerodynamic characteristics of the slatted blade are computed by using Incompressible Navier–Stokes equations and k-omega turbulence modeling. Results are compared with the results of linear programming method and direct search optimization method. The computational results reveal that the proposed methodology for performance optimization is more effective than other methods to obtain high-performance value of the CL/CD. The maximum value of the CL/CD is obtained as 25.1 leading the maximum efficiency of 0.52. [ABSTRACT FROM AUTHOR]

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, α -cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately. [ABSTRACT FROM AUTHOR]

In this article, we consider some well-known approaches for solving fuzzy linear programming (FLP) problems. We present some of the difficulties of these approaches. Then, crisp linear programming problems are suggested for solving FLP problems. A new algorithm is also given. The proposed approach has advantages over the other methods. For example, we can achieve higher membership degrees for objective function and constraints. Moreover, we show that the fuzzy optimal solutions obtained by the proposed approach are efficient enough. Also, we see that unlike the previous methods, our method finds efficient solutions by solving only one crisp linear problem instead of solving two or three crisp problems. Finally some numerical examples are presented to show the efficiency of the given approach over the other approaches. [ABSTRACT FROM AUTHOR]

In this paper, steelmaking-continuous casting (SCC) scheduling problem is investigated and a mixed integer linear programming model is developed. Since the technical constraints in the mathematical model are not defined exactly, fuzzy sets are used to present them. With using fuzzy constraints, a compromise between different criteria is made based on expert’s ideas in steel industry. Since the mathematical model is suitable only for small size problems, a hybrid algorithm is developed to solve the SCC scheduling problem. The proposed algorithm is based on a combination of particle swarm optimization and fuzzy linear programming (FLP) methods. In this algorithm, the process of generating a solution consists of two phases. In the first phase, assigning and sequencing the charges on machines is done, while in the second phase, a FLP model is applied to determine start time of charges on assigned machines. To evaluate the proposed procedure, it is compared with an algorithm reported in the literature through solving different problems. Numerical results show that the proposed algorithm can obtain very good solutions for SCC scheduling problem. The results also reveal the higher efficiency of the proposed approach in decreasing waiting time of charges between processing. [ABSTRACT FROM AUTHOR]

The real life transportation problems (TP) face a lot of problems due to uncertainties and lack of precise data. The present paper focuses on the two methods for solving intuitionistic fuzzy TP. One of the methods uses intuitionistic fuzzy programming technique together with the three different membership functions-linear, exponential and hyperbolic and the other method uses crisp linear programming taking intuitionistic fuzzy data in both the methods for the cost objective functions in the TP. The first method uses the membership and non-membership degrees separately to find the crisp solution using the fuzzy programming technique and then the optimal solution is calculated in terms of intuitionistic fuzzy data with the help of defined cost membership functions using the different membership functions. The satisfaction degree is then calculated to check the better solution. The second method directly solves the TP to find crisp solution considering a single objective function. The cost objective function is taken as intuitionistic fuzzy data and the methods have been used as such for the first time. A large scale real life intuitionistic TP has been solved using the two methods. The results obtained for different membership functions have been compared. [ABSTRACT FROM AUTHOR]

Climate change exposes economic systems to numerous risks, including reduced agricultural production and electric power supply shortages. The interdependent nature of economic systems causes disruptions in any sector to cascade to other sectors via forward and backward linkages. This work develops an optimization model with which allocation of scarce goods or resources can be optimized; the model uses an overall index of satisfaction of fuzzy economic output goals under conditions of scarcity caused by climatic disruptions. The proposed model includes a vulnerability measure that integrates information elicited from expert judgment. A case study based on a scenario of drought-induced electricity shortage in the Philippine economy is examined. Results show that trade, transportation and service-oriented industries suffer losses in gross domestic product in the Philippine case. [ABSTRACT FROM AUTHOR]

Transportation problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving interval-valued trapezoidal fuzzy numbers for the transportation costs and values of supplies and demands. We propose a fuzzy linear programming approach for solving interval-valued trapezoidal fuzzy numbers transportation problem based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To illustrate the proposed approach an application example is solved. It is demonstrated that study of interval-valued trapezoidal fuzzy numbers transportation problem gives rise to the same expected results as those obtained for TP with trapezoidal fuzzy numbers. [ABSTRACT FROM AUTHOR]

