Multicriteria decision making under uncertainty: a visual approach

Decision problems at the strategic level tend to have multiple criteria and outcomes that are uncertain. Many of the current decision‐making tools are too simplistic to incorporate the important features. This paper considers a multicriteria decision‐making scenario in which the outcomes of the decisions, evaluated on different criteria, are uncertain. The main contribution of this paper is the presentation of a tool that enables decision makers to visualize the expected payoff and likelihood that the payoff of a decision does not fall short of a preset target value. Furthermore, it presents decision makers with a tool that shows the tradeoff between expected payoff and downside risk. A variety of solution techniques are suggested that build upon this visualization.     

Relating decision under uncertainty and multicriteria decision making models

This short overview paper points out the striking similarity between decision under uncertainty and multicriteria decision making problems, two areas which have been developed in an almost completely independent way until now. This pertains both to additive and non‐additive (including qualitative) approaches existing for the two decision paradigms. This leads to an emphasis on the remarkable formal equivalence between postulates underlying these approaches (like between the “sure‐thing principle” and mutual preferential independence of criteria). This analogy is exploited by surveying classical results as well as very recent advances. This unified view should be fruitful for a better understanding of the postulates underlying the approaches, for cross‐fertilization, and for adapting artificial intelligence uncertainty representation frameworks to preference modelling. © 2000 John Wiley & Sons, Inc.     

Fuzzy modeling for intelligent decision making under uncertainty

We consider here the problem of decision making under uncertainty. We suggest an approach for the construction of decision functions which allow for the inclusion of probabilistic information as well as for the inclusion of information about the decision maker's attitude and preferences. Use is made of the fuzzy modeling technology to construct these functions from specifications provided by the decision maker.     

An approach to fuzzy multiattribute decision making under uncertainty

It seems that there is little investigation on fuzzy multiattribute decision making (FMADM) problems under uncertainty, which are of important to scientific researches and real life applications. FMADM problems under uncertainty are investigated in this paper. Novel mathematical programming models are constructed for FMADM problems under uncertainty, and corresponding solving methods are proposed. The approach proposed in this paper may reflect both subjective judgment and objective information. Moreover, pairwise chain comparison methods for determination of relative membership degrees and weights are also proposed. Feasibility and effectiveness of the models and approach proposed in this paper are illustrated with a numerical example.     

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.     

Exploring scientific information for policy making under deep uncertainty

Each actor evaluating potential management strategies brings her/his own distinct set of objectives to a complex decision space of system uncertainties. The diversity of these objectives and uncertainties requires detailed and rigorous analyses that respond to multifaceted challenges. The utility of this information depends on the accessibility of scientific information to decision makers. This paper demonstrates data visualization tools for presenting scientific results to decision makers in two case studies, La Paz/El Alto, Bolivia, and Yuba County, California. Visualization output from the case studies combines spatiotemporal, multivariate and multirun/multiscenario information to produce information corresponding to the objectives and uncertainties described by key actors. These tools can manage complex data and distill scientific information into accessible formats. Using the visualizations, scientists and decision makers can navigate the decision space and potential objective trade-offs to facilitate discussion and consensus building. These efforts can help identify stable negotiated agreements between different stakeholders.     

Formal models and algorithms for decentralized decision making under uncertainty

Over the last 5 years, the AI community has shown considerable interest in decentralized control of multiple decision makers or “agents” under uncertainty. This problem arises in many application domains, such as multi-robot coordination, manufacturing, information gathering, and load balancing. Such problems must be treated as decentralized decision problems because each agent may have different partial information about the other agents and about the state of the world. It has been shown that these problems are significantly harder than their centralized counterparts, requiring new formal models and algorithms to be developed. Rapid progress in recent years has produced a number of different frameworks, complexity results, and planning algorithms. The objectives of this paper are to provide a comprehensive overview of these results, to compare and contrast the existing frameworks, and to provide a deeper understanding of their relationships with one another, their strengths, and their weaknesses. While we focus on cooperative systems, we do point out important connections with game-theoretic approaches. We analyze five different formal frameworks, three different optimal algorithms, as well as a series of approximation techniques. The paper provides interesting insights into the structure of decentralized problems, the expressiveness of the various models, and the relative advantages and limitations of the different solution techniques. A better understanding of these issues will facilitate further progress in the field and help resolve several open problems that we identify. This work was done while S. Seuken was a graduate student in the Computer Science Department of the University of Massachusetts, Amherst.     

