A comparison of factorial and random experimental design methods for the development of regression and neural network simulation metamodels

This paper compares two forms of experimental design methods that may be used for the development of regression and neural network simulation metamodels. The experimental designs considered are full factorial designs and random designs. The paper shows that, for two example problems, neural network metamodels using a randomised experimental design produce more accurate and efficient metamodels than those produced by similar sized factorial designs with either regression or neural networks. The metamodelling techniques are compared by their ability to predict the results from two manufacturing systems that have different levels of complexity. The results of the comparison suggest that neural network metamodels outperform conventional regression metamodels, especially when data sets based on randomised simulation experimental designs are used to produce the metamodels rather than data sets from similar sized full factorial experimental designs.     

A class of multiobjective linear programming model with fuzzy random coefficients

The aim of this paper is to deal with a multiobjective linear programming problem with fuzzy random coefficients. Some crisp equivalent models are presented and a traditional algorithm based on an interactive fuzzy satisfying method is proposed to obtain the decision maker’s satisfying solution. In addition, the technique of fuzzy random simulation is adopted to handle general fuzzy random objective functions and fuzzy random constraints which are usually hard to be converted into their crisp equivalents. Furthermore, combined with the techniques of fuzzy random simulation, a genetic algorithm using the compromise approach is designed for solving a fuzzy random multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.     

Fuzzy random regression based multi-attribute evaluation and its application to oil palm fruit grading

Multi-attribute decision-making is usually concerned with weighting alternatives, thereby requiring weight information for decision attributes from a decision maker. However, the assignment of an attribute’s weight is sometimes difficult, and may vary from one decision maker to another. Additionally, imprecision and vagueness may affect each judgment in the decision-making process. That is, in a real application, various statistical data may be imprecise or linguistically as well as numerically vague. Given this coexistence of random and fuzzy information, the data cannot be adequately treated by simply using the formalism of random variables. To address this problem, fuzzy random variables are introduced as an integral component of regression models. Thus, in this paper, we proposed a fuzzy random multi-attribute evaluation model with confidence intervals using expectations and variances of fuzzy random variables. The proposed model is applied to oil palm fruit grading, as the quality inspection process for fruits requires a method to ensure product quality. We include simulation results and highlight the advantage of the proposed method in handling the existence of fuzzy random information.     

Regularized fuzzy clusterwise ridge regression

Fuzzy clusterwise regression has been a useful method for investigating cluster-level heterogeneity of observations based on linear regression. This method integrates fuzzy clustering and ordinary least-squares regression, thereby enabling to estimate regression coefficients for each cluster and fuzzy cluster memberships of observations simultaneously. In practice, however, fuzzy clusterwise regression may suffer from multicollinearity as it builds on ordinary least-squares regression. To deal with this problem in fuzzy clusterwise regression, a new method, called regularized fuzzy clusterwise ridge regression, is proposed that combines ridge regression with regularized fuzzy clustering in a unified framework. In the proposed method, ridge regression is adopted to estimate clusterwise regression coefficients while handling potential multicollinearity among predictor variables. In addition, regularized fuzzy clustering based on maximizing entropy is utilized to systematically determine an optimal degree of fuzziness in memberships. A simulation study is conducted to evaluate parameter recovery of the proposed method as compared to the extant non-regularized counterpart. The usefulness of the proposed method is illustrated by an application concerning the relationship among the characteristics of used cars.     

A revisit of numerical approach for solving linear fractional programming problem in a fuzzy environment

In the article, Veeramani and Sumathi [10] presented an interesting algorithm to solve a fully fuzzy linear fractional programming (FFLFP) problem with all parameters as well as decision variables as triangular fuzzy numbers. They transformed the FFLFP problem under consideration into a bi-objective linear programming (LP) problem, which is then converted into two crisp LP problems. In this paper, we show that they have used an inappropriate property for obtaining non-negative fuzzy optimal solution of the same problem which may lead to the erroneous results. Using a numerical example, we show that the optimal fuzzy solution derived from the existing model may not be non-negative. To overcome this shortcoming, a new constraint is added to the existing fuzzy model that ensures the fuzzy optimal solution of the same problem is a non-negative fuzzy number. Finally, the modified solution approach is extended for solving FFLFP problems with trapezoidal fuzzy parameters and illustrated with the help of a numerical example.     

