具有不确定次品率的EPQ模型及其求解算法

假设在具有衰变特性的生产过程中次品率为随机变量或模糊变量的情形下,分别建立了经济生产批量模型;给出了次品率为随机变量情形下最优经济生产批量的解析表达式;设计了模糊模拟算法以及基于模糊模拟的粒子群优化算法对次品率为模糊变量情形下的经济生产批量模型进行求解。最后给出了两种情形下的数值实例来说明模型的求解过程以及所设计算法的有效性。     

Random fuzzy mean-absolute deviation models for portfolio optimization problem with hybrid uncertainty

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. The existing mean-absolute deviation models are devoted to either stochastic portfolio optimization or fuzzy one. However, practical investment decision problems often involve the mixture of randomness and fuzziness such as stochastic returns with fuzzy information. Thus it is necessary to model portfolio selection problem in such a hybrid uncertain environment. In this paper, we employ random fuzzy variable to describe the stochastic return on individual security with ambiguous information. We first define the absolute deviation of random fuzzy variable and then employ it as risk measure to formulate mean-absolute deviation portfolio optimization models. To find the optimal portfolio, we design random fuzzy simulation and simulation-based genetic algorithm to solve the proposed models. Finally, a numerical example for synthetic data is presented to illustrate the validity of the method.     

粉态原料自动称重控制算法应用研究

介绍了粉料称重系统的硬件组成及工作原理,详细分析了粉料自身的理化特性、主料和辅料在上料过程中对称重准确度和称重速度的影响,提出了“四段式”和“变频模糊控制”两种控制算法,并给出了低速或点动称重时随机误差自动补偿预测控制算法。通过实践证明：这两种控制算法及其辅助修正算法在粉料加工生产中具有良好的应用价值。     

Multi-item partial backlogging inventory models over random planninghorizon in random fuzzy environment

In this paper, some multi-item inventory models for deteriorating items are developed in a random planning horizon under inflation and time value money with space and budget constraints. The proposed models allow stock dependent consumption rate and partially backlogged shortages. Here the time horizon is a random variable with exponential distribution. The inventory parameters other than planning horizon are deterministic in one model and in the other, the deterioration and net value of the money are fuzzy, available budget and space are fuzzy and random fuzzy respectively. Fuzzy and random fuzzy constraints have been defuzzified using possibility and possibility–probability chance constraint techniques. The fuzzy objective function also has been defuzzified using possibility chance constraint against a goal. Both deterministic optimization problems are formulated for maximization of profit and solved using genetic algorithm (GA) and fuzzy simulation based genetic algorithm (FAGA). The models are illustrated with some numerical data. Results for different achievement levels are obtained and sensitivity analysis on expected profit function is also presented.Scope and purposeThe traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However for more sale, inventory should be maintained at a higher level. Of course, this would result in higher holding or procurement cost, etc. Also, in many real situations, during a shortage period, the longer the waiting time is, the smaller the backlogging rate would be. For instance, for fashionable commodities and high-tech products with short product life cycle, the willingness for a customer to wait for backlogging diminishes with the length of the waiting time. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But at present, the economic situation of most of the countries has been much deteriorated due to large scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any further. The purpose of this article is to maximize the expected profit of two inventory control systems in the random planning horizon.     

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.     

EPQ model with learning consideration,imperfect production and partial backlogging in fuzzy random environment

The article scrutinises the learning effect of the unit production time on optimal lot size for the uncertain and imprecise imperfect production process, wherein shortages are permissible and partially backlogged. Contextually, we contemplate the fuzzy chance of production process shifting from an ‘in-control’ state to an ‘out-of-control’ state and re-work facility of imperfect quality of produced items. The elapsed time until the process shifts is considered as a fuzzy random variable, and consequently, fuzzy random total cost per unit time is derived. Fuzzy expectation and signed distance method are used to transform the fuzzy random cost function into an equivalent crisp function. The results are illustrated with the help of numerical example. Finally, sensitivity analysis of the optimal solution with respect to major parameters is carried out.     

Optimal production run length with imperfect production processes and backorder in fuzzy random environment

This article considers the economic production run time problem with imperfect production processes and allowable shortages. The elapsed time until the production process shifts is assumed to be a fuzzy random variable, and fuzzy random total cost per unit time model is constructed. The expectation theory and signed distance are employed to transform the fuzzy random model into crisp model. An effective approximate algorithm is developed to search for the optimal production run length. Furthermore, numerical examples are provided to illustrate the results of proposed model.     

