GM(n,h)模型建模序列数据数乘变换特性研究

基于数乘变换是灰色系统建模过程中数据处理的基础,讨论了ＧＭ（n,h）模型与其他几类灰色模型的内在联系．将各类灰色模型统一于共同的分析体系,并在此基础上研究了数乘变换对ＧＭ（n,h）模型参数取值的影响．指出了模型的模拟和预测值只与因变量的数乘变换有关,而与自变量的变换无关．最后分析了几个特殊灰色模型的数乘变换性质,该结果对研究系列灰色模型参数特征有重要意义．     

基于蕴涵算子族L-λ-R0的模糊推理α-三I约束算法

提出了基于蕴涵算子族L-λ-R₀的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-R₀给出了模糊推理的FMP模型及FMT模型的α-三I约束算法。     

基于蕴涵算子族Lλ0λG的反向α-三I支持算法

提出了基于蕴涵算子族Lλ0λG的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族Lλ0λG给出了模糊推理的FMP模型及FMT模型的反向α-三I支持算法。     

基于蕴涵算子族L-λ-G的反向三I约束算法

提出了基于蕴涵算子族L-λ-G的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-G给出了模糊推理的FMP模型及FMT模型的反向三I约束算法、α-反向三I约束算法。     

基于含参数蕴涵算子族L-λ -R0的三I支持算法 ——仅就FMP模型进行讨论

提出了基于蕴涵算子族L-λ-R₀的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-R₀给出了模糊推理的FMP模型的三I支持算法、α-三I支持算法。     

模糊随机决策环境下的核电站不常用条件（Q，r）库存模型

针对固定提前期内的需求为三角模糊变量,且用户总需求为梯形模糊随机变量的情形下,构建了不常用备件连续盘点模式下的（Q,r）模型,并推导出模糊成本最小化函数,进而利用基于模糊数期望值理论的去模糊化方法,求出最优订货点及订货量．最后,通过一个实例验证了模型的科学性和实用性．

     

基于蕴涵算子族L-λ-R0的FMT三I约束算法

提出了基于蕴涵算子族L-λ-R₀的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族L-λ-R₀给出了FMT模型的三I约束算法、α-三I约束算法。给出了FMT模型的三I约束算法、α-三I约束算法计算公式。     

基于蕴涵算子L-λ-0-λ-G的模糊推理的三I算法

研究了基于蕴涵算子L-λ-0-λ-G模糊推理的FMP三I支持算法,给出了FMP模型和FMT模型的三I算法的计算公式。     

基于蕴涵算子Lp的模糊推理的FMP反向三I算法

研究了基于蕴涵算子L_p模糊推理的FMP反向三I支持算法及α-反向三I支持算法,给出了FMP模型的反向三I算法及α-反向三I算法的计算公式。     

基于蕴涵算子族Lλ0λG的模糊推理三I约束算法

提出了基于蕴涵算子族Lλ0λG的模糊推理的思想,这将有助于提高推理结果的可靠性。针对蕴涵算子族Lλ0λG给出了模糊推理的FMP模型及FMT模型的三I约束算法。     

一种模糊滑模变结构控制方案及其在混沌系统控制中的应用

采用模糊动态模型逼近非线性系统，将非线性 系统模糊化为局部线性模型．用Lyapunov稳定性理论设计出确保模糊动态模型全局渐近稳 定的变结构控制器．应用到两类混沌系统的稳定控制中，验证了方案的有效性．模糊控制器 简单，规则少．     

Triangular fuzzification of random variables and power of distribution tests: Empirical discussion

A fuzzifying process of finitely valued random variables by means of triangular fuzzy sets is analyzed. Empirical studies show that if the random variable takes on a small number of different values, the one-sample test about the (fuzzy) mean of the fuzzified random variable is frequently more powerful than the classical test about the mean of the original random variable. This empirical conclusion is theoretically supported as follows: whenever the number of different values of a random variable X is up to 4, the mean of the fuzzified random variable captures the whole information on its distribution. As a consequence, the statistical test about the mean of the fuzzified random variable can be considered in fact as a goodness-of-fit test for the original random variable and, analogously, the J-sample test becomes a test for the equality of J distributions. Comparative simulation studies of these procedures with respect to other well-known methods are carried out. A real-life example illustrates the introduced methodology.     

Ranking function-based solutions of fully fuzzified minimal cost flow problem

The aim of minimal cost flow problem (MCFP) is to find the least transportation cost of a single commodity through a capacitated network. This paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers. For easier reference, hereafter, we refer to this group of problems as fully fuzzified MCFP. To represent our model, Hukuhara’s difference and approximated multiplication are used. Thereafter, we sort fuzzy numbers by an order using a ranking function and show that it is a total order, i.e., a reflexive, anti-symmetric, transitive and complete binary relation. Utilizing the proposed ranking function, we transform the fully fuzzified MCFP into three crisp problems solvable in polynomial time. From this standpoint, combinatorial algorithms are provided to solve the above-mentioned problem and find the fuzzy optimal flow. Furthermore, the proposed order is related to the importance weights of the center, the left spread and the right spread of each fuzzy number. Thus, this method is capable of handling the decision maker’s risk taking. By comparing some previous ranking function-based works with our method, the efficiency of the latter is revealed. Finally, an application of our proposed method to petroleum industry is presented.     

