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Considering the double uncertainty caused by the ambiguity of statistical data and the ambiguity produced by the subjective assessment of decision makers, the crisp values of criteria may be insufficient to model the multi-criteria decision-making (MCDM) problem in the real world. This paper proposes a fuzzy best-worst method (FBWM) based on a dual-interval solution algorithm to extend the best-worst method (the most recent MCDM method) to fuzzy environments. The reference comparisons for the best criteria and for the worst criteria are represented by fuzzy numbers. Then, according to the BWM method, a nonlinear constrained optimization problem with fuzzy parameters is formulated. We decompose the membership function in fuzzy numbers into several interval numbers of special form and solve the aforementioned fuzzy BWM problem by compound interval algorithm to obtain fuzzy weights of different criteria. Meanwhile, an integral type-reduced method is proposed for determining the fuzzy consistency ratio in order to assess the reliability of the FBWM results. The viability of the new algorithm to expand the BWM method into fuzzy environments has been validated through three numerical examples. In contrast to the existing FBWM method, the proposed method avoids the arithmetic operation between fuzzy numbers during the solution process, directly transfers the uncertain information in the membership function corresponding to the fuzzy comparison vector to the result, and generates fuzzy weight value, which indicates that the proposed algorithm is able to obtain accurate BWM results in fuzzy environments. The results of the study provide new solution ideas for multi-criteria optimization problems under uncertainty. [ABSTRACT FROM AUTHOR]

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]

In this paper, new concepts of (ˆ-feasibility and ã-efficiency of solutions for fuzzy mathematical programming problems are used, where ã is a vector of distinct satisfaction degrees. Recently, a special kind of fuzzy mathematical programming entitled Fuzzy Flexible Linear programming (FFLP) is attracted much interest. Using the mentioned concepts, we propose a two-phase approach to solve FFLP. In the first phase, the original FFLP problem converts to a Multi-Objective Linear Programming (MOLP) problem, and then in phase II a weighting technique for the reduced program is introduced. We saw that it was observed that using this concept as a generalization of the parametric approach in linear programming provides a more appropriate tool for modeling real problems and improving the solving process. Thus, by using this two-phase approach, we achieve better utilization of available resources. Further, the solution resulting from these two approaches is always an ã-efficient solution. Finally, an example in the real world is described to express this approach. [ABSTRACT FROM AUTHOR]

When some coefficients of the constraints are uncertain with only their possible ranges being given, a conventional linear programming (LP) problem can be generalised to the one with set-inclusive constraints. We consider the case where the possible ranges are given by fuzzy sets in this paper. The set-inclusive constraints with fuzzy coefficients have been treated by a necessity measure. However, the usual necessity measure cannot express well the decision-maker's requirement about the trade-off between the robustness level and the satisfaction level of the constraints. We extend the necessity measure to incorporate the trade-off between the robustness level and the satisfaction level of the constraints. We apply the extended necessity measure to LP problems with fuzzy coefficients. After the problem is formulated and reduced to the conventional programming problem, we propose a solution algorithm. Numerical examples are given to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

