The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties

Many multiple attribute decision analysis (MADA) problems are characterised by both quantitative and qualitative attributes with various types of uncertainties. Incompleteness (or ignorance) and vagueness (or fuzziness) are among the most common uncertainties in decision analysis. The evidential reasoning (ER) approach has been developed in the 1990s and in the recent years to support the solution of MADA problems with ignorance, a kind of probabilistic uncertainty. In this paper, the ER approach is further developed to deal with MADA problems with both probabilistic and fuzzy uncertainties.In this newly developed ER approach, precise data, ignorance and fuzziness are all modelled under the unified framework of a distributed fuzzy belief structure, leading to a fuzzy belief decision matrix. A utility-based grade match method is proposed to transform both numerical data and qualitative (fuzzy) assessment information of various formats into the fuzzy belief structure. A new fuzzy ER algorithm is developed to aggregate multiple attributes using the information contained in the fuzzy belief matrix, resulting in an aggregated fuzzy distributed assessment for each alternative. Different from the existing ER algorithm that is of a recursive nature, the new fuzzy ER algorithm provides an analytical means for combining all attributes without iteration, thus providing scope and flexibility for sensitivity analysis and optimisation. A numerical example is provided to illustrate the detailed implementation process of the new ER approach and its validity and wide applicability.     

The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty

The evidential reasoning (ER) approach is a method for multiple attribute decision analysis (MADA) under uncertainties. It improves the insightfulness and rationality of a decision making process by using a belief decision matrix (BDM) for problem modelling and the Dempster–Shafer (D–S) theory of evidence for attribute aggregation. The D–S theory provides scope and flexibility to deal with interval uncertainties or local ignorance in decision analysis, which is not explored in the original ER approach and will be investigated in this paper. Firstly, interval uncertainty will be defined and modelled in the ER framework. Then, an extended ER algorithm, IER, is derived, which enables the ER approach to deal with interval uncertainty in assessing alternatives on an attribute. It is proved that the original ER algorithm is a special case of the IER algorithm. The latter is demonstrated using numerical examples.     

Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty

Multiple attribute decision analysis (MADA) problems having both quantitative and qualitative attributes under uncertainty can be modelled and analysed using the evidential reasoning (ER) approach. Several types of uncertainty such as ignorance and fuzziness can be consistently modelled in the ER framework. In this paper, both interval weight assignments and interval belief degrees are considered, which could be incurred in many decision situations such as group decision making. Based on the existing ER algorithm, several pairs of preference programming models are constructed to support global sensitivity analysis based on the interval values and to generate the upper and lower bounds of the combined belief degrees for distributed assessment and also the expected values for ranking of alternatives. A post-optimisation procedure is developed to identify non-dominated solutions, examine the robustness of the partial ranking orders generated, and provide guidance for the elicitation of additional information for generating more desirable assessment results. A car evaluation problem is examined to show the implementation process of the proposed approach.     

The group consensus based evidential reasoning approach for multiple attributive group decision analysis

Many multiple attribute decision analysis problems include both quantitative and qualitative attributes with various kinds of uncertainties such as ignorance, fuzziness, interval data, and interval belief degrees. An evidential reasoning (ER) approach developed in the 1990s and in recent years can be used to model these problems. In this paper, the ER approach is extended to group consensus (GC) situations for multiple attributive group decision analysis problems. In order to construct and check the GC, a compatibility measure between two belief structures is developed first. Considering two experts’ utilities, the compatibility between their assessments is naturally constructed using the compatibility measure. Based on the compatibility between two experts’ assessments, the GC at a specific level that may be the attribute level, the alternative level, or the global level, can be constructed and reached after the group analysis and discussion within specified times. Under the condition of GC, we conduct a study on the forming of group assessments for alternatives, the achievement of the aggregated utilities of assessment grades, and the properties and procedure of the extended ER approach. An engineering project management software selection problem is solved by the extended ER approach to demonstrate its detailed implementation process, and its validity and applicability.     