The concepts of both duality and fuzzy uncertainty in linear programming have been theoretically analyzed and comprehensively and practically applied in an abundance of cases. Consequently, their joint application is highly appealing for both scholars and practitioners. However, the literature contributions on duality in fuzzy linear programming (FLP) are neither complete nor consistent. For example, there are no consistent concepts of weak duality and strong duality. The contributions of this survey are (1) to provide the first comprehensive overview of literature results on duality in FLP, (2) to analyze these results in terms of research gaps in FLP duality theory, and (3) to show avenues for further research. We systematically analyze duality in fuzzy linear programming along potential fuzzifications of linear programs (fuzzy classes) and along fuzzy order operators. Our results show that research on FLP duality is fragmented along both dimensions; more specifically, duality approaches and related results vary in terms of homogeneity, completeness, consistency with crisp duality, and complexity. Fuzzy linear programming is still far away from a unifying theory as we know it from crisp linear programming. We suggest further research directions, including the suggestion of comprehensive duality theories for specific fuzzy classes while dispensing with restrictive mathematical assumptions, the development of consistent duality theories for specific fuzzy order operators, and the proposition of a unifying fuzzy duality theory. [ABSTRACT FROM AUTHOR]

To formulate fuzzy linear programming, Gaussian membership functions rather than triangular or trapezoidal ones are usually recognized as more reasonable descriptions for fuzziness. However, the strong nonlinearity of Gaussian membership functions is readily to cause increasing difficulties in achieving optimum solutions accordingly. Motivated by this challenge, we introduce a novel piecewise linear membership function-based decomposition-coordination algorithm, which can initially decompose a fuzzy linear programming problem with Gaussian membership functions into several crisp linear programming models and then coordinate solutions of the sub-models to eventually achieve an overall optimum one. In this paper, detailed algorithmic procedures are presented along with corresponding theoretical analysis. In addition, an application of production planning programming in a workshop of an oil refinery is provided to demonstrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

Several authors have proposed different methods for solving fuzzy minimum cost flow (MCF) problems. In this paper, some single and multi-objective fuzzy MCF problems are chosen which cannot be solved by using any of the existing methods and a new method is proposed for solving such type of problems. The main advantage of the proposed method over existing methods is that the fuzzy MCF problems which can be solved by using the existing methods can also be solved by the proposed method. But, there exist several fuzzy MCF problems which can be solved only by using the proposed method i.e., it is not possible to solve these problems by using the existing methods. To illustrate the proposed method and also to show the advantages of the proposed method over existing methods some single and multi-objective fuzzy MCF problems which cannot be solved by using the existing methods are solved by using the proposed method and the obtained results are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we first extend the dual simplex method to a type of fuzzy linear programming problem involving symmetric trapezoidal fuzzy numbers. The results obtained lead to a solution for fuzzy linear programming problems that does not require their conversion into crisp linear programming problems. We then study the ranges of values we can achieve so that when changes to the data of the problem are introduced, the fuzzy optimal solution remains invariant. Finally, we obtain the optimal value function with fuzzy coefficients in each case, and the results are described by means of numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, shortcomings and limitations of the existing methods for solving fuzzy linear programming (FLP) problems are pointed out. To overcome the limitations as well as to resolve the shortcomings, a new method is proposed for solving FLP problems. To show the advantage of the proposed method over existing methods, a FLP problem is solved by the existing methods as well as the proposed method, and the obtained results are compared. [ABSTRACT FROM AUTHOR]

Problems concerning the distribution routes for frozen products need to incorporate constraints that avoid breaks in the cold chain. The decision making process under uncertain environments is a common one in real logistics problems. The purpose of this study is to apply a fuzzy approach which will provide an optimal solution to the distribution of frozen food with uncertainty in its time values. A soft computing approach is used where fuzzy constraints are included in the modeling and the solution of the problem. [ABSTRACT FROM AUTHOR]