A selection of suitable sustainability management systems (SMS) is a major part of supply chain strategies to create a competitive advantage, reduce total costs, and manage long-term sustainability. A framework and method for prioritizing supply chain SMSs are presented in this research. Analytic hierarchy process (AHP) is the most common method for alternative selection in multi-criteria decision-making (MCDM). However, complex information is mixed with ambiguity and uncertainty, which makes decision makers unable to use precise or crisp numbers, so fuzzy numbers are presented to remedy this difficulty. Therefore, this research proposes a fuzzy additive preference programming (FAPP) to select the optimum SMS for a supply chain. FAPP method can produce the unique normalized optimal priority vector of fuzzy pairwise comparison matrices for SMS selection effectively with linear constraints. The additive linear constraints can eliminate the weaknesses of existing methods and equalize the upper and lower triangular fuzzy judgments. In addition, the proposed method can identify abnormal pairs of fuzzy judgments that cause inconsistency. The proposed methodology can prioritize the key criteria which lead to the selection of the most appropriate SMS. An example of SMS selection in a rubber factory demonstrates the feasibility and validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this manuscript, three contributions are proposed. First contribution is proposing a good evaluation between the fuzzy and neutrosophic approaches using a novel fuzzy-neutrosophic transfer. Second contribution is introducing a general framework for solving the neutrosphic linear programming problems using the advantages of the method of Abdel-Basset et al. and the advantages of Singh et al.'s method. Third contribution is proposing a new neutrosophic exterior point simplex algorithm NEPSA and its fuzzy version FEPSA. NEPSA has two paths to get optimal solutions. One path consists of basic not feasible solutions but the other path is feasible. Finally, the numerical examples and results analysis show that NEPSA more than accurate FEPSA. [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 paper, we consider the problem of determining the optimal production quantity under uncertainties. The treated problem has a critical effect on the achievement of business goals, which further propagates to the competitive advantage of manufacturing company. The considered problem is stated as the fuzzy linear programming task. The objective function is defined as the maximization of all profit over the time period. The set of constraints consists of constraints deriving from the enterprise (available capacities) and from the market (demand). The fuzzy rating coefficient values of objective function of each pair of the considered products are described by linguistic expressions which are modelled by triangular fuzzy numbers. Handling of uncertainties of the stated fuzzy pair-wise comparison matrix is performed by using the extent analysis. The right-hand-side values of the capacity constraints are determined by decision makers and modelled by the triangular fuzzy numbers. The market constraint values are given according to evidence data. Determination of the optimal quantities of considered products for each time period is based on the concept of equal possibilities. The proposed model is illustrated by an example with real-life data. [ABSTRACT FROM AUTHOR]

Abstract Traditional games theory is based on the idea of having a set of deterministic payoffs to represent actions taken by homogeneous individuals (interaction among players) while in several real scenarios, social and business conflicts are handled by groups of actors with different technical/social skills. This way, a group-game problem can be seen as to two-groups of players who individually select a strategy to win, so the information given by every player in their group affects the payoffs of such game. Sometimes, deterministic payoffs are not available, and even when they can be obtained from negotiation between players, they are not clearly defined. Indeed within groups, individual players could have different perceptions of the payoffs for which we propose a uncertain based matrix games model involving Interval-valued fuzzy payoffs. [ABSTRACT FROM AUTHOR]

Abstract Recycling aims at preventing rapid depletion of natural resources while transforming produced waste into value for economy. However, this process becomes a major challenge in automotive industry, which requires cooperative engagement of multiple players within a complex supply chain. In line with the essence of the topic, government agencies around the world issue directives drawing regulatory frameworks for designing recycling operations comprising various activities such as collection of end-of-life vehicles (ELVs), recovery of reusable components, shredding ELV's body, recycling valuable materials and disposal of the hazardous waste. In general, the amount of returned product in a reverse logistics network is highly uncertain, and the ELV market in Turkey is no exception to this. For that purpose, this study aims developing a fuzzy mixed integer location-allocation model for reverse logistic network of ELVs conforming to the existing directives in Turkey. Accordingly, this study uses a novel approach and assumes that ELV supply in the network is uncertain. The merit of the proposed mathematical model is proved on a real world scenario addressing the reverse logistics design problem for ELVs generated in metropolitan area of Istanbul. The network generated specifies that recycling process is not profitable under the existing circumstances with the given level of supplied ELV and the returned product records per capita in Istanbul are far beyond the EU averages. Consequently, sensitivity analyses question the reliability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper we focus on a polynomial order even penalty function for solving a fuzzy linear programming problem and develop an algorithm which gives a better rate of convergence to achieve the optimal solution to the problem in hand. Some numerical examples are included to exhibit the efficiency of the new algorithmic procedure developed by us. [ABSTRACT FROM AUTHOR]

We know that the linear programming model (LPM) is one of the most approach used in operation research and decision making, it represent a mathematical model for finding optimum allocation of resources, to satisfy certain objective, like maximize profit or minimize cost. In (LPM), we consider all coefficients of operation function and constraints are real but in real life problem, the wright hand side of (LP), and coefficients of variables of operation function may be a fuzzy number, so this research deals with explaining fuzzy linear programming model with definitions of required and with operation on fuzzy number, then how to solve fuzzy linear programming. [ABSTRACT FROM AUTHOR]