Random fuzzy chance-constrained programming based on adaptive chaos quantum honey bee algorithm and robustness analysis

This paper proposes an adaptive chaos quantum honey bee algorithm (CQHBA) for solving chance-constrained programming in random fuzzy environment based on random fuzzy simulations. Random fuzzy simulation is designed to estimate the chance of a random fuzzy event and the optimistic value to a random fuzzy variable. In CQHBA, each bee carries a group of quantum bits representing a solution. Chaos optimization searches space around the selected best-so-far food source. In the marriage process, random interferential discrete quantum crossover is done between selected drones and the queen. Gaussian quantum mutation is used to keep the diversity of whole population. New methods of computing quantum rotation angles are designed based on grads. A proof of convergence for CQHBA is developed and a theoretical analysis of the computational overhead for the algorithm is presented. Numerical examples are presented to demonstrate its superiority in robustness and stability, efficiency of computational complexity, success rate, and accuracy of solution quality. CQHBA is manifested to be highly robust under various conditions and capable of handling most random fuzzy programmings with any parameter settings, variable initializations, system tolerance and confidence level, perturbations, and noises.     

Tools for fuzzy random variables: Embeddings and measurabilities

The concept of fuzzy random variable has been shown to be as a valuable model for handling fuzzy data in statistical problems. The theory of fuzzy-valued random elements provides a suitable formalization for the management of fuzzy data in the probabilistic setting. A concise overview of fuzzy random variables, focussed on the crucial aspects for data analysis, is presented.     

Expected model for portfolio selection with random fuzzy returns

This paper researches portfolio selection problem in combined uncertain environment of randomness and fuzziness. Due to the complexity of the security market, expected values of the security returns may not be predicted accurately. In the paper, expected returns of securities are assumed to be given by fuzzy variables. Security returns are regarded as random fuzzy variables, i.e. random returns with fuzzy expected values. Following Markowitz's idea of quantifying investment return by the expected value of the portfolio and risk by the variance, a new type of mean–variance model is proposed. In addition, a hybrid intelligent algorithm is provided to solve the new model problem. A numeral example is also presented to illustrate the optimization idea and the effectiveness of the proposed algorithm.     

风力发电机组的变论域自适应模糊控制

建立了变速变浆距风力发电机组的简化模型。在此基础上，将变论域自适应模糊控制应用到风力发电机组的转速和浆距控制系统中，改善风力发电机组的风能捕获性能。变论域自适应模糊控制器在保持规则形式不变的前提下。论域随着误差的变化而变化。这种控制器不但具有经典模糊控制的优点，如不需要精确的数学模型，产生非线性控制动作，良好的动态性能等．而且具有较高的控制精度。仿真结果证明该方法改善了风力发电机组的控制性能。     

一种改进的三级倒立摆变论域模糊控制器设计

在传统变论域模糊控制系统中, 论域随着输入的变化实时改变, 论域的反复调整降低了控制的实时性, 同时伸缩因子的函数结构和参数也不易确定. 基于上述问题本文设计了基于改进型变论域算法的三级倒立摆模糊控制器: 首先提出了相对变论域控制思想, 然后采用模糊逻辑推理器构造了伸缩因子, 实时调整输入变量, 从而相对性地改变论域大小, 避免了传统伸缩因子的函数结构和参数不易确定的问题, 并根据系统闭环响应曲线设计了控制 器输出调整因子. 最后采用极点配置方法对状态变量进行综合, 避免了规则爆炸问题. 三级倒立摆的仿真结果表明了该方法具有较好的控制效果.     

Importance measure system of fuzzy and random input variables and its solution by point estimates

For structure system with fuzzy input variables as well as random ones, a new importance measure system is presented for evaluating the effects of the two kinds of input variables on the output response. Based on the fact that the fuzziness of the output response is determined by that of the input variable, the presented measure system defines the importance measures which evaluate the effect of the fuzzy input variable. And for the random input variable, the importance measure system analyzes its effect fr...     

DF控制推理模型的研究

针对控制系统中对象的模糊性和动态性,基于动态模糊集(Dynamic Fuzzy Sets)及动态模糊逻辑(Dynamic FuzzyLogic)系统理论,给出DF控制推理模型的相关概念,如DF向量、DF语言变量、DF语言规则和DF蕴涵关系等,并在此基础上探讨基于DF语言规则的DF推理方法,最后通过实例说明这些概念和方法的应用。     

聚焦式模糊变结构控制及其在主汽温控制中的应用

针对具有纯滞后、大惯性、参数漂移大的非线性复杂系统,本文提出一种聚焦式模糊变结构控制算法,使系统在多种干扰下具有较强鲁棒性的同时,具有较快的响应速度．控制器采用偏差e、偏差变化速率de/dt和偏差累积∫edt作为输入信号,利用聚焦式量化算法对这3个输入论域进行离散化,模糊化后采用模糊变结构算法对三维输入进行二维的模糊推理,大大简化了模糊推理的过程．仿真结果表明:新算法具有很好的动态品质,可以有效地消除系统的稳态误差．该算法在广东某电厂2#机组锅炉的汽温控制系统中得到成功的应用,其控制效果良好．     

