三维水平井轨道设计模糊最优控制模型

建立了三维水平井井眼轨道设计模糊非线性多目标最优控制模型 ,利用模糊集理论把该模型转化为非线性规划问题 ,并把该模型应用到水平井的实际生产中 ,得到满意的结果 .     

Fuzzy modelling of a moving grate biomass furnace for simulation and control purposes

Takagi–Sugeno (TS) fuzzy models are developed for a moving grate biomass furnace for the purpose of simulating and predicting the main process output variables, which are heat output, oxygen concentration of flue gas, and temperature of flue gas. Numerous approaches to modelling biomass furnaces have been proposed in the literature. Usually their objective is to simulate the furnace as accurately as possible. Hence, very complex model architectures are utilized which are not suited for applications like model predictive control. TS fuzzy models are able to approximate the global non-linear behaviour of a moving grate biomass furnace by interpolating between local linear, time-invariant models. The fuzzy partitions of the individual TS fuzzy models are constructed by an axis-orthogonal, incremental partitioning scheme. Validation results with measured process data demonstrate the excellent performance of the developed fuzzy models.     

Genetic algorithms for portfolio selection problems with minimum transaction lots

Conventionally, portfolio selection problems are solved with quadratic or linear programming models. However, the solutions obtained by these methods are in real numbers and difficult to implement because each asset usually has its minimum transaction lot. Methods considering minimum transaction lots were developed based on some linear portfolio optimization models. However, no study has ever investigated the minimum transaction lot problem in portfolio optimization based on Markowitz’ model, which is probably the most well-known and widely used. Based on Markowitz’ model, this study presents three possible models for portfolio selection problems with minimum transaction lots, and devises corresponding genetic algorithms to obtain the solutions. The results of the empirical study show that the portfolios obtained using the proposed algorithms are very close to the efficient frontier, indicating that the proposed method can obtain near optimal and also practically feasible solutions to the portfolio selection problem in an acceptable short time. One model that is based on a fuzzy multi-objective decision-making approach is highly recommended because of its adaptability and simplicity.     

Robust scheduling of parallel machines with sequence-dependent set-up costs

In this paper we propose a robust approach for solving the scheduling problem of parallel machines with sequence-dependent set-up costs. In the literature, several mathematical models and solution methods have been proposed to solve such scheduling problems, but most of which are based on the strong assumption that input data are known in a deterministic way. In this paper, a fuzzy mathematical programming model is formulated by taking into account the uncertainty in processing times to provide the optimal solution as a trade-off between total set-up cost and robustness in demand satisfaction. The proposed approach requires the solution of a non-linear mixed integer programming (NLMIP), that can be formulated as an equivalent mixed integer linear programming (MILP) model. The resulting MILP model in real applications could be intractable due to its NP-hardness. Therefore, we propose a solution method technique, based on the solution of an approximated model, whose dimension is remarkably reduced with respect to the original counterpart. Numerical experiments conducted on the basis of data taken from a real application show that the average deviation of the reduced model solution over the optimum is less than 1.5%.     

模糊需求下订购批量问题的研究

库存管理模型在现实生活中有着广泛的运用,它为管理决策者有效地确定最佳订购批量提供帮助.然而,由于历史数据的缺乏,需求量在很多情况下往往被主观地确定,因而带有一定的模糊性.本文针对两种不同类型的模糊需求:离散型与连续型,运用模糊理论分别建立了相应的模糊库存模型.该模型不同于已有的模糊库存模型如下:在现有的模糊库存的文献中,大多采用的是利用模糊集的知识对确定EOQ模型加以研究,而本文从模糊理论的角度对报童问题进行研究.     

Detecting fuzzy relationships in regression models: The case of insurer solvency surveillance in Germany

We develop a test for the fuzziness of regression coefficients based on the Tanaka et al. (1982) and He et al. (2007) possibilistic fuzzy regression models. We interpret the spread of the regression coefficients as a statistic measuring the fuzziness of the relationship between the corresponding independent variable and the dependent variable. We derive test distributions based on the null hypothesis that such spreads could have been obtained by estimating a possibilistic regression with data generated by a classical regression model with random errors. As an example, we show how our test detects a fuzzy regression coefficient in a solvency prediction model for German property-liability insurance companies.     