In this paper we analyze a special case of Fuzzy Linear Programming (FLP) in which its constraints are composed by fuzzy numbers contained into an interval. The binary relation between crisp constraints and fuzzy coefficients is analyzed, and the membership degree of a random realization of fuzzy parameters is de fined. An application example is presented and solved. [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]

Fuzzy Linear Programming is among the best and most studied topics in the Fuzzy Sets and Systems area. In this paper, the author describes the main developments, results and solution methods achieved in this topic throughout the last 35 years, from a personal point of view. Short descriptions on different Fuzzy Linear Programming problems are provided and future research lines are briefly pointed out. [ABSTRACT FROM AUTHOR]

Selecting a suitable outsourcing provider is one of the most critical activities in supply chain management. In this paper, a new fuzzy linear programming method is proposed to select outsourcing providers by formulating it as a fuzzy inhomogeneous multi-attribute decision making (MADM) problems with fuzzy truth degrees and incomplete weight information. In this method, the decision maker's preferences are represented as trapezoidal fuzzy numbers (TrFNs), which obtained through pair-wise comparisons of alternatives. Based on the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS), the fuzzy consistency and inconsistency indices are defined by the relative closeness degrees in TrFNs. The attribute weights are estimated by solving the proposed fuzzy linear programming. And then the selection ranking is determined by the comprehensive relative closeness degree of each alternative to the FPIS. An industrial IT outsourcing provider selection example is analyzed to demonstrate the implementation process of this method. [ABSTRACT FROM AUTHOR]

Linear programming (LP) is a widely used optimization method for solving real-life problems because of its efficiency. Although precise data are fundamentally indispensable in conventional LP problems, the observed values of the data in real-life problems are often imprecise. Fuzzy sets theory has been extensively used to represent imprecise data in LP by formalizing the inaccuracies inherent in human decision-making. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand-side, and/or the elements of the coefficient matrix. We propose a new method for solving FLP problems in which the coefficients of the objective function and the values of the right-hand-side are represented by symmetric trapezoidal fuzzy numbers while the elements of the coefficient matrix are represented by real numbers. We convert the FLP problem into an equivalent crisp LP problem and solve the crisp problem with the standard primal simplex method. We show that the method proposed in this study is simpler and computationally more efficient than two competing FLP methods commonly used in the literature. [ABSTRACT FROM AUTHOR]

There are several methods in the literature to deal with the sensitivity analysis of fuzzy linear programming (FLP) problems. In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method is proposed to handle the sensitivity analysis of that kind of FLP problems in which the elements of the coefficient matrix of the constraints are represented by real numbers, and the remaining parameters are represented by symmetric trapezoidal fuzzy numbers. To the best of our knowledge, till now there is no method in the literature to deal with the sensitivity analysis of such FLP problems without converting them to the crisp linear programming problems. The advantages of the proposed method over existing methods are discussed. To illustrate the approach a numerical example is examined by using the proposed method and the obtained results are discussed. The method is easy to understand and to apply for dealing with the sensitivity analysis of the same problems occurring in real life situations. [ABSTRACT FROM AUTHOR]

Abstract: Fuzzy linear programming with trapezoidal fuzzy numbers (TrFNs) is considered and a new method is developed to solve it. In this method, TrFNs are used to capture imprecise or uncertain information for the imprecise objective coefficients and/or the imprecise technological coefficients and/or available resources. The auxiliary multi-objective programming is constructed to solve the corresponding possibility linear programming with TrFNs. The auxiliary multi-objective programming involves four objectives: minimizing the left spread, maximizing the right spread, maximizing the left endpoint of the mode and maximizing the middle point of the mode. Three approaches are proposed to solve the constructed auxiliary multi-objective programming, including optimistic approach, pessimistic approach and linear sum approach based on membership function. An investment example and a transportation problem are presented to demonstrate the implementation process of this method. The comparison analysis shows that the fuzzy linear programming with TrFNs developed in this paper generalizes the possibility linear programming with triangular fuzzy numbers. [Copyright &y& Elsevier]

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]