To the best of our knowledge, till now there is no method in the literature to find the fuzzy optimal solution of unbalanced fully fuzzy minimal cost flow (FFMCF) problems. In this paper, a new method is proposed to find the fuzzy optimal solution of these problems. The proposed method is illustrated with the help of a numerical example. Also, the proposed method is used to find the fuzzy optimal solution of an unbalanced real life FFMCF problem. [ABSTRACT FROM AUTHOR]

We propose a bi-objective cell formation problem with demand of products expressed in a number of probabilistic scenarios. To deal with the uncertain demand of products, a framework of two-stage stochastic programming model is presented. The proposed model considers minimizing the sum of the miscellaneous costs (machine constant cost, expected machine variable cost, cell fixed-charge cost, and expected intercell movement cost) and expected total cell loading variation. Because of conflicting objectives, we develop a two-phase fuzzy linear programming approach for solving bi-objective cell formation problem. To show the effectiveness of the proposed approach, numerical examples are solved and the results are compared with the two existing approaches in the literature. The computational results show that the proposed fuzzy method achieves lower objective functions as well as higher satisfaction degrees. [ABSTRACT FROM AUTHOR]

This paper is concentrated on two types of fuzzy linear programming problems. First type with fuzzy coefficients in the objective function and the second type with fuzzy right-hand side values and fuzzy variables. Considering fuzzy derivative and fuzzy differential equations, these kinds of problems are solved using a fuzzy neural network model. To show the applicability of the method, it is applied to solve the fuzzy shortest path problem and the fuzzy maximum flow problem. Numerical results illustrate the method accuracy and it's simple implementation. [ABSTRACT FROM AUTHOR]

a consequence of more extensive collaboration between countries, the need for better humanitarian relief assistance has become a significant challenge to the international community. In case of a disaster exceeding the national response capacity of the affected country, donor countries provide the relief items, which are then consolidated at collection points to be shipped to points of delivery in the stricken country. After the items are transported to the point of delivery, the responsible authority in distributing aids to vulnerable populations then becomes the national relief agencies. In this context, we propose an international relief planning model that can handle the uncertain information while maximizing the credibility of the international agencies in the most cost efficient way. [ABSTRACT FROM AUTHOR]

In this paper, the operation of a complex system of multireservoirs with multiple objectives is being demonstrated. The multireservoir system includes uncertainties of inflows, demands to the large extent. Fuzzy set theory has been proved as a robust theory where these kinds of uncertainties have major role. In this study, the fuzzy linear programming method is used to get the better policy for the system operation with the uncertainty in various parameters i.e. resources, technological coefficients, objective function coefficients. A four reservoir system (a compound parallel and series) is taken as a case study and the fuzzification of all parameters is tried on the system. The effect of fluctuations in irrigation demand and release, power demand and release and available storage volume are considered. The consequences on the objectives i.e. maximization of returns from irrigation release, maximization of returns from power releases are also examined. The operation policies thus evolved give a better understanding of the problem and the intricate complexities associated and there effects. With this the policy makers (a decision maker) can have a wide range of options at his disposal for suitable action. [ABSTRACT FROM AUTHOR]

Supplier selection and related issues are among the most important decisions in the supply chain management area. Even though there have been so many articles and studies that focused on the mentioned problem in the literature, a few of them considered the major decisions related to supplier selection. In an attempt to fulfill that void, we present an integrated framework that involves two stages: suppliers’ evaluation and order allocation. For supplier evaluation, a fuzzy TOPSIS model with a combination of two validated coefficients is conducted. Then, an integer programming with fuzzy objectives and constraints is formulated to assign optimal quantity of order to allocated supplier. Finally, the framework is implemented in a case study organization, and the results are presented. [ABSTRACT FROM AUTHOR]

Multifacility location problems are considered to find optimal location of new facilities with respect to a set of existing ones. Generally, the objective of the problem is minimizing the total distance traveled between facilities. In this paper, a methodology is proposed for multifacility location problem, investigating decision makers’ opinion as a group decision-making problem. Since uncertainty of information in decision-making environment exists, we consider it by applying a fuzzy set theory. At first, the problem is formulated as a fuzzy multiobjective model. After introducing a decision support system based on fuzzy inference system and using fuzzy analytic hierarchy process approach for obtaining weights between facilities, at last, a two-phase fuzzy linear programming considering the concept of degree of satisfaction of each objective is applied to solve the multiobjective problem. Finally, a numerical example is given to illustrate the proposed method and a sensitivity analysis is expressed to show capability of the method for generating different optimal solutions based on the importance of each decision maker’s opinion. [ABSTRACT FROM AUTHOR]

