A new fuzzy neural network model for solving fuzzy linear programming problems and its applications

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.     

Computation of probabilistic linear programming problems involving normal and log-normal random variables with a joint constraint

A method for solving single- and multi-objective probabilistic linear programming problems with a joint constraint is presented. It is assumed that the parameters in the probabilistic linear programming problems are random variables, and the probabilistic problem is converted to an equivalent deterministic mathematical programming problem. In this paper the parameters are generally considered as normal and log-normal random variables. A non-linear programming method is used to solve the single-objective deterministic problem, and a fuzzy programming method is used to solve the multi-objective deterministic problem. Finally, a numerical example is presented to illustrate the methodology.     

Neural network technique for fuzzy multiobjective linear programming

Neural Network(NN) is well-known as one of powerful computing tools to solve optimization problems. Due to the massive computing unit-neurons and parallel mechanism of neural network approach we can solve the large-scale problem efficiently and optimal solution can be gotten. In this paper, we intoroduce improvement of the two-phase approach for solving fuzzy multiobjectve linear programming problem with both fuzzy objectives and constraints and we propose a new neural network technique for solving fuzzy multiobjective linear programming problems. The procedure and efficiency of this approach are shown with numerical simulations.     

Interactive fuzzy random cooperative two-level linear programming through level sets based probability maximization

In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems under fuzzy random environments are considered. To deal with the formulated fuzzy random two-level linear programming problems, α-level sets of fuzzy random variables are introduced and an α-stochastic two-level linear programming problem is defined for guaranteeing the degree of realization of the problem. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the α-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through probability maximization, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.     

A fuzzy linear programming model for production planning in coal mines

This article shows how fuzzy linear programming may be used to solve production scheduling problem in coal industry. First, a fuzzy linear programming model is presented. The proposed model is then tested on a hypothetical problem developed by using production cost estimates from independent coal mines in the states of Virginia, Illinois and Pennsylvania. The results of the model indicate that the model has potential for solving production scheduling problems in the coal industry.     

Fuzzy linear regression model based on fuzzy scalar product

The new concept and method of imposing imprecise (fuzzy) input and output data upon the conventional linear regression model is proposed in this paper. We introduce the fuzzy scalar (inner) product to formulate the fuzzy linear regression model. In order to invoke the conventional approach of linear regression analysis for real-valued data, we transact the α-level linear regression models of the fuzzy linear regression model. We construct the membership functions of fuzzy least squares estimators via the form of “Resolution Identity” which is a well-known formula in fuzzy sets theory. In order to obtain the membership value of any given least squares estimate taken from the fuzzy least squares estimator, we transform the original problem into the optimization problems. We also provide two computational procedures to solve the optimization problems.     

/spl epsiv/-insensitive fuzzy c-regression models: introduction to /spl epsiv/-insensitive fuzzy modeling

This paper introduces a new epsilon-insensitive fuzzy c-regression models (epsilonFCRM), that can be used in fuzzy modeling. To fit these regression models to real data, a weighted epsilon-insensitive loss function is used. The proposed method make it possible to exclude an intrinsic inconsistency of fuzzy modeling, where crisp loss function (usually quadratic) is used to match real data and the fuzzy model. The epsilon-insensitive fuzzy modeling is based on human thinking and learning. This method allows easy control of generalization ability and outliers robustness. This approach leads to c simultaneous quadratic programming problems with bound constraints and one linear equality constraint. To solve this problem, computationally efficient numerical method, called incremental learning, is proposed. Finally, examples are given to demonstrate the validity of introduced approach to fuzzy modeling.     