Efficient generation of alternative perspectives in public environmental policy formulation: applying co-evolutionary simulation–optimization to municipal solid waste management

In public policy formulation, it is generally preferable to create several quantifiably good alternatives that provide very different approaches to the particular situation. This is because public sector decision-making typically involves complex problems that are riddled with incompatible performance objectives and possess competing design requirements which are very difficult—if not impossible—to quantify and capture at the time supporting decision models are constructed. There are invariably unmodelled design issues, not apparent at the time of model construction, which can greatly impact the acceptability of the model’s solutions. Furthermore, public environmental policy formulation problems often contain considerable stochastic uncertainty and there are frequently numerous stakeholders with irreconcilable perspectives involved. Consequently, it is preferable to generate several alternatives that provide multiple, disparate perspectives to the problem. These alternatives should possess near-optimal objective measures with respect to the known modelled objective(s), but be fundamentally different from each other in terms of the system structures characterized by their decision variables. By generating a set of very different solutions, it is hoped that some of these dissimilar alternatives can provide very different perspectives that may serve to satisfy the unmodelled objectives. This study provides a co-evolutionary simulation–optimization modelling-to-generate-alternatives approach that can be used to efficiently create multiple solution alternatives that satisfy required system performance criteria in highly uncertain environments and yet are maximally different in their decision space. This new stochastic approach is very computationally efficient, since it permits the simultaneous generation of good solution alternatives in a single computational run of the SO algorithm. The efficacy and efficiency of this technique is specifically demonstrated using an earlier waste management case to enable direct comparisons to previous methods. Waste management systems provide an ideal setting for illustrating the modelling techniques used for such public environmental policy formulation, since they possess all of the prevalent incongruencies and system uncertainties inherent in complex planning processes.     

环境评价中不存在污染指标权重的原因

当今环境评价都以权重反映评价指标重要性程度的差异,并且在定权方法上存在不同意见.实际上环评中的指标权重只针对定性指标,对制定了"分级标准"的污染指标并不存在权重概念,更不存在确定权重的问题,这是环评特点.如果环评中不再确定污染指标权重,那么仅此一点已足可改变当今所有环评的评价结果,所以从理论上论证为什么环评领域对污染指标不存在权重问题是十分必要的,也是规范环评方法的一个必要条件.     

Interconnected games and international environmental problems,II

Some features of international environmental problems are considered. A basic problem is to induce countries to adopt a cooperative approach. One of the instruments to induce countries to cooperate is an exchange of concessions in fields of relative strengths, such as swapping trade concessions for cooperation on international environmental problems. This instrument will be modelled in this paper with tensor games. Both tradeoff and non-tradeoff tensor games will be addressed, with emphasis on tradeoff tensor games with linear strict weights. The relationship between the Pareto equilibria of a non-tradeoff tensor game and the Nash equilibria of the associated tradeoff tensor games will be studied. Due to structural similarities between tensor games and repeated multiple objective games, some attention will also be paid to the latter. Relationships between objects related to Folk theorems for the tradeoff tensor game with completely additive weights and the corresponding objects for its constituting isolated games will be studied. Since many international environmental problems have prisoners' dilemma characteristics, it is analyzed how interconnection may enhance cooperation in prisoners' dilemma games.     

Algorithms for solving discrete optimal control problems with infinite time horizon and determining minimal mean cost cycles in a directed graph as decision support tool

Time-discrete systems with a finite set of states are considered. Discrete optimal control problems with infinite time horizon for such systems are formulated. We introduce a certain graph-theoretic structure to model the transitions of the dynamical system. Algorithms for finding the optimal stationary control parameters are presented. Furthermore, we determine the optimal mean cost cycles. This approach can be used as a decision support strategy within such a class of problems; especially so-called multilayered decision problems which occur within environmental emission trading procedures can be modelled by such an approach.     

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.     

Multicriteria evidential reasoning decision modelling and analysis—prioritizing voices of customer

In this paper, a new methodology is investigated to support the prioritization of the voices of customers through various customer satisfaction surveys. This new methodology consists of two key components: an innovative evidence-driven decision modelling framework for representing and transforming large amounts of data sets and a generic reasoning-based decision support process for aggregating evidence to prioritize the voices of customer on the basis of the Evidential Reasoning (ER) approach. Methods and frameworks for data collection and representation via multiple customer satisfaction surveys were examined first and the distinctive features of quantitative and qualitative survey data are analysed. Several novel yet natural and pragmatic rule-based functions are then proposed to transform survey data systematically and consistently from different measurement scales to a common scale, with the original features and profiles of the data preserved in the transformation process. These new transformation functions are proposed to mimic expert judgement processes and designed to be sufficiently flexible and rigorous so that expert judgements and domain specific knowledge can be taken into account naturally, systematically and consistently in the transformation process. The ER approach is used for synthesizing quantitative and qualitative data under uncertainty that can be caused due to missing data and ambiguous survey questions. A new generic method is also proposed for ranking the voices of customer based on qualitative measurement scales without having to quantify assessment grades to fixed numerical values. A case study is examined using an Intelligent Decision System (IDS) to illustrate the application of the decision modelling framework and decision support process for prioritizing the voices of customer for a world-leading car manufacturer.     