Fuzzy Optimization models and methods has been one of the most and well studied topics inside the broad area of Soft Computing. Particularly relevant is the field of fuzzy linear programming (FLP). Its applications as well as practical realizations can be found in all the real world areas. As FLP problems constitute the basis for solving fuzzy optimization problems, in this paper a basic introduction to the main models and methods in FLP is presented and, as a whole, Linear Programming problems with fuzzy costs, fuzzy constraints and fuzzy coefficients in the technological matrix are analyzed. But fuzzy sets and systems based optimization methods do not end with FLP, and hence in order to solve more complex optimization problems, fuzzy sets based Meta-heuristics are considered, and two main operative approaches described. Provided that these techniques obtain efficient and/or effective solutions, we present a fuzzy rule based methodology for coordinating Meta-heuristics and in addition, to provide intelligence, we propose a process of extraction of the knowledge to conduct the coordination of the system. [ABSTRACT FROM AUTHOR]

The objective of this paper is to deal with a kind of fuzzy linear programming problem involving symmetric trapezoidal fuzzy numbers. Some important and interesting results are obtained which in turn lead to a solution of fuzzy linear programming problems without converting them to crisp linear programming problems. [ABSTRACT FROM AUTHOR]

In this paper first, we find a canonical symmetrical trapezoidal(triangular) for the solution of the fuzzy linear system A~x = ~b, where the elements in A and ~b are crisp and arbitrary fuzzy numbers, respectively. Then, a model for fuzzy linear programming problem with fuzzy variables (FLPFV), in which, the right hand side of constraints are arbitrary numbers, and coefficients of the objective function and constraint matrix are regarded as crisp numbers, is discussed. A numerical procedure for calculating a canonical symmetrical trapezoidal representation for the solution of fuzzy linear system and the optimal solution of FLPFV, (if there exist) is proposed. Several examples illustrate these ideas. [ABSTRACT FROM AUTHOR]

In the real world there are many linear programming problems where all decision parameters are fuzzy numbers. Several approaches exist which use different ranking functions for solving these problems. Unfortunately when there exist alternative optimal solutions, usually with different fuzzy value of the objective function for these solutions, these methods can not specify a clear approach for choosing a solution. In this paper we propose a method to remove the above shortcoming in solving fuzzy number linear programming problems using the concept of expectation and variance as ranking functions. [ABSTRACT FROM AUTHOR]

In this paper a fuzzy linear programming problem is presented. Then using the concept of comparison of fuzzy numbers, by the aid of the Mellin transform, we introduce a method for solving this problem. [ABSTRACT FROM AUTHOR]

In this paper a fuzzy linear programming problem is presented. Then using the concept of comparison of fuzzy numbers, by the aid of the Mellin transform, we introduce a method for solving this problem. [ABSTRACT FROM AUTHOR]

The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval-valued fuzzy sets (IVFLP) through the medium of procedure that turns IVFLP into parametric linear programming via the mathematical programming. Some useful results for the benefit of solving IVFLP are expounded and proved, developed and discussed. Furthermore, that the proposed techniques in this paper allow the decision-maker to assign a different degree of importance can provide a useful way to efficiently help the decision-maker make their decisions. [ABSTRACT FROM AUTHOR]

Because of its complexity from both a legal and economic standpoint, the problem of optimal waste load allocation is multiobjective by nature and should be treated accordingly. To perform this task, an optimization technique known as fuzzy linear programming is utilized in solving a multiple-discharge, two-objective waste load allocation problem. The two objectives considered are: (1) the maximization of waste discharge and (2) the minimization of the largest difference in equity measure between the various dischargers. Results from this study reveal that fuzzy linear programming is a valuable tool for solving the multiple-objective water quality management problems. Moreover, it is shown that the selection of a linear or logistic membership function in providing preference criteria between the two objects, has no effect on the 'best compromising solution'. [ABSTRACT FROM AUTHOR]

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