Fuzzy approaches for multiple objective linear fractional optimization

The problem of finding a solution to a multiple objective linear fractional program arises in several real world situations.In this paper we advocate that fuzzy sets theory provides a basis for solving this problem with sufficient consistency and rigorousness.After representing imprecise aspirations of the decision maker by structured linguistic variables or converting the original problem via approximations or change of variables into a multiple objective linear program, techniques of fuzzy linear programming may be used to reach a satisfactory solution.It is shown that under reasonable restrictions, this solution is efficient (Pareto optimal) for the original problem. Numerical examples are also included for illustration.     

Solution and Application of the Matrix Equation AX~=b~

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模糊线性回归模型的约束最小二乘估计

自Tanaka等1982年提出模糊回归概念以来,该问题已得到广泛的研究。作为主要估计方法之一的模糊最小二乘估计以其与统计最小二乘估计的密切联系更受到人们的重视。本文依据适当定义的两个模糊数之间的距离,提出了模糊线性回归模型的一个约束最小二乘估计方法,该方法不仅能使估计的模糊参数的宽度具有非负性而且估计的模糊参数的中心线与传统的最小二乘估计相一致。最后,通过数值例子说明了所提方法的具体应用。     

An interactive fuzzy satisficing method for structured multiobjective linear fractional programs with fuzzy numbers

In this paper, by considering the experts' vague or fuzzy understanding of the nature of the parameters in the problem formulation process, multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers are formulated. Using the a-level sets of fuzzy numbers, the corresponding nonfuzzy a-multiobjective linear fractional programming problem is introduced. The fuzzy goals of the decision maker for the objective functions are quantified by eliciting the corresponding membership functions including nonlinear ones. Through the introduction of extended Pareto optimality concepts, if the decision maker specifies the degree a and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method and Ritter's partitioning procedure are applicable. Then a linear programming-based interactive fuzzy satisficing method with decomposition procedures for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.     

带模糊回归参数的线性回归模型

本文讨论了数值输入模糊数输出的观测数据的线性最小二乘拟合问题，建立了数值空间到模糊数空间的带模糊回归参数的线性回归模型，证明了模型解的存在性和唯一性，并得到了解的表达式。本模型应用简便，具有实用价值。     

Process planning in a fuzzy environment

Mixed-integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted. As precise forecasts are difficult to obtain, process planning usually involves uncertainty and ambiguity in the data. This paper presents an application of fuzzy programming to process planning. The forecast parameters are assumed to be fuzzy with a linear or triangular membership function. The process planning problem is then formulated in terms of decision making in a fuzzy environment with fuzzy constraints and fuzzy net present value goals. The model is transformed to a deterministic mixed-integer linear program or mixed-integer nonlinear program depending on the type of uncertainty involved in the problem. For the nonlinear case, a global optimization algorithm is developed for its solution. This algorithm is applicable to general possibilistic programs and can be used as an alternative to the commonly used bisection method. Illustrative examples and computational results for a petrochemical complex with 38 processes and 24 products illustrate the applicability of the developed models and algorithms.     

Optimal design of the auto parts supply chain for JIT operations: Sequential bifurcation factor screening and multi-response surface methodology

This research proposes a solution framework based on discrete-event simulation, sequential bifurcation (SB) and response surface methodology (RSM) to address a multi-response optimization problem inherent in an auto parts supply chain. The objective is to identify the most efficient operating setting that would maximize the logistics performance after the expansion of the assembly plant’s capacity due to market growth. In the proposed framework, we first construct a comprehensive simulation as a platform to model the physical flow of the auto parts operations. We then apply the SB to identify the most important factors that influence system performance. To determine the optimal levels of these key factors, we employ RSM to develop metamodels that best describe the relationship between key decision variables and the multiple system responses. We adapt the Derringer–Suich’s desirability function to find the optimal solution of the metamodels. Computational study shows that our method enables the greatest improvement on system performance. The proposed method helps the case firm develop insights into system dynamics and to optimize the operating condition. It realizes the performance objective of the auto parts supply chain without the need for additional fiscal investment.     