Progressive hedging as a meta-heuristic applied to stochastic lot-sizing

In a great many situations, the data for optimization problems cannot be known with certainty and furthermore the decision process will take place in multiple time stages as the uncertainties are resolved. This gives rise to a need for stochastic programming (SP) methods that create solutions that are hedged against future uncertainty. The progressive hedging algorithm (PHA) of Rockafellar and Wets is a general method for SP. We cast the PHA in a meta-heuristic framework with the sub-problems generated for each scenario solved heuristically. Rather than using an approximate search algorithm for the exact problem as is typically the case in the meta-heuristic literature, we use an algorithm for sub-problems that is exact in its usual context but serves as a heuristic for our meta-heuristic. Computational results reported for stochastic lot-sizing problems demonstrate that the method is effective.     

Combining principal component analysis and the evidential reasoning approach for healthcare quality assessment

Patient experience and satisfaction surveys have been adopted worldwide to evaluate healthcare quality. Nevertheless, national governments and the general public continue to search for optimal methods to assess healthcare quality from the patient’s perspective. This study proposes a new hybrid method, which combines principal component analysis (PCA) and the evidential reasoning (ER) approach, for assessing patient satisfaction. PCA is utilized to transform correlated items into a few uncorrelated principal components (PCs). Then, the ER approach is employed to aggregate extracted PCs, which are considered as multiple attributes or criteria within the ER framework. To compare the performance of the proposed method with that of another assessment method, analytic hierarchy process (AHP) is employed to acquire the weight of each assessment item in the hierarchical assessment framework, and the ER approach is used to aggregate patient evaluation for each item. Compared with the combined AHP and ER approach, which relies on the respondents’ subjective judgments to calculate criterion and subcriterion weights in the assessment framework, the proposed method is highly objective and completely based on survey data. This study contributes a novel and innovative hybrid method that can help hospital administrators obtain an objective and aggregated healthcare quality assessment based on patient experience.     

Using extended Monte Carlo simulation method for the improvement of risk management: Consideration of relationships between uncertainties

This paper considers the relationship of the major uncertainties of a project by using proposed approach. This approach by using rotary algorithm intellectualized the classic Monte Carlo simulation. This will help utility function to come closer to reality so that decision making and risk analysis would be done based on the real and possible modes, providing better conditions for decision making. Analyzing and investigating uncertainties are done in the risk management frame work. Because opportunities and threats are not separated, Monte Carlo simulation analysis is implemented as an integrated tool to reach the project goals, analyzing and investigating a variety of uncertainty permutations simultaneously. This method is a powerful tool for investigating the effects of all uncertainties’ occurrence, so it has noticeable benefits such as simultaneous consideration of uncertainties and the capability of representing several dimensions of utility function. In spite of these benefits, not considering the type and level of relationships, some permutations of uncertainties will occur that are not possible in real world. This would divert the utility function from reality. A simple example is used to illustrate the application of the model in practice.     

Possibilistic analysis of arity-monotonic aggregation operators and its relation to bibliometric impact assessment of individuals

A class of arity-monotonic aggregation operators, called impact functions, is proposed. This family of operators forms a theoretical framework for the so-called Producer Assessment Problem, which includes the scientometric task of fair and objective assessment of scientists using the number of citations received by their publications.The impact function output values are analyzed under right-censored and dynamically changing input data. The qualitative possibilistic approach is used to describe this kind of uncertainty. It leads to intuitive graphical interpretations and may be easily applied for practical purposes.The discourse is illustrated by a family of aggregation operators generalizing the well-known Ordered Weighted Maximum (OWMax) and the Hirsch h-index.     