Linear programming method for multiattribute group decision making using IF sets

The purpose of this paper is to develop a linear programming methodology for solving multiattribute group decision making problems using intuitionistic fuzzy (IF) sets. In this methodology, IF sets are constructed to capture fuzziness in decision information and decision making process. The group consistency and inconsistency indices are defined on the basis of pairwise comparison preference relations on alternatives given by the decision makers. An IF positive ideal solution (IFPIS) and weights which are unknown a priori are estimated using a new auxiliary linear programming model, which minimizes the group inconsistency index under some constraints. The distances of alternatives from the IFPIS are calculated to determine their ranking order. Moreover, some properties of the auxiliary linear programming model and other generalizations or specializations are discussed in detail. Validity and applicability of the proposed methodology are illustrated with the extended air-fighter selection problem and the doctoral student selection problem.     

Weighted Constraint Aggregation in Fuzzy Optimization

Many practical optimization problems are characterized by some flexibility in the problem constraints, where this flexibility can be exploited for additional trade-off between improving the objective function and satisfying the constraints. Fuzzy sets have proven to be a suitable representation for modeling this type of soft constraints. Conventionally, the fuzzy optimization problem in such a setting is defined as the simultaneous satisfaction of the constraints and the goals. No additional distinction is assumed to exist amongst the constraints and the goals. This paper proposes an extension of this model for satisfying the problem constraints and the goals, where preference for different constraints and goals can be specified by the decision-maker. The difference in the preference for the constraints is represented by a set of associated weight factors, which influence the nature of trade-off between improving the optimization objectives and satisfying various constraints. Simultaneous weighted satisfaction of various criteria is modeled by using the recently proposed weighted extensions of (Archimedean) fuzzy t-norms. The weighted satisfaction of the problem constraints and goals are demonstrated by using a simple fuzzy linear programming problem. The framework, however, is more general, and it can also be applied to fuzzy mathematical programming problems and multi-objective fuzzy optimization.     

Fuzzy random programming with equilibrium chance constraints

To model fuzzy random decision systems, this paper first defines three kinds of equilibrium chances via fuzzy integrals in the sense of Sugeno. Then a new class of fuzzy random programming problems is presented based on equilibrium chances. Also, some convex theorems about fuzzy random linear programming problems are proved, the results provide us methods to convert primal fuzzy random programming problems to their equivalent stochastic convex programming ones so that both the primal problems and their equivalent problems have the same optimal solutions and the techniques developed for stochastic convex programming can apply. After that, a solution approach, which integrates simulations, neural network and genetic algorithm, is suggested to solve general fuzzy random programming problems. At the end of this paper, three numerical examples are provided. Since the equivalent stochastic programming problems of the three examples are very complex and nonconvex, the techniques of stochastic programming cannot apply. In this paper, we solve them by the proposed hybrid intelligent algorithm. The results show that the algorithm is feasible and effectiveness.     

Fuzzy decision making of profit function in production planning using S-curve membership function

Any modern industrial manufacturing unit inevitably faces problems of vagueness in various aspects such as raw material availability, human resource availability, processing capability and constraints and limitations imposed by marketing department. Such a complex problem of vagueness and uncertainty can be handled by the theory of fuzzy linear programming. In this paper, a new fuzzy linear programming based methodology using a modified S-curve membership function is used to solve fuzzy mix product selection problem in Industrial Engineering. Profits and satisfactory level have been computed using fuzzy programming approach. Since there are several decisions to be taken, a performance measure has been defined to identify the decision for high level of profit with high degree of satisfaction.     

A two-phase approach for multi-objective programming problems with fuzzy coefficients

In this study, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP), for solving real life multiple objective programming problems with all fuzzy coefficients. The interactive concept of the procedure is performed to reach simultaneous optimal solutions for all objective functions for different grades of precision according to the preferences of the decision-maker (DM). The procedure can be also performed to obtain lexicographic optimal and/or additive solutions if it is needed. In the first phase of the procedure, a family of vector optimization models is constructed by using FPP. Then in the second phase, each model is solved by FLP. The solutions are optimal and each one is an alternative decision plan for the DM.     