模糊环境下动态供应商选择的混合整数非线性规划模型

基于供应商选择问题的动态性和模糊性,考虑在每个周期内生产商的需求能力及供应商的供应能力为模糊变量,本文将一个多阶段多商品多渠道的供应商选择问题视为一个0-1混合整数模糊动态非线性规划问题,目标函数为总成本最小化。然后建立了0-1混合整数模糊动态非线性规划模型。为了求解该模型,通过可信性理论把模型中模糊机会约束清晰化,将该模型转化为一个确定型的0-1混合整数动态非线性规划模型。最后给出了一个数值算例验证了模型的可行性。     

An online identification algorithm of unknown time-varying delay and internal multimodel control for discrete non-linear systems

In this paper, an online algorithm is proposed for the identification of unknown time-varying input delay in the case of discrete non-linear systems described by decoupled multimodel. This method relies on the minimization of a performance index based on the error between the real system and the partial internal models outputs. In addition, a decoupled internal multimodel control is proposed for the compensation of discrete non-linear systems with time-varying delay. This control scheme incorporates partial internal model controls. Each partial controller is associated to a specified operating zone of the non-linear system. The switching between these controllers is ensured by a supervisor that contains a set of local predictors. A simulation example is carried out to illustrate the significance of the proposed time-varying delay identification algorithm and the proposed internal multimodel control scheme.     

Data-driven fuzzy models for nonlinear identification of a complex heat exchanger

This paper presents and discusses experimental results on nonlinear model identification method applied to a real pilot thermal plant. The aim of this work is to develop a moderately complex model with interpretable structure for a complex parallel flow heat exchanger which is the main component of the thermal plant using a fuzzy clustering technique. The proposed Takagi–Sugeno-type (TS) fuzzy rule-based model is derived through an iterative fuzzy clustering algorithm using a set of input–output measurements. It is shown that the identified multivariable fuzzy rule-based model captures well the key dynamical properties of the physical plant over a wide operating range and under varying operating conditions. For validation, the model is run in parallel and series-parallel configurations to the real process. The experimental results show clearly the high performance of the proposed fuzzy model in achieving good prediction of the main process variables.     

Bayesian analysis of non-linear structural equation models with non-ignorable missing outcomes from reproductive dispersion models

Non-linear structural equation models are widely used to analyze the relationships among outcomes and latent variables in modern educational, medical, social and psychological studies. However, the existing theories and methods for analyzing non-linear structural equation models focus on the assumptions of outcomes from an exponential family, and hence can’t be used to analyze non-exponential family outcomes. In this paper, a Bayesian method is developed to analyze non-linear structural equation models in which the manifest variables are from a reproductive dispersion model (RDM) and/or may be missing with non-ignorable missingness mechanism. The non-ignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings algorithm is used to obtain the joint Bayesian estimates of structural parameters, latent variables and parameters in the logistic regression model, and a procedure calculating the Bayes factor for model comparison is given via path sampling. A goodness-of-fit statistic is proposed to assess the plausibility of the posited model. A simulation study and a real example are presented to illustrate the newly developed Bayesian methodologies.     

Analysis and prediction of hazard risks caused by tropical cyclones in Southern China with fuzzy mathematical and grey models

A hazard-risk assessment model and a grey hazard-year prediction model (GHYPM) are constructed by integrating recent advances in the fuzzy mathematics, grey theory and information spread technique, and then applied to 17-year tropical cyclones (TCs) hazards in Southern China. In constructing the models, a genetic fuzzy mathematical algorithm is first developed to calculate the categorical and ranking weights of TC hazard impact and cause indicators, from which their combined weights are obtained after optimization. The hazard impact and cause index series are then found by coupling the combined weights with their corresponding down-scaled indicators. A two-dimensional normal-spread technique is employed to create a primitive information matrix and a fuzzy relation matrix in order to make fuzzy rough inference of hazard risks with the factorial space theory. An exceeded probability model is developed to assess the possibility of exceeding any given hazard-year category. Results from the GHYPM show that the simulated hazard risk values are more or less consistent with the hazard-impact index series, with more than 60% probability of exceeding a moderate hazard year in Southern China. Results also show small relative errors of the GHYPM, indicating its applicability to the prediction of TC hazard-years up to 20 years.     