Analyzing the performance of simultaneous generalized hill climbing algorithms

Simultaneous generalized hill climbing (SGHC) algorithms provide a framework for using heuristics to simultaneously address sets of intractable discrete optimization problems where information is shared between the problems during the algorithm execution. Many well-known heuristics can be embedded within the SGHC algorithm framework. This paper shows that the solutions generated by an SGHC algorithm are a stochastic process that satisfies the Markov property. This allows problem probability mass functions to be formulated for particular sets of problems based on the long-term behavior of the algorithm. Such results can be used to determine the proportion of iterations that an SGHC algorithm will spend optimizing over each discrete optimization problem. Sufficient conditions that guarantee that the algorithm spends an equal number of iterations in each discrete optimization problem are provided. SGHC algorithms can also be formulated such that the overall performance of the algorithm is independent of the initial discrete optimization problem chosen. Sufficient conditions are obtained guaranteeing that an SGHC algorithm will visit the globally optimal solution for each discrete optimization problem. Lastly, rates of convergence for SGHC algorithms are reported that show that given a rate of convergence for the embedded GHC algorithm, the SGHC algorithm can be designed to preserve this rate.     

Fuzzy chance-constrained programming model for a multi-echelon reverse logistics network for household appliances

Efficient planning and design of an appropriate reverse logistics network is crucial to the economical collection and disposal of scrapped household appliances and electrical products. Such systems are commonly modelled as mixed-integer programs, whose solutions will determine the location of individual facilities that optimize material flow. One of the major drawbacks of current models is that they do not adequately address the important issue of uncertainty in demand and supply. Another deficiency in current models is that they are restricted to a two-echelon system. This study addresses these deficiencies by embodying such uncertainties in the model using the technique of fuzzy-chance constrained programming, and by extending the model to a three-echelon system. A heuristic in the form of a hybrid genetic algorithm is then employed to generate low-cost solutions. The overall objective is to find economical solutions to the general problem of determining the volume of appliances to be moved between the three echelons of customer base to collection sites, collection sites to disposal centres and disposal centre to landfill centre/remanufacturing centre; and to the problems of positioning the disposal centres and the landfill centre/remanufacturing centres within the problem domain. A case example in China is presented and the quality and robustness of the solutions are explored through sensitivity analysis.     

A mixed-method optimisation and simulation framework for supporting logistical decisions during offshore wind farm installations

With a typical investment in excess of £100 million for each project, the installation phase of offshore wind farms (OWFs) is an area where substantial cost-reductions can be achieved; however, to-date there have been relatively few studies exploring this. In this paper, we develop a mixed-method framework which exploits the complementary strengths of two decision-support methods: discrete-event simulation and robust optimisation. The simulation component allows developers to estimate the impact of user-defined asset selections on the likely cost and duration of the full or partial completion of the installation process. The optimisation component provides developers with an installation schedule that is robust to changes in operation durations due to weather uncertainties. The combined framework provides a decision-support tool which enhances the individual capability of both models by feedback channels between the two, and provides a mechanism to address current OWF installation projects. The combined framework, verified and validated by external experts, was applied to an installation case study to illustrate the application of the combined approach. An installation schedule was identified which accounted for seasonal uncertainties and optimised the ordering of activities.     

Structural reliability analysis with imprecise random and interval fields

This paper investigates the issue of reliability assessment for engineering structures involving mixture of stochastic and non-stochastic uncertain parameters through the Finite Element Method (FEM). Non-deterministic system inputs modelled by both imprecise random and interval fields have been incorporated, so the applicability of the structural reliability analysis scheme can be further promoted to satisfy the intricate demand of modern engineering application. The concept of robust structural reliability profile for systems involving hybrid uncertainties is discussed, and then a new computational scheme, namely the unified interval stochastic reliability sampling (UISRS) approach, is proposed for assessing the safety of engineering structures. The proposed method provides a robust semi-sampling scheme for assessing the safety of engineering structures involving multiple imprecise random fields with various distribution types and interval fields simultaneously. Various aspects of structural reliability analysis with multiple imprecise random and interval fields are explored, and some theoretically instructive remarks are also reported herein.     

Strong guidance on mitigating the effects of uncertainties in the brass casting blending problem: a hybrid optimization approach

The scrap charge optimization problem in the brass casting process is a critical management concern that aims to reduce the charge while preventing specification violations. Uncertainties in scrap material compositions often cause violations in product standards. In this study, we have discussed the aleatory and epistemic uncertainties and modelled them by using probability and possibility distributions, respectively. Mathematical models including probabilistic and possibilistic parameters are generally solved by transforming one type of parameter into the other. However, the transformation processes have some handicaps such as knowledge losses or virtual information production. In this paper, we have proposed a new solution approach that needs no transformation process and so eliminates these handicaps. The proposed approach combines both chance-constrained stochastic programming and possibilistic programming. The solution of the numerical example has shown that the blending problem including probabilistic and possibilistic uncertainties can be successfully handled and solved by the proposed approach.