Abstract: The aim of this article is to introduce a formulation of fuzzy linear programming problems involving the level -interval-valued trapezoidal fuzzy numbers as parameters. Indeed, such a formulation is the general form of trapezoidal fuzzy number linear programming problems. Then, it is demonstrated that study of the sensitivity analysis for the level -interval-valued trapezoidal fuzzy number linear programming problems gives rise to the same expected results as those obtained for trapezoidal fuzzy number linear programming problems. [Copyright &y& Elsevier]

Fuzzy linear programming problem occur in many fields such as mathematical modeling, Control theory and Management sciences, etc. In this paper we focus on a kind of Linear Programming with fuzzy numbers and variables namely Fully Fuzzy Linear Programming (FFLP) problem, in which the constraints are in inequality forms. Then a new method is proposed to fine the fuzzy solution for solving (FFLP). Numerical examples are providing to illustrate the method. [ABSTRACT FROM AUTHOR]

Although crisp data are fundamentally indispensable in the conventional linear programming technique for multidimensional analysis of preference (LINMAP), the observed values in the real-world problems are often imprecise or vague. These imprecise or vague data can be suitably characterized by linguistic terms which are fuzzy in nature. LINMAP has been widely used to solve multi-attribute decision making (MADM) problems. This paper extends the conventional LINMAP model to a fuzzy group decision making framework using trapezoidal fuzzy numbers. The ranking approach is used to transform the fuzzy model into a crisp model. The fuzzy LINMAP method proposed in this paper is a simple and effective tool for tackling the uncertainty and imprecision associated with the group MADM problems. A case study in fast food industry is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures. [ABSTRACT FROM AUTHOR]

Abstract: To the best of our knowledge, there is no method in literature for solving such fully fuzzy linear programming (FLP) problems in which some or all the parameters are represented by unrestricted L-R flat fuzzy numbers. Also, to propose such a method, there is need to find the product of unrestricted L-R flat fuzzy numbers. However, there is no method in the literature to find the product of unrestricted L-R flat fuzzy numbers. In this paper, firstly the product of unrestricted L-R flat fuzzy numbers is proposed and then with the help of proposed product, a new method (named as Mehar’s method) is proposed for solving fully FLP problems. It is also shown that the fully FLP problems which can be solved by the existing methods can also be solved by the Mehar’s method. However, such fully FLP problems in which some or all the parameters are represented by unrestricted L-R flat fuzzy numbers can be solved by Mehar’s method but can not be solved by any of the existing methods. [Copyright &y& Elsevier]

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]

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming (LP) with fuzzy variables. In this paper, an approximate but convenient method for solving these problems with fuzzy non-negative technical coefficient and without using the ranking functions, is proposed. With the help of numerical examples, the method is illustrated. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. [ABSTRACT FROM AUTHOR]

This study investigates the performance and efficiency of using variant Differential Evolution (DE) strategies on two classical optimization problems along with fuzzy coefficients. Two classical problems considered in this study are fuzzy transportation and fuzzy linear programming. The fuzzy coefficients in the objective function of the problems are represented by fuzzy numbers. The signed-distance ranking method is used to rank these fuzzy numbers during the evaluation and the selection processes of the DE algorithm for solving the fuzzy optimization problems. The success of DE in solving a specific optimization problem crucially depends on appropriately choosing mutation strategies and their associated control parameter values. There are several variants of mutation constituting several corresponding DE strategies can be used on the optimization problem with fuzzy coefficients. The performance of using five variant mutation strategies on two classical problems are investigated and compared. The experiments conducted show that DE/best/1 strategy generally outperforms the other variant DE strategies in terms of efficiency and convergence on the fuzzy transportation and the fuzzy linear programming problems. [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]

In this paper, by a definite linear function for ranking symmetric triangular fuzzy numbers, in a Fuzzy Linear Programming problem (FLP) model, we introduced a Fuzzy Degenerate Solution (FDS). In the physical meaning, occurrence of degeneracy in a Fuzzy Minimal Cost Flow Network is investigated. To prevent of falling into Cycling phenomenon in optimization process, we defined two new techniques of Cycling prevention proper to fuzzy environment. [ABSTRACT FROM AUTHOR]