Improving weak efficiency frontiers in the fuzzy data envelopment analysis models

Evaluating the performance of activities or organization by common data envelopment analysis models requires crisp input/output data. However, the precise inputs and outputs of production processes cannot be always measured. Thus, the data envelopment analysis measurement containing fuzzy data, called “fuzzy data envelopment analysis”, has played an important role in the evaluation of efficiencies of real applications. This paper focuses on the fuzzy CCR model and proposes a new method for determining the lower bounds of fuzzy inputs and outputs. This improves the weak efficiency frontiers of the corresponding production possibility set. Also a numerical example illustrates the capability of the proposed method.     

Multidimensional least-squares fitting of fuzzy models

We describe a new method for the fitting of differentiable fuzzy model functions to crisp data. The model functions can be either scalar or multidimensional and need not be linear. The data are n-component vectors. An efficient algorithm is achieved by restricting the fuzzy model functions to sets which depend on a fuzzy parameter vector and assuming that the vector has a conical membership function. The fuzzy model function, equated to zero, defines a fuzzy hypersurface in the n-space. The model fitting is done in a least-squares sense by minimizing the squares of the deviations from unity of the membership values of the fitted hypersurface at the observed points. Under the outlined restriction, the problem can be reduced to an ordinary least-squares formulation for which software is available.Application of the new method is illustrated by two examples. In one example, we are concerned with the hazards caused by enemy fire on armor. An important item of information for the assessment of the involved risks is a predictive model for the hole size in terms of physical properties of the projectile and target plate, respectively. We use a non-linear fuzzy model function for this analysis. The second example involves a linear model function and is of theoretical interest because it allows comparison of the new method with a previously developed method.     

Forecasting stock index price based on M-factors fuzzy time series and particle swarm optimization

In real time, one observation always relies on several observations. To improve the forecasting accuracy, all these observations can be incorporated in forecasting models. Therefore, in this study, we have intended to introduce a new Type-2 fuzzy time series model that can utilize more observations in forecasting. Later, this Type-2 model is enhanced by employing particle swarm optimization (PSO) technique. The main motive behind the utilization of the PSO with the Type-2 model is to adjust the lengths of intervals in the universe of discourse that are employed in forecasting, without increasing the number of intervals. The daily stock index price data set of SBI (State Bank of India) is used to evaluate the performance of the proposed model. The proposed model is also validated by forecasting the daily stock index price of Google. Our experimental results demonstrate the effectiveness and robustness of the proposed model in comparison with existing fuzzy time series models and conventional time series models.     

Interpretability assessment of fuzzy knowledge bases: A cointension based approach

Computing with words (CWW) relies on linguistic representation of knowledge that is processed by operating at the semantical level defined through fuzzy sets. Linguistic representation of knowledge is a major issue when fuzzy rule based models are acquired from data by some form of empirical learning. Indeed, these models are often requested to exhibit interpretability, which is normally evaluated in terms of structural features, such as rule complexity, properties on fuzzy sets and partitions. In this paper we propose a different approach for evaluating interpretability that is based on the notion of cointension. The interpretability of a fuzzy rule-based model is measured in terms of cointension degree between the explicit semantics, defined by the formal parameter settings of the model, and the implicit semantics conveyed to the reader by the linguistic representation of knowledge. Implicit semantics calls for a representation of user’s knowledge which is difficult to externalise. Nevertheless, we identify a set of properties - which we call “logical view” - that is expected to hold in the implicit semantics and is used in our approach to evaluate the cointension between explicit and implicit semantics. In practice, a new fuzzy rule base is obtained by minimising the fuzzy rule base through logical properties. Semantic comparison is made by evaluating the performances of the two rule bases, which are supposed to be similar when the two semantics are almost equivalent. If this is the case, we deduce that the logical view is applicable to the model, which can be tagged as interpretable from the cointension viewpoint. These ideas are then used to define a strategy for assessing interpretability of fuzzy rule-based classifiers (FRBCs). The strategy has been evaluated on a set of pre-existent FRBCs, acquired by different learning processes from a well-known benchmark dataset. Our analysis highlighted that some of them are not cointensive with user’s knowledge, hence their linguistic representation is not appropriate, even though they can be tagged as interpretable from a structural point of view.     

