Approach to decision making in fuzzy environment

A general approach to solving a wide class of optimization problems with fuzzy coefficients in objective functions and constraints is described. It is based on a modification of traditional mathematical programming methods and consists in formulating and solving one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective function alone. This approach allows one to maximally cut off dominated alternatives from below as well as from above. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment. The approach is applied within the context of fuzzy discrete optimization models, that is based on a modification of discrete optimization algorithms. The results of the paper are of a universal character and are already being used to solve problems of the design and control of power systems and subsystems.     

Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation

A large number of stakeholders take part in the process of decision making, namely, large-scale group decision making (LGDM) problems. Every stakeholder utilises a linguistic preference relation (LPR) to represent her/his preference information for alternatives. Then, a probabilistic LPR (PLPR) is established to represent the group preference. However, some stakeholders may only provide partial preference information about the alternatives. Thus, a PLPR with incomplete probabilities can be used to manage LGDM problems in complex environments. Based on the defined expected multiplicative consistency of PLPR, a probability computation model is established by mathematical programming to derive the missing probabilities of PLPR. In addition, an iterative algorithm to improve the consistency is proposed to obtain the PLPR with satisfactory consistency. Finally, a real-world investment decision-making problem with multiple stakeholders is solved to demonstrate the effectiveness of the proposed method.     

Simulating engineering systems under uncertainty and optimal decision making

A new technology (technique) that helps construct a mathematical model of a complex engineering system by optimal decision making based on it is given. To construct the model of an engineering system, methods of regressive analysis are used to transform the initial (experimental) data into a vector (multiobjective) mathematical programming problem. To solve it, methods are presented that rely on criteria normalization and principle of guaranteed result. The technique of constructing models of engineering systems, methods of solving the vector mathematical programming problem and optimal decision making are demonstrated by the test examples in Matlab.     

Applying software engineering techniques in the development and management of linear and integer programming applications

This work addresses characteristics of software environments for mathematical modeling and proposes a system for developing and managing models of linear and integer programming (IP) problems. The main features of this modeling environment are: version control of models and data; client‐server architecture, which allows the interaction among modelers and decision makers; the use of a database to store information about the models and data scenarios; and the use of remote servers of optimization, which allows the optimization problems to be solved on different machines. The modeling environment proposed in this work was validated using mathematical programming models that exploit different characteristics, such as the treatment of conditions for generating variables and constraints, the use of calculated parameters derived from other parameters, and the use of integer and continuous variables in mixed IP models among others. This validation showed that the proposed environment is able to treat models found in various application areas of operations research and to solve problems with tens of thousands of variables and constraints.     

基于数学规划的救援物资分配优化模型及其求解算法综述

为了提高救援物资利用率、减少各种损失与缓解幸存者痛苦，如何采用数学规划方法优化救援物资分配策略是当前亟待解决的重要问题。根据目标数量和“府际”关系两个准则梳理了救援物资分配数学规划模型的研究现状，综述了救援物资分配优化模型求解算法的研究进展，总结并指出了救援物资分配优化问题未来的研究方向。研究表明：构建救援物资分配优化支撑框架是必要的，而且救援物资分配优化模型从单目标规划向多目标规划延伸，救援物资分配问题的研究视角从横向“府际”关系向纵向“府际”关系转变，从确定条件下的救援物资分配优化问题向不确定条件下的救援物资分配优化问题发展，从传统的救援物资分配优化问题向融入可持续发展理念的救援物资分配问题转变，从精确算法向启发式算法设计解法发展，将大数据、数字孪生、区块链等新信息与通信技术（ICT）应用于构建救援物资分配模型都是必要的。     