A fuzzy bi-criteria transportation problem

In this paper, a fuzzy bi-criteria transportation problem is studied. Here, the model concentrates on two criteria: total delivery time and total profit of transportation. The delivery times on links are fuzzy intervals with increasing linear membership functions, whereas the total delivery time on the network is a fuzzy interval with a decreasing linear membership function. On the other hand, the transporting profits on links are fuzzy intervals with decreasing linear membership functions and the total profit of transportation is a fuzzy number with an increasing linear membership function. Supplies and demands are deterministic numbers. A nonlinear programming model considers the problem using the max–min criterion suggested by Bellman and Zadeh. We show that the problem can be simplified into two bi-level programming problems, which are solved very conveniently. A proposed efficient algorithm based on parametric linear programming solves the bi-level problems. To explain the algorithm two illustrative examples are provided, systematically.     

Application of fuzzy sets to multi-objective project management decisions

In real-world project management (PM) decision problems, input data and/or related parameters are frequently imprecise/fuzzy over the planning horizon owing to incomplete or unavailable information, and the decision maker (DM) generally faces a fuzzy multi-objective PM decision problem in uncertain environments. This work focuses on the application of fuzzy sets to solve fuzzy multi-objective PM decision problems. The proposed possibilistic linear programming (PLP) approach attempts to simultaneously minimise total project costs and completion time with reference to direct costs, indirect costs, relevant activities times and costs, and budget constraints. An industrial case illustrates the feasibility of applying the proposed PLP approach to practical PM decisions. The main advantage of the proposed approach is that the DM may adjust the search direction during the solution procedure, until the efficient solution satisfies the DM's preferences and is considered to be the preferred satisfactory solution. In particular, computational methodology developed in this work can easily be extended to any other situations and can handle the realistic PM decision problems with simplified triangular possibility distributions.     

Solving fuzzy assembly-line balancing problem with genetic algorithms

Assembly-line balancing problem is known as one of difficult combinatorial optimization problems. This problem has been solved with linear programming, dynamic programming approaches, but unfortunately these approaches do not lead to efficient algorithms. Recently, genetic algorithm has been recognized as an efficient and usefull procedure for solving large and hard combinatorial optimization problems, such as scheduling problems, travelling salesman problems, transportation problems, and so on. Fuzzy sets theory is frequently used to represent uncertainty of information. In this paper, to treat the data of real-world problems we use a fuzzy number to represent the processing time and show that we can get a good performance in solving this problem using genetic algorithms.     

矿山产能分配的变量模糊线性规划模型

针对矿山资源开采过程中产能不确定的分配问题,引入了模糊结构元素理论。将产能用结构元表示,并利用结构元加权序将模糊数比较转化为单调函数比较,将含有模糊变量的线性规划问题等价转化为经典线性规划问题。以某矿山为例,建立矿山产能分配的变量模糊线性规划模型,并进行求解。结果表明：实现了将实际问题中的模糊事件进行精确表达,原问题的求解更简便。得到矿山产能取得最大可能利润时的可能分配。应用结构元加权序求解的线性规划模型优于结构元元序的。     

基于线性判别分析的Choquet积分的符号模糊测度提取

在解决分类问题时,建立在Choquet积分上的分类器以其非线性和不可加性的特点,扮演着越来越重要的角色。由于Choquet积分中的符号模糊测度可以描述各特征对结果的影响,因此Choquet积分在解决数据分类及融合 问题方面具有显著的优势。但是,关于Choquet积分符号模糊测度值的求解,学术界一直缺乏有效的方法。目前最常用的方法是遗传算法,但是遗传算法在解决符号模糊测度值的优化问题时存在算法较为复杂、耗时较长等缺陷。由于符号模糊测度值在Choquet积分分类器中是决定性的重要参数,因此设计出一种有效的符号模糊测度提取方法十分必要。文中提出基于线性判别分析的Choquet积分符号模糊测度的提取方法,推导出在分类问题下Choquet积分的符号模糊测度值的解析式表达,其能够有效、快速地得出关键性参数。分别在人工数据集及基准实际数据集上进行测试与验证,实验结果表明所提方法能有效解决Choquet积分分类器中符号模糊测度的优化问题。