A single-period inventory model with fuzzy demand

The single-period inventory models have wide applications in the real world in assisting the decision maker to determine the optimal quantity to order. Due to lack of historical data, the demand has to be subjectively determined in many cases. In this paper, a single-period inventory model for cases of fuzzy demand is constructed. The costs considered include the procurement cost, shortage cost, and holding cost. For different fuzzy total cost resulted from different order quantity, a method for ranking fuzzy numbers is adopted to find the optimal order quantity in terms of the cost. When the profit gained from selling one item is less (greater) than the loss incurred due to one unsold item, the optimal order quantity lies in the range defined for the left-shape (right-shape) function of the fuzzy demand. If the unit profit is equal to the unit loss, then all quantities with a membership grade 1 are optimal to be ordered. The methodology of this paper can be applied to construct other inventory models with fuzzy demand.     

A fuzzy mid-term single-fab production planning model

Production planning is a complicated task for a semiconductor fabrication plant because of the uncertainties in demand, product prices, cycle times, and product yields. Traditionally, mid-term production planning for a semiconductor fabrication plant is handled with MRP systems or optimized by solving LP or FLP problems. In this study, the philosophy of prioritizing demand classes with higher certainties as proposed by Leachman (1993) is applied to the FLP model of Chen and Wang (1998), and a new FLP model for planning the mid-term production of single wafer fabrication plant is constructed. Parameters in this model are given in the form of trapezoidal fuzzy numbers. Fuzzy comparison is adopted in dealing with the fuzzy objective function and expanding inequalities. The outputs are projected using Chen and Wang's fuzzy dynamic production function. The uncertain demand is classified and satisfied with four successively optimized FLP submodels according to their ascending uncertainties. Chen and Wang's example is adopted to demonstrate the proposed methodology and to make some comparisons. By moving more capacity to demand classes with higher certainties that are usually nearer and have larger discounted revenues, the proposed methodology achieves a higher value of the discounted cash flows than the two referenced models.     

Optimising multi-product multi-chance-constraint inventory control system with stochastic period lengths and total discount under fuzzy purchasing price and holding costs

While the usual assumptions in multi-periodic inventory control problems are that the orders are placed at the beginning of each period (periodic review) or depending on the inventory level they can happen at any time (continuous review), in this article, we relax these assumptions and assume that the periods between two replenishments of the products are independent and identically distributed random variables. Furthermore, assuming that the purchasing price are triangular fuzzy variables, the quantities of the orders are of integer-type and that there are space and service level constraints, total discount are considered to purchase products and a combination of back-order and lost-sales are taken into account for the shortages. We show that the model of this problem is a fuzzy mixed-integer nonlinear programming type and in order to solve it, a hybrid meta-heuristic intelligent algorithm is proposed. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology and to compare its performance with one of the existing algorithms in real world inventory control problems.     

Interactive fuzzy programming for random fuzzy two-level programming problems through possibility-based fractile model

This paper focuses on interactive decision making methods for random fuzzy two-level linear programming problems. Considering the probabilities that the decision makers’ objective function values are smaller than or equal to target variables, fuzzy goals of the decision makers are introduced. Using the fractile model to optimize the target variables under the condition that the degrees of possibility with respect to the attained probabilities are greater than or equal to certain permissible levels, the original random fuzzy two-level programming problems are reduced to deterministic ones. Interactive fuzzy nonlinear programming to obtain 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 demonstrates the feasibility and efficiency of the proposed method.     

A class of multi-objective supply chain networks optimal model under random fuzzy environment and its application to the industry of Chinese liquor

An important issue, when shipping cost and customers demand are random fuzzy variables in supply chain network (SCN) design problem, is to find the network strategy that can simultaneously achieve the objectives of minimization total cost comprised of fixed costs of plants and distribution centers (DCs), inbound and outbound distribution costs, and maximization customer services that can be rendered to customers in terms of acceptable delivery time. In this paper, we propose a random fuzzy multi-objective mixed-integer non-linear programming model for the SCN design problem of Luzhou Co., Ltd. which is representative in the industry of Chinese liquor. By the expected value operator and chance constraint operator, the model has been transformed into a deterministic multi-objective mixed-integer non-linear programming model. Then, we use spanning tree-based genetic algorithms (st-GA) by the Prüfer number representation to find the SCN to satisfy the demand imposed by customers with minimum total cost and maximum customer services for multi-objective SCN design problem of this company under condition of random fuzzy customers demand and transportation cost between facilities. Furthermore, the efficacy and the efficiency of this method are demonstrated by the comparison between its numerical experiment results and those of tradition matrix-based genetic algorithm.     