INTERACTIVE DECISION MAKING FOR MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMINGPROBLEMS WITH FUZZY PARAMETERS

Abstract

In this paper, we focus on multiobjective linear fractional programming problems with fuzzy parameters and present a new interactive decision making method for obtaining the satisficing solution of the decision maker (DM) on the basis of the linear programming method. The fuzzy parameters in the objective functions and the constraints are characterized by fuzzy numbers. The concept of a-Pareto optimality is introduced in which the ordinary Pareto optimality is extended based on the α-level sets of the fuzzy numbers. In our interactive decision making method, in order to generate a candidate for the satisficing solution which is also a-Pareto optimal, if the DM specifies the degree α of the a-level sets and the reference objective values, the minimax problem is solved by combined use of the bisection method and the linear programming method and the DM is supplied with the corresponding α-Pareto optimal solution together with the trade-off rates among the values of the objective functions and the degree a. Then by considering the current values of the objective functions and a as well as the trade-off rates, the DM acts on this solution by updating his/her reference objective values and/or degree a. In this way the satisficing solution for the DM can be derived efficiently from among an a-Pareto optimal solution set. A numerical example illustrates various aspects of the results developed in this paper.     

Optimal decisions for complex systems—Software packages

This paper proposes the software package SISCON, dedicated to the evaluation of optimal decisions for large-scale systems. SISCON firstly evaluates mathematical models developed from experimental data using LS methods for linear and non-linear systems and after that computes the optimal decision problems, solving the mathematical non-linear programming problems. The large-scale systems have generally a complex structure and global approach computation cannot be carried out. The authors present a decentralised decision structure having a well-defined distribution of supervisory functions. After decomposition of large-scale problems is carried out, sub problems are solved using standard optimization techniques. SISCON offers opportunities for solving non-linear mathematical programming problems and for evaluating optimal decisions in large-scale systems control.     

A survey on metaheuristics for optimization in food manufacturing industry

This paper surveys recent articles on the applications of metaheuristics for solving optimization problems in the food manufacturing industry. Metaheuristics for decision making has attracted significant research and industry attention due to the increasing complexity of models and quick decision making requirements in the industry. Metaheuristics have been applied to food processing/production technologies including fermentation, thermal drying and distillation and other system wide optimization such as transportation, storage (warehousing), production planning and scheduling. In terms of metaheuristics algorithms, Genetic Algorithm and Differential Evolution are the most popular while other algorithms have also demonstrated their effectiveness in addressing various optimization problems. Most problems were typically formulated as single objective mathematical models constructed from experimental or collected data. Recently, multi-objective optimization is becoming more popular because it is able to consider problems from several perspectives and attain more practical results.     

基于优化模型、 规则和人机协调的转库决策支持系统

介绍一个在联机事务处理（OLTP）环境下构建的基于优化模型、规则和人机协调的决策支持系统。通过对某钢铁企业发货部门内部物流管理业务的分析，建立了转库决策整数规划模型，设计了专家规则与整数规划求解相结合的问题求解方法，并在此基础上构建了转库决策支持系统。针对此类 系统的构建，提出了所应考虑的问题并给出解决办法。这是一个运用运筹学方法解决实际问题的成功例子。     

A two-phase approach for multi-objective programming problems with fuzzy coefficients

In this study, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP), for solving real life multiple objective programming problems with all fuzzy coefficients. The interactive concept of the procedure is performed to reach simultaneous optimal solutions for all objective functions for different grades of precision according to the preferences of the decision-maker (DM). The procedure can be also performed to obtain lexicographic optimal and/or additive solutions if it is needed. In the first phase of the procedure, a family of vector optimization models is constructed by using FPP. Then in the second phase, each model is solved by FLP. The solutions are optimal and each one is an alternative decision plan for the DM.     

Consensus reaching for group decision making with multi-granular unbalanced linguistic information: A bounded confidence and minimum adjustment-based approach

In group decision making problems, there exist the situations that decision makers may use unbalanced linguistic term sets that are not uniformly and symmetrically distributed to provide their linguistic assessments over alternatives. Moreover, due to the difference in knowledge and culture backgrounds, it is also possible that multi-granular linguistic term sets may also be used by decision makers. How to manage multi-granular unbalanced linguistic information in consensus-based group decision making has becoming an important topic in linguistic decision making. In this paper, we first revise Herrera’s unbalanced linguistic term sets and propose a simplified linguistic computational model to fuse multi-granular unbalanced linguistic terms. Afterwards, for multi-criteria group decision making problems with multi-granular unbalanced linguistic information, we develop two optimization models to generate adjustment advice for decision makers who have to change his/her opinions in consensus reaching process, which consider both the bounded confidence levels and minimum adjustment of decision makers’ linguistic assessments. Moreover, an algorithm is further proposed to help decision makers reach consensus in group decision making. Eventually, an application example for ERP system supplier selection and some simulation results are presented to illustrate and justify the consensus reaching algorithm.     