一种基于ETSK模糊模型的模糊控制算法

基于扩张原理的ＴＳＫ模型（ＥＴＳＫ模型）,推导出一种ＥＴＳＫ模型的等价表达形式（变权ＴＳＫ模型）。该模型将规则后件中的模糊数及其扩展运算转化为普通数的运算。进而给出一种基于ＥＴＳＫ模型的模糊控制算法（ＭＢＦＣ）。仿真结果表明,该算法具有较好的控制效果。     

Random and fuzzy sets in coarse data analysis

The theoretical aspects of statistical inference with imprecise data, with focus on random sets, are considered. On the setting of coarse data analysis imprecision and randomness in observed data are exhibited, and the relationship between probability and other types of uncertainty, such as belief functions and possibility measures, is analyzed. Coarsening schemes are viewed as models for perception-based information gathering processes in which random fuzzy sets appear naturally. As an implication, fuzzy statistics is statistics with fuzzy data. That is, fuzzy sets are a new type of data and as such, complementary to statistical analysis in the sense that they enlarge the domain of applications of statistical science.     

Modeling project time–cost trade-off in fuzzy random environment

In real projects, the trade-off between the project cost and the project completion time, and the environmental uncertainty are aspects of considerable importance for managers. For complex environment with more than one type of uncertainty, this paper presents three types of time–cost trade-off models, in which the project environment is described via introducing the fuzzy random theory. The expected value and the chance measure of fuzzy random variable are introduced for modeling the problem under different decision-making criteria. After that, this paper is devoted to designing a searching method integrating the technique of fuzzy random simulations and genetic algorithm for searching the quasi-optimal schedules. Finally, some numerical examples are given to demonstrate the effectiveness of the designed method for solving the proposed models.     

Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments

In this paper, we have investigated multi-item integrated production-inventory models of supplier and retailer with a constant rate of deterioration under stock dependent demand. Here we have considered supplier’s production cost as nonlinear function depending on production rate, retailers procurement cost exponentially depends on the credit period and suppliers transportation cost as a non-linear function of the amount of quantity purchased by the retailer. The models are optimized to get the value of the credit periods and total time of the supply chain cycle under the space and budget constraints. The models are also formulated under fuzzy random and bifuzzy environments. The ordering cost, procurement cost, selling price of retailer’s and holding costs, production cost, transportation cost, setup cost of the supplier’s and the total storage area and budget are taken in imprecise environments. To show the validity of the proposed models, few sensitivity analyses are also presented under the different rate of deterioration. The models are also discussed in non deteriorating items as a special case of the deteriorating items. The deterministic optimization models are formulated for minimizing the entire monetary value of the supply chain and solved using genetic algorithm (GA). A case study has been performed to illustrate those models numerically.     

Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators

The fuzzy rough set model and interval-valued fuzzy rough set model have been introduced to handle databases with real values and interval values, respectively. Variable precision rough set was advanced by Ziarko to overcome the shortcomings of misclassification and/or perturbation in Pawlak rough sets. By combining fuzzy rough set and variable precision rough set, a variety of fuzzy variable precision rough sets were studied, which cannot only handle numerical data, but are also less sensitive to misclassification. However, fuzzy variable precision rough sets cannot effectively handle interval-valued data-sets. Research into interval-valued fuzzy rough sets for interval-valued fuzzy data-sets has commenced; however, variable precision problems have not been considered in interval-valued fuzzy rough sets and generalized interval-valued fuzzy rough sets based on fuzzy logical operators nor have interval-valued fuzzy sets been considered in variable precision rough sets and fuzzy variable precision rough sets. These current models are incapable of wide application, especially on misclassification and/or perturbation and on interval-valued fuzzy data-sets. In this paper, these models are generalized to a more integrative approach that not only considers interval-valued fuzzy sets, but also variable precision. First, we review generalized interval-valued fuzzy rough sets based on two fuzzy logical operators: interval-valued fuzzy triangular norms and interval-valued fuzzy residual implicators. Second, we propose generalized interval-valued fuzzy variable precision rough sets based on the above two fuzzy logical operators. Finally, we confirm that some existing models, including rough sets, fuzzy variable precision rough sets, interval-valued fuzzy rough sets, generalized fuzzy rough sets and generalized interval-valued fuzzy variable precision rough sets based on fuzzy logical operators, are special cases of the proposed models.