基于模糊模型相似测量的字符无监督分类法

该文提出一种基于模糊模型相似测量的文本分析系统的字符预分类方法 ,用于对字符的无监督分类 ,以提高整个字符识别系统的速度、正确性和鲁棒性 .作者在字符印刷结构归类的基础上 ,采用模板匹配方法将各类字符分别转换成基于一非线性加权相似函数的模糊样板集合 .模糊字符的无监督分类是字符匹配的一种自然范例并发展了加权模糊相似测量的研究 .该文讨论了该模糊模型的特性、模糊样板匹配的规则 ,并用于加快字符分类处理 ,经过字符分类 ,在字符识别时由于只需针对较小的模糊样板集合而变得容易和快速     

ON STOCHASTIC CONVERGENCE THEOREMS FOR THE FUZZY C-MEANS CLUSTERING PROCEDURE∗

The fuzzy c-means clustering algorithm has been well studied for equal weight distributions on a finite set. Suppose that this situation is generalized to an arbitrary probability distribution on a finite dimensional Euclidean space, assuming that the second moment of the distribution is finite. Now choose ever larger finite random samples from this distribution and compute the standard optimal membership functions for a fuzzy partition into c clusters. Then the convergence of the cluster center points is established in the Hausdorff sense with probability one, provided that there is a unique optimal center point set. These optimal center points are the fixed point of a simple operator, and there is a corresponding iterative algorithm that generalizes the usual procedure.     

Computation of a multi-objective production planning model with probabilistic constraints

In this paper, a multi-objective production planning model has been presented for a captive plant. The model includes multi-products, multi-plants, and multi-objective with some probabilistic constraints. The probabilistic constraints have been transformed into deterministic constraints assuming the parameters as independent normal random variables. The deterministic problem has been computed with two different methods, namely weighting method and fuzzy programming method. Finally, the integral solution obtained by these two methods have been compared.     

Robust disturbance attenuation for uncertain nonlinear networked control systems

This paper considers the problem of robust disturbance attenuation for a class of uncertain nonlinear networked control systems. Takagi-Sugeno fuzzy models are firstly employed to describe the nonlinear plant. Markov processes are used to model the random network-induced delays and data packet dropouts. The Lyapunov-Razumikhin method has been used to derive such a controller for this class of nonlinear systems such that it is stochastically stabilizable with a disturbance attenuation level. Sufficient conditions for the existence of such a controller are derived in terms of the solvability of bilinear matrix inequalities. An iterative algorithm is proposed to change this non-convex problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools. The effectiveness of the proposed design methodology is verified by a numerical example.     

双枝模糊时间Petri网可修复网络攻击模型

以具有时间特性的模糊时间Petri网为研究方法建立了一种新的网络攻击模型。在模型中主要引入双枝模糊集理论和可靠性理论。利用双枝模糊集中的上域（下域）表示攻击的促进因素（阻碍因素）,并在此基础上进行双枝模糊决策以决定变迁（攻击行为）激发对其后集中库所（攻击状态）的影响效果。该模型认为攻击过程是一个可修复的复杂系统,库所代表的攻击状态在随机失效后,便进入一个具有模糊时间区间的修复期,并在修复期后恢复攻击状态,这样做更符合攻击者总是维持攻击状态,使其利于攻击的事实。最后,对这种模型的攻击路径和系统的可靠性进行了分析,并以例子对模型进行了仿真验证。     

Inventory policy of a deteriorating item with variable demand under trade credit period

In this paper, an inventory model of a deteriorating item with stock and selling price dependent demand under two-level credit period has been developed. Here, the retailer enjoys a price discount if he pays normal purchase cost on or before the first level of credit period, or an interest is charged for the delay of payments. In return, retailer also offers a fixed credit period to his customers to boost the demand. In this regard, the authors develop an EOQ model incorporating the effect of inflation and time value of money over all the costs. Keeping the business of seasonal products in mind, it is assumed that planning horizon of business is random and follows a normal distribution with a known mean and standard deviation. The model is formulated as retailer’s profit maximization problem for both crisp and fuzzy inventory costs and solved using a modified Genetic Algorithm (MGA). This algorithm is developed following fuzzy age based selection process for crossover and gradually reducing mutation parameter. For different values of MGA parameters, optimum results are obtained. Numerical experiments are performed to illustrate the model.     

Fuzzy set theory applications in production management research: a literature survey

Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in production management when the dynamics of the production environment limit the specification of model objectives, constraints and the precise measurement of model parameters. This paper provides a survey of the application of fuzzy set theory in production management research. The literature review that we compiled consists of 73 journal articles and nine books. A classification scheme for fuzzy applications in production management research is defined. We also identify selected bibliographies on fuzzy sets and applications.     