计算机优化设计在阻燃配方中的应用

介绍了自行研制的阻燃材料配方优化的专业软件ＦＲ－ＦＩ，对所涉及的均匀实验设计法，多目标优化技术，非线性规划技术进行了评述。该软件能够完成对阻燃材料配方的实验设计，因素分析，单目标优化，多目标优化等多项工作，用它来研究ＥＰＤＭ的阻燃配方，最后根据多项目标的要求优化得到了综合性能优越的配方。应用证明了ＦＲ－Ｆ１操作简便，运行可靠。     

Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees

As an important component of group decision making, the hybrid multi-criteria group decision making (MCGDM) is very complex and interesting in real applications. The purpose of this paper is to develop a novel interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for hybrid MCGDM considering alternative comparisons with hesitancy degrees. The subjective preference relations between alternatives given by each decision maker (DM) are formulated as an IVIF set (IVIFS). The IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers (TrFNs), linguistic variables, intervals and real numbers are used to represent the multiple types of criteria values. The information of criteria weights is incomplete. The IVIFS-type consistency and inconsistency indices are defined through considering the fuzzy positive and negative ideal solutions simultaneously. To determine the criteria weights, we construct a novel bi-objective IVIF mathematical programming of minimizing the inconsistency index and meanwhile maximizing the consistency index, which is solved by the technically developed linear goal programming approach. The individual ranking order of alternatives furnished by each DM is subsequently obtained according to the comprehensive relative closeness degrees of alternatives to the fuzzy positive ideal solution. The collective ranking order of alternatives is derived through establishing a new multi-objective assignment model. A real example of critical infrastructure evaluation is provided to demonstrate the applicability and effectiveness of this method.     

递阶优化问题理论及其算法研究与进展

递阶优化问题用来描述具有层次结构的决策问题,两级优化问题是最基本的递阶问题,又称为两层规划或静态Stackelberg问题。这里比较系统地介绍两级以及多级优化问题的模型以及其特征,并探讨了该领域有待研究的几个方向。     

Multi-objective decision support system in numerical reliability optimization of modern electronic packaging

Nowadays, numerical prototyping methods in electronic packaging are widely used. This is mainly due to cost and time reduction and improved functionality and reliability of final products. Recently, there has been a lot of interest and work conducted on advanced numerical optimization, which can be directly applied to prototyping. So far, the optimization is focused on one criteria while neglecting problem of multi-objectivity, which is not the best approach from practical point of view. Nevertheless, such an approach is jusitified from the point of view of complex analysis, interdisciplinary issues and reduced accuracy of numerical models. In reality, there are usually many criteria which, in order to solve the problem, have to be taken into consideration. There are many multi-objective methods, of which the Pareto set approach is mostly cited in the literature. The “problem” of multi-objective optimization is that not a single optimal solution has resulted but the set of equivalent optimal solutions. This set of equivalent optimal solutions is referenced as “the Pareto set”. From the mathematical point of view, every value from this set can be treated as optimal for certain assumed constraints. However, there could be some additional conditions which cannot be applied to optimization process and some of the results from the Pareto set are more likely (i.e., the fabrication process will be more repeatable) then the others. So, the question is: which value from the Pareto set should be taken to further processing? There are two possibilities: asking an expert for the advice or use the decision making system. Decision making methods based on multi-objective optimization could be referenced as “Multiple criteria decision making” (MCDM) or “Multiple criterial decision aid” (MCDA) systems. There are several groups of these methods: (a) mathematical multi-objective programming, (b) artificial intelligence methods, (c) simple arithmetic methods, and (d) advanced mathematical methods. The current paper will focus on designing and application of the decision support system for multi-objective numerical reliability optimization of electronic packaging. The work will be based on the self developed numerical tool based on Python Scrippting language and will present its application to selected microelectronic packages based on its numerical model elaborated in ABAQUS.     