Incorporating human learning into a fuzzy EOQ inventory model with backorders

Even though publications on fuzzy inventory problems are constantly increasing, modelling the decision maker’s characteristics and their effect on his/her decisions and consequently on the planning outcome has not attracted much attention in the literature. In order to fill this research gap and model reality more accurately, this paper develops a new fuzzy EOQ inventory model with backorders that considers human learning over the planning horizon. The paper is an extension of an existing EOQ inventory model with backorders in which both demand and lead times are fuzzified. Here, the assumption of constant fuzziness is relaxed by incorporating the concept of learning in fuzziness into the model considering that the degree of fuzziness reduces over the planning horizon. The proposed fuzzy EOQ inventory model with backorders and learning in fuzziness has a good performance in efficiency. Finally, it is worth mentioning that learning in fuzziness decreases the total inventory cost.     

An effective neural network and fuzzy time series-based hybridized model to handle forecasting problems of two factors

Fuzzy time series forecasting method has been applied in several domains, such as stock market price, temperature, sales, crop production and academic enrollments. In this paper, we introduce a model to deal with forecasting problems of two factors. The proposed model is designed using fuzzy time series and artificial neural network. In a fuzzy time series forecasting model, the length of intervals in the universe of discourse always affects the results of forecasting. Therefore, an artificial neural network- based technique is employed for determining the intervals of the historical time series data sets by clustering them into different groups. The historical time series data sets are then fuzzified, and the high-order fuzzy logical relationships are established among fuzzified values based on fuzzy time series method. The paper also introduces some rules for interval weighing to defuzzify the fuzzified time series data sets. From experimental results, it is observed that the proposed model exhibits higher accuracy than those of existing two-factors fuzzy time series models.     

Fuzzy inventory models for items with imperfect quality and shortage backordering under crisp and fuzzy decision variables

This paper considers inventory models for items with imperfect quality and shortage backordering in fuzzy environments by employing two types of fuzzy numbers, which are trapezoidal and triangular. Two fuzzy models are developed. In the first model the input parameters are fuzzified, while the decision variables are treated as crisp variables. In the second model, not only the input parameters but also the decision variables are fuzzified. For each fuzzy model, a method of defuzzification, namely the graded mean integration method, is employed to find the estimate of the profit function in the fuzzy sense, and then the optimal policy for the each model is determined. The optimal policy for the second model is determined by using the Kuhn–Tucker conditions after the defuzzification of the profit function. Numerical examples are provided in order to ascertain the sensitiveness in the decision variables with respect to fuzziness in the components.     

Optimization of variable demand fuzzy economic order quantity inventory models without and with backordering

A variable demand inventory model was developed for minimizing inventory cost, treating the holding and ordering costs and demand as independent fuzzy variables. Thereafter, backordering cost was also considered as an independent fuzzy variable. Fuzzy expected value model and fuzzy dependent chance programming model were constructed to find the optimal economic order quantity, which would minimize the fuzzy expected value of the total cost, so that the credibility of the total cost not exceeding a certain budget level was maximized. Optimization was carried out using genetic algorithms and particle swarm optimization algorithm, and their performances were compared. The developed model was found to be efficient not only in one artificial case study but also in two data sets collected from the industries. Therefore, this model could solve real-world problems, too.     

An efficient time series forecasting model based on fuzzy time series

In this paper, we present a new model to handle four major issues of fuzzy time series forecasting, viz., determination of effective length of intervals, handling of fuzzy logical relationships (FLRs), determination of weight for each FLR, and defuzzification of fuzzified time series values. To resolve the problem associated with the determination of length of intervals, this study suggests a new time series data discretization technique. After generating the intervals, the historical time series data set is fuzzified based on fuzzy time series theory. Each fuzzified time series values are then used to create the FLRs. Most of the existing fuzzy time series models simply ignore the repeated FLRs without any proper justification. Since FLRs represent the patterns of historical events as well as reflect the possibility of appearances of these types of patterns in the future. If we simply discard the repeated FLRs, then there may be a chance of information lost. Therefore, in this model, it is recommended to consider the repeated FLRs during forecasting. It is also suggested to assign weights on the FLRs based on their severity rather than their patterns of occurrences. For this purpose, a new technique is incorporated in the model. This technique determines the weight for each FLR based on the index of the fuzzy set associated with the current state of the FLR. To handle these weighted FLRs and to obtain the forecasted results, this study proposes a new defuzzification technique. The proposed model is verified and validated with three different time series data sets. Empirical analyses signify that the proposed model have the robustness to handle one-factor time series data set very efficiently than the conventional fuzzy time series models. Experimental results show that the proposed model also outperforms over the conventional statistical models.     

Iterative inversion of fuzzified neural networks

The inversion of a neural network is a process of computing inputs that produce a given target when fed into the neural network. The inversion algorithm of crisp neural networks is based on the gradient descent search in which a candidate inverse is iteratively refined to decrease the error between its output and the target. In this paper. we derive an inversion algorithm of fuzzified neural networks from that of crisp neural networks. First, we present a framework of learning algorithms of fuzzified neural networks and introduce the idea of adjusting schemes for fuzzy variables. Next, we derive the inversion algorithm of fuzzified neural networks by applying the adjusting scheme for fuzzy variables to total inputs in the input layer. Finally, we make three experiments on the parity-three problem, examine the effect of the size of training sets on the inversion, and investigate how the fuzziness of inputs and targets of training sets affects the inversion     

The solution and duality of imprecise network problems

Duality properties have been investigated by many researchers in the recent literature. They are introduced in this paper for a fully fuzzified version of the minimal cost flow problem, which is a basic model in network flow theory. This model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes. First, we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper. By applying Hukuhara’s difference, approximated and exact multiplication and Wu’s scalar production, we exhibit the flow in network models. Then, we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified MCFP to acquire fuzzy optimal flows. To give duality theorems, we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms. Finally, we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision-making problems.