多目标模糊决策算法研究

在Vague多目标决策的研究中,引入两两比较决策行为,并通过拉格朗日乘数法解决一致性问题,最终找到最优方案。案例验证了该方法的有效性和可行性。     

Decision making under uncertainty in a decision support system for the Red River

Decision support systems (DSSs) are increasingly being used in water management for the evaluation of impacts of policy measures under different scenarios. The exact impacts generally are unknown and surrounded with considerable uncertainties. It may therefore be difficult to make a selection of measures relevant for a particular water management problem. In order to support policy makers to make a strategic selection between different measures in a DSS while taking uncertainty into account, a methodology for the ranking of measures has been developed. The methodology has been applied to a pilot DSS for flood control in the Red River basin in Vietnam and China. The decision variable is the total flood damage and possible flood reducing measures are dike heightening, reforestation and the construction of a retention basin. The methodology consists of a Monte Carlo uncertainty analysis employing Latin Hypercube Sampling and a ranking procedure based on the significance of the difference between output distributions for different measures. The mean flood damage in the base situation is about 2.2 billion US$ for the year 1996 with a standard deviation due to parameter uncertainty of about 1 billion US$. Selected applications of the measures reforestation, dike heightening and the construction of a retention basin reduce the flood damage by about 5, 55 and 300 million US$, respectively. The construction of a retention basin significantly reduces flood damage in the Red River basin, while dike heightening and reforestation reduce flood damage, but not significantly.     

A family of dominance rules for multiattribute decision making under uncertainty

Multiattribute decision-making involves choosing from a set of alternatives each of which is evaluated along multiple criteria that reflect the dimensions of interest to the goals and values of the decision-maker. Dominance-based decision-making narrows down the focus of the decision to the Pareto optimal set. The elimination of dominated alternatives is a compelling principle of rationality since each dominated alternative is logically inferior to its dominating alternative, given the criteria of evaluation. One kind of uncertainty in multiattribute decision making arises out of noisy or inaccurate criteria evaluations. The application of the principle of dominance is not quite rational if the criteria evaluations are known to be noisy. In this paper, we see how dominance-based decision-making can be applied to multiattribute decision-making problems with uncertainty due to noisy criteria values. In particular it will be shown that, for bounded uncertainty it is possible to produce the smallest sufficient subset that is guaranteed to contain all of the nondominated alternatives, and the largest necessary subset that contains only nondominated alternatives. For unbounded uncertainty, we will see how these notions of sufficiency and necessity can be adapted to varying degrees of probabilistic assurances desired by the decision-maker, and that the varying degrees of user assurance map naturally to a family of dominance rules.     

Multiple-attribute decision making under uncertainty: the evidential reasoning approach revisited

In multiple-attribute decision making (MADM) problems, one often needs to deal with decision information with uncertainty. During the last decade, Yang and Singh (1994) have proposed and developed an evidential reasoning (ER) approach to deal with such MADM problems. Essentially, this approach is based on an evaluation analysis model and Dempster's rule of combination in the Dempster-Shafer (D-S) theory of evidence. This paper reanalyzes the ER approach explicitly in terms of D-S theory and then proposes a general scheme of attribute aggregation in MADM under uncertainty. In the spirit of such a reanalysis, previous ER algorithms are reviewed and two other aggregation schemes are discussed. Theoretically, it is shown that new aggregation schemes also satisfy the synthesis axioms, which have been recently proposed by Yang and Xu (2002) for which any rational aggregation process should grant. A numerical example traditionally examined in published sources on the ER approach is used to illustrate the discussed techniques.     

On the methods of decision making under uncertainty with probability information

By considering the decision maker's attitude of profit and risk, we propose an alternative selection method that can include the methods of decision making under ignorance and decision making under risk as special cases. An index to measure the decision maker's risk‐averse degree is proposed. With a given optimistic level of profit and risk, the evaluation results of the alternatives can be obtained with a geometric ordered weighted average (OWA) operator and a basic defuzzification distribution (BADD) neat OWA operator. Some properties of these two kinds of OWA operator in the problem of decision making under uncertainty are also proposed. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1217–1238, 2004.     

Context-aware decision making under uncertainty for voice-based control of smart home

This paper presents a framework to build home automation systems reactive to voice for improved comfort and autonomy at home. The focus of this paper is on the context-aware decision process which must reason from uncertain facts inferred from real sensor data. This framework for building context aware systems uses a hierarchical knowledge model so that different inference modules can communicate and reason with same concepts and relations. The context-aware decision module is based on a Markov Logic Network, a recent approach which make it possible to benefit from formal logical representation and to model uncertainty of this knowledge. In this work, uncertainty of the decision model has been learned from data. Although some expert systems are able to deal with uncertainty, the Markov Logic Network approach brings a unified theory for dealing with logical entailment, uncertainty and missing data. Moreover, the ability to use a priori knowledge and to learn weights and structure from data make this model appealing to address the challenge of adaptation of expert systems to new applications. Finally, the framework has been implemented in an on-line system which has been evaluated in a real smart home with real naive users. Results of the experiment show the interest of context-aware decision making and the advantages of a statistical relational model for the framework.     