部分权重信息下对方案有偏好的多属性决策法

研究只有部分权重信息且对方案有偏好的多属性决策问题．首先对方案的偏好信息以互反判断矩阵和互补判断矩阵这两种形式给出的情形，分别建立一个目标规划模型，通过求解这两个模型可确定属性的权重；然后提出一种基于目标规划模型的多属性决策方法；最后通过实例说明了该方法的可行性和有效性。     

Application of a combined fuzzy multiple criteria decision making and optimization programming model to the container transportation demand split

The container transportation demand split is one of the most important decision issues for government transportation departments and port organizations. In previous studies, many researchers assumed that the shipping carrier would aim to minimize the total operation cost by selecting an appropriate port as the most favorable one to call, and the shipper would aim to minimize the inland freight cost by selecting the nearest port as the most favorable one to import and export international trade containers. Thus, a number of mathematical programming models have been developed. But in practice, the shipping carrier not only aims to minimize the total operation cost but also takes into account other criteria such as the volume of containers and port facility conditions when choosing an appropriate port as the most favorable one to call. The shipper not only aims to minimize the inland freight cost but also takes into account the frequency of ship callings when choosing an appropriate port as the most favorable one to import and export international trade containers.Thus, the purpose of this paper is to formulate a combined fuzzy multiple criteria decision making and optimization programming model for solving the container transportation demand split problem. There are two stages in this combined model: in stage one, we first compute the container transportation demand split rate by using fuzzy multiple criteria decision making (MCDM) method; whereas in stage two, an optimization mathematical programming network model is proposed for determining the inland origin destination (O-D) of import/export containers. The utilization of the proposed model is demonstrated with a case of Taiwanese ports. The results show that the proposed combined fuzzy MCDM and optimization programming model can be used to explain the container transportation demand split practice.     

基于混合整数规划的智能车横纵向一体化滚动优化决策

本文针对智能车辆的行为决策问题, 设计了基于混合整数规划的智能车横纵向一体化滚动优化决策方法. 该方法首先将纵向车速表示为非整数, 将期望车道表示为整数控制量, 建立了混合整数智能车决策简化模型; 然后, 设计了横纵向一体化滚动优化决策方法, 决策出纵向车速和换道动作, 根据系统输出与非线性约束的时域关系证明 了优化问题的递归可行性并通过遗传算法求解非线性混合整数规划优化问题. 基于车辆动力学仿真软件veDYNA 和Simulink进行了联合仿真, 并在红旗E-HS3智能车上开展了实车试验, 结果表明, 本文提出的基于混合整数规划的 智能车横纵向一体化决策方法能够实现超车、避障、跟车、停车和弯道工况下的行为决策.     

Asset portfolio optimization using fuzzy mathematical programming

By morphing mean-variance optimization (MVO) portfolio model into semi-absolute deviation (SAD) model, we apply multi criteria decision making (MCDM) via fuzzy mathematical programming to develop comprehensive models of asset portfolio optimization (APO) for the investors’ pursuing either of the aggressive or conservative strategies.     

Application of decision-making techniques in supplier selection: A systematic review of literature

Despite the importance of decision-making (DM) techniques for construction of effective decision models for supplier selection, there is a lack of a systematic literature review for it. This paper provides a systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection. By using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches, we finally selected and reviewed 123 journal articles. To examine the research trend on uncertain supplier selection, these articles are roughly classified into seven categories according to different uncertainties. Under such classification framework, 26 DM techniques are identified from three perspectives: (1) Multicriteria decision making (MCDM) techniques, (2) Mathematical programming (MP) techniques, and (3) Artificial intelligence (AI) techniques. We reviewed each of the 26 techniques and analyzed the means of integrating these techniques for supplier selection. Our survey provides the recommendation for future research and facilitates knowledge accumulation and creation concerning the application of DM techniques in supplier selection.