Application of fuzzy time series in prediction of time between failures &; faults in software reliability assessment

Since last seventies, various software reliability growth models (SRGMs) have been developed to estimate different measures related to quality of software like: number of remaining faults, software failure rate, reliability, cost, release time, etc. Most of the exiting SRGMs are probabilistic. These models have been developed based on various assumptions. The entire software development process is performed by human being. Also, a software can be executed in different environments. As human behavior is fuzzy and the environment is changing, the concept of fuzzy set theory is applicable in developing software reliability models. In this paper, two fuzzy time series based software reliability models have been proposed. The first one predicts the time between failures (TBFs) of software and the second one predicts the number of errors present in software. Both the models have been developed considering the software failure data as linguistic variable. Usefulness of the models has been demonstrated using real failure data.     

Credibilistic Markov decision processes: The average case

Using a concept of random fuzzy variables in credibility theory, we formulate a credibilistic model for unichain Markov decision processes under average criteria. And a credibilistically optimal policy is defined and obtained by solving the corresponding non-linear mathematical programming. Also we give a computational example to illustrate the effectiveness of our new model.     

Shortest Path Problem on a Network with Imprecise Edge Weight

A network with its arc lengths as imprecise number, instead of a real number, namely, interval number and triangular fuzzy number is considered here. Existing ideas on addition and comparison between two imprecise numbers of same type are introduced. To obtain a fuzzy shortest path from a source vertex to all other vertices, a common algorithm is developed which works well on both types of imprecise numbers under consideration. In the proposed algorithm, a decision-maker is to negotiate with the obtained fuzzy shortest paths according to his/her view only when the means are same but the widths are different of the obtained paths. Otherwise, a fuzzy optimal path is obtained to which the decision-maker always satisfies with different grades of satisfaction. All pairs fuzzy shortest paths can be found by repeated use of the proposed algorithm.     

Thermal behaviour prediction utilizing artificial neural networks for an open office

This study investigates a neural network-based non-linear autoregressive model with external inputs (NNARX), a non-linear autoregressive moving average model with external inputs (NNARMAX), and a non-linear output error model (NNOE) to predict the thermal behaviour of an open-plan office in a modern commercial building. External and internal climate data recorded over one summer, autumn and winter season were used to build and validate the models. The paper illustrates the potential of using these models to predict room temperature and relative humidity for different time scales ahead (30 min or 2 h ahead). The prediction performance is evaluated using the criteria of goodness of fit, coefficient of determination, mean absolute error and mean squared error between predicted model output and real measurements. To obtain an optimal network structure (avoiding overfitting) after training, a pruning algorithm called optimal brain surgeon (OBS) was used to remove unnecessary input signals, weights and hidden neurons. The results demonstrate that all models provide reasonably good predictions but the NNARX and NNARMAX models outperform the NNOE model. These models can all potentially be used for improving the performance of thermal environment control systems.     

A solid transportation problem with mixed constraint in different environment

In this paper, we have introduced a Solid Transportation Problem where the constrains are mixed type. The model is developed under different environment like, crisp, fuzzy and intuitionistic fuzzy etc. Using the interval approximation method we defuzzify the fuzzy amount and for intuitionistic fuzzy set we use the ($\alpha,\beta$)-cut sets to get the corresponding crisp amount. To find the optimal transportation units a time and space based with order of convergence $O (MN^2)$ meta-heuristic Genetic Algorithm have been proposed. Also the equivalent crisp model so obtained are solved by using LINGO 13.0. The results obtained using GA treats as the best solution by comparing with LINGO results for this present study. The proposed models and techniques are finally illustrated by providing numerical examples. Degree of efficiency have been find out for both the algorithm.