Abstract: We propose Fuzzy UTASTAR, a method for inferring fuzzy utility functions from a partial preorder of options evaluated on multiple criteria. It is an extension of the well-known UTASTAR method capable to handle both ordinary (crisp) and fuzzy evaluation data. This property gives much flexibility to decision makers because the majority of real-life decision problems involve a considerable level of uncertainty that hinders them from assigning exact evaluations (scores) to options. In case all evaluation data are crisp the method behaves exactly as the original UTASTAR. The proposed method builds fuzzy additive value functions taking as input a partial preorder on a subset of the options, called reference set, along with their associated scores on the criteria. The resulting fuzzy utility functions can subsequently be used to estimate the (fuzzy) utility of each option, thus allowing their ranking, prioritization, selection or classification. The ranking of the options in partial preorder is as compatible as possible to the original one. The method is implemented into a decision support system and is applied to an example from the transportation domain. Results are found to be in concordance with those of the original method. To the best of our knowledge this is the first attempt to extend UTASTAR method to handle both crisp and fuzzy evaluation data. [Copyright &y& Elsevier]

Abstract: In a recent paper, Ganesan and Veermani [K. Ganesan, P. Veeramani, Fuzzy linear programs with trapezoidal fuzzy numbers, Ann. Oper. Res. 143 (2006) 305–315] considered a kind of linear programming involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems and then proved fuzzy analogues of some important theorems of linear programming that lead to a new method for solving fuzzy linear programming (FLP) problems. In this paper, we obtain some another new results for FLP problems. In fact, we show that if an FLP problem has a fuzzy feasible solution, it also has a fuzzy basic feasible solution and if an FLP problem has an optimal fuzzy solution, it has an optimal fuzzy basic solution too. We also prove that in the absence of degeneracy, the method proposed by Ganesan and Veermani stops in a finite number of iterations. Then, we propose a revised kind of their method that is more efficient and robust in practice. Finally, we give a new method to obtain an initial fuzzy basic feasible solution for solving FLP problems. [Copyright &y& Elsevier]

Abstract: We present a new methodology for the analysis of fuzzy payoff matrix games. The main difficulty that appears in the study of these games is the comparison between the payoff values associated to the strategies of the players because these payoffs are fuzzy quantities. Our approach does not transform the fuzzy payoffs to crisp numbers via standard defuzzyfication but we use standard fuzzy orders which allows us to find solutions within the same space of fuzzy numbers. Moreover, we provide a method to solve these games finding equivalent fuzzy linear programs whose maximal solutions give the solutions of the games. [Copyright &y& Elsevier]

The fluctuations that have taken place in the worldwide economy over the past few years make it difficult to estimate the costs of the equipment that have to be used in order to design a telecommunications network. The literature is replete with prescriptive integer programming models for various network design problems that do not take into account the problems inherent vagueness due to equipment costs. This paper considers the real-world wavelength division multiplexing (WDM) network design problem. The vagueness that appears in this problem is assumed and handled by means of fuzzy-set-based methodologies. A fuzzy integer linear programming model is then proposed to be used as an auxiliary model to solve the former problem. With the purpose to obtain cost-effective network designs, this model is then solved using Cplex, which is a commercial high-performance optimization engine. [ABSTRACT FROM AUTHOR]

The paper deals with the group prioritization problem in the fuzzy analytic hierarchy process. We extend the fuzzy preference programming method to fuzzy group prioritization by introducing important weights of decision-makers (DMs). The modified prioritization problem is represented as a weighted fuzzy goal programming model. Additionally, we represent the uncertain DMs' importance weights as fuzzy numbers and modify the goal programming model by a possibilistic approach. Both proposed models transform the initial prioritization problems with fuzzy or crisp important weights into equivalent crisp linear programs. Unlike the known fuzzy prioritization methods, the proposed approach does not require an additional defuzzification procedure for final ranking of alternatives and can deal with incomplete set of comparison judgments. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the best approximation for fuzzy valued functions using Chebyshev nodes. We prove a result on the best near-minimax approximation in the fuzzy sense. As an application, Runge’s phenomenon is fuzzified in two different cases, i.e. the best approximation and the best near-minimax approximation. [Copyright &y& Elsevier]