A structured solution framework for fuzzy minimum spanning tree problem and its variants under different criteria

This paper develops a unified and structured solution framework for the minimum spanning tree (MST) problem and its variants (e.g., constrained MST problem and inverse MST problem) on networks with fuzzy link weights. It is applicable to any additive decision criterion under fuzziness (e.g., expected value, value at risk, and conditional value at risk), for generalized cases that the link weights may be represented by arbitrary types of fuzzy variables. It also applies to the entropy criterion while the link weights are continuous fuzzy variables. Following the optimality conditions of the fuzzy MST under different decision criteria proved first in this paper, it is shown that the MST problem and its variants on a fuzzy network can be converted into equivalent deterministic counterparts on their corresponding crisp networks. Consequently, these problems can be effectively solved via their deterministic counterparts without fuzzy simulation, and meanwhile, the performance of the trees under a specified criterion is precisely measured. The accuracy and efficiency are both significantly improved compared with other fuzzy simulation-based approaches. Numerical examples illustrate the superiority of the proposed solution framework. Furthermore, some new theoretical conclusions on the MST problem under fuzziness are also presented.

     

Kriging metamodeling in simulation: A review

This article reviews Kriging (also called spatial correlation modeling). It presents the basic Kriging assumptions and formulas—contrasting Kriging and classic linear regression metamodels. Furthermore, it extends Kriging to random simulation, and discusses bootstrapping to estimate the variance of the Kriging predictor. Besides classic one-shot statistical designs such as Latin Hypercube Sampling, it reviews sequentialized and customized designs for sensitivity analysis and optimization. It ends with topics for future research.     

Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution

This paper discusses full fuzzy linear programming (FFLP) problems of which all parameters and variable are triangular fuzzy numbers. We use the concept of the symmetric triangular fuzzy number and introduce an approach to defuzzify a general fuzzy quantity. For such a problem, first, the fuzzy triangular number is approximated to its nearest symmetric triangular number, with the assumption that all decision variables are symmetric triangular. An optimal solution to the above-mentioned problem is a symmetric fuzzy solution. Every FLP models turned into two crisp complex linear problems; first a problem is designed in which the center objective value will be calculated and since the center of a fuzzy number is preferred to (its) margin. With a special ranking on fuzzy numbers, the FFLP transform to multi objective linear programming (MOLP) where all variables and parameters are crisp.     

基于EEMD与模糊回归的投资组合选择模型及实证

随着模糊理论的不断发展与其在证券市场的广泛应用,越来越多的学者关注到参数模糊化对投资组合优化具有重要作用。本文利用集合经验模态分解(EEMD)和模糊线性回归相结合的预测方法,构建了基于对称三角模糊数的投资组合模型。并将提出的模型与集合经验模态分解和普通最小二乘结合的方法、单一模糊线性回归方法进行了对比分析,结果表明基于集合经验模态分解和模糊线性回归建立的投资组合模型最优,这对构建最优投资组合具有参考意义。     

模糊数据的线性回归模型

研究观测数据为模糊数据的统计线性回归模型 ,由该模型所得回归系数非模糊 ,易于应用。对于对称三角模糊数据一元线性回归给出最优解的解析表达式 ;将对称三角模糊数多元线性回归问题给出转化为一类二次规划问题的方法 ;证明了最优解的存在性和估计量的无偏性。     

一类不分明时间序列的回归预测

研究了一类不分明时间序列的线性回归预测问题,通过模糊数空间中的距离,建立了模糊环境中最小二乘回归模型,证明了回归模型解的存在性和唯一性,并给出了确定模型的模糊参数及检验模型拟合度的计算公式。