Novel methods on comparing grey numbers

Uncertain decision-making is an important branch of decision-making theory. It is crucial to describe uncertain information, which determine the decision-making is effective or not. This paper first presents a brief survey of the existing methods on denoting uncertain information, such as fuzzy mathematics, stochastic and interval methods, analyzes the merits and demerits of these methods. Then the paper proposes a novel method grey systems theory to describe uncertain information and gives the novel definition of grey number on the basis of probability distribution. Subsequently a novel probability method on comparing grey numbers, especially discrete grey numbers and interval grey numbers, is studied. When an interval grey number satisfied to continuous uniform distribution, it will be degenerated into an interval number. Finally three numerical examples are investigated to demonstrate the effectiveness of the present method.     

Two-Stage Approach for Quantitative Policy Analysis Using Bilevel Programming

Quantitative policy analysis problems with hierarchical decision-making can be modeled as bilevel mathematical programming problems. In general, the solution of these models is very difficult; however, special cases exist in which an optimal solution can be obtained by ordinary mathematical programming techniques. In this paper, a two-stage approach for the formulation, construction, solution, and usage of bilevel policy problem is presented. An outline of an example for analyzing Israel's public expenditure policy is also given.     

由某些函数构造的状态变权

研究状态变权的构造问题,给出一种由多元函数和已知状态变权构造新状态变权和三种由多元函数直接构造状态变权的方法。特别地,证明了文[5]由状态均值构造状态变权的方法都可看作是函数构造状态变权的特例,并进一步给出一种基于几何均值的状态变权构造方法。     

Individual forecasting behavior

Participants of a laboratory experiment judgmentally forecast a time series. In order to support their forecasts they are given a highly correlated indicator with a constant lead period of one. The subjects are not given any other information than the time series realizations and have to base their forecasts on pure eyeballing/chart-reading. Standard economic models do not appropriately account for the features of individual forecasts: These are typically affected by intra- and inter-individual instability of behavior. We extend the scheme theory by Otwin Becker for the explanation of individual forecasts by simple schemes based on visually perceived characteristics of the time series. We find that the forecasts of most subjects can be explained very accurately by only a few schemes.     

Dynamic maintenance decision-making for series–parallel manufacturing system based on MAM–MTW methodology

Proper maintenance schedule is required to improve manufacturing systems’ profitability and productivity. A novel dynamic maintenance strategy is thus developed to incorporate both the single-machine optimization and the whole-system schedule for series–parallel system. Firstly, multiple attribute value theory and maintenance effects are considered in the single-machine optimization. A developed multi-attribute model (MAM) is used to determine the optimal maintenance intervals. Then, a series–parallel structure of the system is investigated in terms of the whole-system schedule. Maintenance time window (MTW) programming is presented to make a cost-effective system schedule by dynamically utilizing maintenance opportunities. The maintenance scheme achieved by using the proposed MAM–MTW methodology is demonstrated through a case study in a hydraulic steering factory. It is concluded that proper consideration of maintenance effects and time window leads to a significant cost reduction.     

Fuzzy optimization: An appraisal

This paper takes a general look at core ideas that make up the burgeoning body of Fuzzy mathematical programming emphasizing the methodological view.

Although Fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community, some technical hurdles exist to hinder a unanimity. Reasons for this as well as possible ways for improvement are also discussed.     

基于可信性理论的工程投标模糊风险评估

工程项目投资决策需要考虑承包商自身、业主、项目、竞争对手等方面的情况,需要对各种风险因素进行分析.结合我国当前建筑市场信息化程度不高,难以获取充分历史数据的特点以及国内外相关文献,提出了一种基于可信性理论的工程投标模糊风险评估方法,并给出了详细计算步骤.最后结合算例验证了方法的可行性和实用性.     

An approach to the valuation and decision of ERP investment projects based on real options

The risks and uncertainties inherent in most enterprise resources planning (ERP) investment projects are vast. Decision making in multistage ERP projects investment is also complex, due mainly to the uncertainties involved and the various managerial and/or physical constraints to be enforced. This paper tackles the problem using a real-option analysis framework, and applies multistage stochastic integer programming in formulating an analytical model whose solution will yield optimum or near-optimum investment decisions for ERP projects. Traditionally, such decision problems were tackled using lattice simulation or finite difference methods to compute the value of simple real options. However, these approaches are incapable of dealing with the more complex compound real options, and their use is thus limited to simple real-option analysis. Multistage stochastic integer programming is particularly suitable for sequential decision making under uncertainty, and is used in this paper and to find near-optimal strategies for complex decision problems. Compared with the traditional approaches, multistage stochastic integer programming is a much more powerful tool in evaluating such compound real options. This paper describes the proposed real-option analysis model and uses an example case study to demonstrate the effectiveness of the proposed approach.     

Introducing validity in fuzzy probability for judicial decision-making

Since the Age of Enlightenment, most philosophers have associated reasoning with the rules of probability and logic. This association has been enhanced over the years and now incorporates the theory of fuzzy logic as a complement to the probability theory, leading to the concept of fuzzy probability. Our insight, here, is integrating the concept of validity into the notion of fuzzy probability within an extended fuzzy logic (FLe) framework keeping with the notion of collective intelligence. In this regard, we propose a novel framework of possibility–probability–validity distribution (PPVD). The proposed distribution is applied to a real world setting of actual judicial cases to examine the role of validity measures in automated judicial decision-making within a fuzzy probabilistic framework. We compute valid fuzzy probability of conviction and acquittal based on different factors. This determines a possible overall hypothesis for the decision of a case, which is valid only to a degree. Validity is computed by aggregating validities of all the involved factors that are obtained from a factor vocabulary based on the empirical data. We then map the combined validity based on the Jaccard similarity measure into linguistic forms, so that a human can understand the results. Then PPVDs that are obtained based on the relevant factors in the given case yield the final valid fuzzy probabilities for conviction and acquittal. Finally, the judge has to make a decision; we therefore provide a numerical measure. Our approach supports the proposed hypothesis within the three-dimensional contexts of probability, possibility, and validity to improve the ability to solve problems with incomplete, unreliable, or ambiguous information to deliver a more reliable decision.     

区间多属性决策问题研究综述

从区间数决策矩阵的规范化方法、属性权重的确定及区间数决策矩阵的排序方法三方面对现有的区间多属性决策问题研究的主要成果进行了归纳和总结,并对研究方法进行了分析和评价,最后对全文进行了总结,并探讨了该问题未来的研究前景.