Uncertainties in quantities of work items and vagueness in unit price boundaries have mainly been disregarded in unbalanced bidding models. This article presents a fuzzy linear programming (FLP) model which treats the quantities of works and unit price limitations as fuzzy numbers. Fuzzy constraints are used to define upper and lower bounds on the unit prices proposed by the contractor. The uncertainties in quantities of works are addressed through fuzzy coefficients with asymmetric fuzziness ratio in the objective function. Therefore, the problem lends itself to an FLP model with fuzzy coefficients in the objective function and fuzzy constraints. To account for these uncertainties, two different approaches are proposed and tested. Performance of the model is demonstrated using three hypothetical case examples and the results are discussed and compared with those of a deterministic model. [ABSTRACT FROM AUTHOR]

In this paper, we propose a two-phase approach to find the optimal solutions of a class of fuzzy linear programming problems called fully fuzzified linear programming (FFLP), where all decision parameters and variables are fuzzy numbers. Our approach is constructed on the basis of comparison of mean and standard deviation of fuzzy numbers. In this approach, the first phase maximizes the possibilistic mean value of fuzzy objective function and obtains a set of feasible solutions. The second phase minimizes the standard deviation of the original fuzzy objective function, by considering all basic feasible solutions obtained at the end of the first phase. The advantage of the proposed approach is its simplicity in programming and computation. Moreover, we also generalize the concept of linear programming duality and extend the duality as well as the weak duality theory to FFLP. [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, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy resource variables and linear programming problems in which both the resource variables and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with modified s-curve membership functions. We propose here the modified s-curve membership function as a methodology for fuzzy linear programming and use it for solving these problems. We also compare the new proposed method with non-fuzzy linear programming optimization method. Finally, we provide real life application examples in production planning and their numerical solutions. [ABSTRACT FROM AUTHOR]

Decisions made by the experts in the construction industry are usually approximate and contain some sort of imprecision. Classical linear programming (LP) model optimize the decision making situation in a crisp environment. It is difficult to get an optimum decision with imprecise information of the project environment using LP. In the construction industry, identifying optimum number of construction pieces of equipment require experts'' knowledge. When certain degree of flexibility needs to be incorporated in the given model to get more realistic results, fuzzy LP is used. But when the parameters on constraints and objective function are in a state of ambiguity then the extension principle is best suited, which is based on personal opinions and subjective judgments. The objective of this paper is to identify the optimum number of pieces of equipment required to complete the project in the targeted period with fuzzy data. A realistic case study has been considered for optimization and LINGO6 has been used to solve the various non-linear equations. [Copyright &y& Elsevier]

Quality function deployment (QFD) is the product development process to maximize customer satisfaction. The engineering design characteristics related to product performance are specified for this purpose. For dealing with the fuzzy nature in the product design processes, fuzzy approaches are applied to represent the relationships between customer requirements (CRs) and engineering design requirements (DRs) as well as among the DRs. A new measure for evaluating the fuzzy normalized relationships is derived. A fuzzy model is formulated to determine the fulfillment level of each DR for maximizing the customer satisfaction under the resource limitation and the considerations of technical difficulty and market competition. The producing ranges of fulfillment level of each DR and those of customer satisfaction can provide the QFD team with more information. An example is used to illustrate the model. [Copyright &y& Elsevier]

Comparing fuzzy numbers, using the possibility programming approach, was presented by Negi and Lee [1]. In this paper, we are going to state some comments concerning their approach. The case of comparing different fuzzy numbers is considered. Also, the formulation of the crisp problem in the case of fuzzy linear programming and fuzzy multiobjective linear programming is discussed, and a new modified model, in each case, is stated. Our proposed approach is illustrated by numerical examples. [Copyright &y& Elsevier]

Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world decision-making problems that arise in uncertain and ever-changing environments since its introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming (LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development. Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can appear in the model components in different ways. Hence, despite fifty years of research, new formulations of FLP problems and solution methods are still being proposed. Among the existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables for handling inexactness and vagueness in data have experienced a remarkable development in recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is to present an updated review of advances in this particular area. Consequently, the paper briefly examines well-known models and methods for FLP, and expands on methods for fuzzy single- and multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical relevance. For this case, computer codes are provided that can be used to reproduce results presented in the paper and for practical applications. The paper demonstrates that FLP that is focused on lexicographic methods is an active area with promising research lines and practical implications. [ABSTRACT FROM AUTHOR]