基于模糊理论的随机需求系统

需求量是供销系统成本优化中的重要指标.目前常见的研究方法是采用泊松分布来拟合.通过数据统计和分析,我们发现采用模糊三角去拟合随机需求量有更好的拟合度和科学性.采用模糊理论对随机需求进行了建模分析,设计了随机需求系统的算法并最终对其进行了实现.     

燃料电池温度模糊自适应控制

如何控制燃料电池温度性能是燃料电池的一个重要问题。首先基于模糊辨识建模方法建立质子交换膜燃料电池温度性能的T-S模型。模型结构简单,精度高,方便地应用于质子交换膜燃料电池系统控制中。其次针对该模型设计电堆温度的模糊自适应控制器。最后在Matlab平台进行仿真,模糊自适应控制器在较大幅度变化的系统参数下都得到较好的控制性能,证明模糊自适应控制系统具有很好的鲁棒性和良好的控制品质,能够满足质子交换膜燃料电池温度控制系统的要求。     

Boost变换器的T-S模糊建模与控制

针对Boost变换器的非线性特性,考虑变换器参数不同情况对系统模型的影响,分别建立了参数确定和参数不确定条件下Boost变换器的等价T-S模糊模型。基于建立的等价T-S模糊模型,利用Lyapunov函数方法和线性矩阵不等式方法,给出了Boost变换器并行分配补偿模糊控制器的参数化设计方法。仿真结果表明,所建立的Boost变换器T-S模糊模型是可靠的,所设计的模糊控制器与模糊PI相比具有较强的鲁棒性和抗扰性。     

Identification of dynamical systems with a robust interval fuzzy model

In this paper we present a new method of interval fuzzy model identification. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion that minimizes the maximal estimation error between the data and the proposed fuzzy model output is used. The idea is then extended to modelling the optimal lower and upper bound functions that define the band that contains all the measurement values. This results in a lower and an upper fuzzy model or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. We believe that the fuzzy interval model can be very efficiently used, especially in fault detection and in robust control design.     

Design of adaptive fuzzy logic controller based on linguistic-hedgeconcepts and genetic algorithms

In this paper, we propose a novel fuzzy logic controller, called linguistic hedge fuzzy logic controller, to simplify the membership function constructions and the rule developments. The design methodology of linguistic hedge fuzzy logic controller is a hybrid model based on the concepts of the linguistic hedges and the genetic algorithms. The linguistic hedge operators are used to adjust the shape of the system membership functions dynamically, and ran speed up the control result to fit the system demand. The genetic algorithms are adopted to search the optimal linguistic hedge combination in the linguistic hedge module, According to the proposed methodology, the linguistic hedge fuzzy logic controller has the following advantages: 1) it needs only the simple-shape membership functions rather than the carefully designed ones for characterizing the related variables; 2) it is sufficient to adopt a fewer number of rules for inference; 3) the rules are developed intuitionally without heavily depending on the endeavor of experts; 4) the linguistic hedge module associated with the genetic algorithm enables it to be adaptive; 5) it performs better than the conventional fuzzy logic controllers do; and 6) it can be realized with low design complexity and small hardware overhead. Furthermore, the proposed approach has been applied to design three well-known nonlinear systems. The simulation and experimental results demonstrate the effectiveness of this design.     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H ∞ output feedback control with pole placement constraints for uncertain discrete-time fuzzy systems

This paper investigates the problem of multi-objective control for a class of uncertain discrete-time fuzzy systems. The state-space Takagi–Sugeno T–S fuzzy model with linear fractional parameter uncertainties is adopted. Based on a linear matrix inequality approach and via so-called dynamic parallel distributed compensation, a fuzzy full-order dynamic output feedback controller is developed such that the L ₂ gain performance from the exogenous input signals to the controlled output is less than or equal to some prescribed value and, for all admissible uncertainties, the closed-loop poles of each local system are within a pre-specified sub-region of complex plane. Two numerical examples are provided to illustrate the effectiveness of the proposed design method.     

大工业过程稳态优化的模糊双迭代法

在研究大工业过程稳态优化控制算法时, 针对模型–实际存在差异, 将子过程模型作为等式约束, 通过引入模糊系数使其转化为模糊等式约束, 同时对子过程的不等式约束进行模糊化处理, 提出具有模糊不等式约束的模糊双迭代法, 通过实际例子研究了模糊双迭代法. 仿真结果表明, 模糊双迭代法目标函数非常接近实际目标函数值、算法迭代次数较精确双迭代法有明显改善. 这对实际生产非常重要.