Use of decision models under uncertainty in thermal design

A probabilistic approach is described for analysing the results of computer simulation of the thermal behaviour of buildings. This approach takes into account the uncertainties in predicting the climate. The use of models of decision theory enables the designer to compare several design alternatives of a building and to select the best one in terms of use of energy. The application of decision models under uncertainty in the design process of solarium is presented.     

多目标决策的激励策略可行解

针对多目标决策问题,提出一种新的基于一般变权原理的求解方法.利用一般变权原理提出激励策略可行解,证明其为多目标决策的均衡有效解,并给出求激励策略可行解的步骤.通过实际算例表明,所提出算法正确有效,且相对于线性加权和法、平方加权和法而言,具有较好的均衡性.     

A multi-objective model for environmental investment decision making

Investment in landscapes to achieve outcomes that have multiple environmental benefits has become a major priority in many countries. This gives rise to opportunities for mathematical programming methods to provide solutions on where investments could be made on the landscape, to maximise multiple environmental benefits. The problem was formulated as a multi-objective integer programming model, with objective functions representing biodiversity, water run-off and carbon sequestration. We applied a multi-objective Greedy Randomised Adaptive Search Procedure (GRASP) as an evolutionary programming method to find solutions along the Pareto front. This allows the decision maker to explore trade-off's between the objectives. A 142,000 ha case study catchment in eastern Australia was used to test the methodology and assess the sensitivity of the different and often competing environmental benefits.     

Decentralized multi-objective bilevel decision making with fuzzy demands

Decisions in a decentralized organization often involve two levels. The leader at the upper level attempts to optimize his/her objective but is affected by the follower; the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. When model a real-world bilevel decision problem, it also may involve fuzzy demands which appear either in the parameters of objective functions or constraints of the leader or the follower or both. Furthermore, the leader and the follower may have multiple conflict objectives that should be optimized simultaneously in achieving a solution. This study addresses both fuzzy demands and multi-objective issues and propose a fuzzy multi-objective bilevel programming model. It then develops an approximation branch-and-bound algorithm to solve multi-objective bilevel decision problems with fuzzy demands. Finally, two case-based examples further illustrate the proposed model and algorithm.     

The use of ordered weighted averaging method for decision making under uncertainty

A decision making under uncertainty (DMUU) prevails at the outset and often evolves into a decision making under partial uncertainty as information on the states of nature, for example, a probability distribution, is advanced. Many methods have emerged for solving the DMUU problems, which includes the classical decision criteria and the domain criterion. Yager (1988) introduced a new approach, the so‐called ordered weighted averaging (OWA) as a viable method for solving the DMUU problems. The OWA weights to be used in the aggregation are generated under the degree of optimism provided by a decision maker and then combined with the reordered payoffs to produce aggregated payoffs for each strategy. The reordering process, one of the characterizing features of the OWA method, enables us to perform various types of aggregations including maximax, maximin, and Hurwicz‐α index in conjunction with the generated weights. The OWA method obviously extends the Hurwicz approach by taking into account the tradeoffs among the entire payoffs while the Hurwicz approach considers a tradeoff only between the two extremes, the maximum and the minimum payoffs. In this paper, we examine the features of the OWA method in light of Milnor's set of requirements for reasonable decision criteria, thus providing a solid methodological foundation for the DMUU. The OWA method can also be used to solve a group DMUU problem by exploiting individual decision results in the situation when the use of a fuzzy majority is advocated.     

基于扩展原理的混合型证据推理不确定决策方法

提出一种基于扩展原理的混合证据推理不确定决策模型.通过α截集将同一决策问题中各属性使用的精确数、区间数和模糊数等异构评估信度统一分解为区间结构,采用区间证据推理方法求解各隶属度下的效用区间,并按隶属度次序重组方案效用;化简模糊数质心公式,并用于模糊定量评估的信度计算和方案模糊效用的排序;最后,通过具体实例验证了所提出方法的有效性和可行性.将该方法在算例中的适用情况进行比较和分析,结果表明所提出的方法具有良好的适应性.