Multi-Criteria Decision Making under Uncertain Evaluations

Multi-Criteria Decision Making (MCDM) is a branch of operation research that aims to empower decision makers (DMs) in complex decision problems, where merely depending on DMs judgment is insufficient. Conventional MCDM approaches assume that precise information is available to analyze decision problems. However, decision problems in many applications involve uncertain, imprecise, and subjective data. This manuscripts-based thesis aims to address a number of challenges within the context of MCDM under uncertain evaluations, where the available data is relatively small and information is poor. The first manuscript is intended to handle decision problems, where interdependencies exist among evaluation criteria, while subjective and objective uncertainty are involved. To this end, a new hybrid MCDM methodology is introduced, in which grey systems theory is integrated with a distinctive combination of MCDM approaches. The emergent ability of the new methodology should improve the evaluation space in such a complex decision problem. The overall evaluation of a MCDM problem is based on alternatives evaluations over the different criteria and the associated weights of each criterion. However, information on criteria weights might be unknown. In the second manuscripts, MCDM problems with completely unknown weight information is investigated, where evaluations are uncertain. At first, to estimate the unknown criteria weights a new optimization model is proposed, which combines the maximizing deviation method and the principles of grey systems theory. To evaluate potential alternatives under uncertain evaluations, the Preference Ranking Organization METHod for Enrichment Evaluations approach is extended using degrees of possibility. In many decision areas, information is collected at different periods. Conventional MCDM approaches are not suitable to handle such a dynamic decision problem. Accordingly, the third manuscript aims to address dynamic MCDM (DMCDM) problems with uncertain evaluations over different periods, while information on criteria weights and the influence of different time periods are unknown. A new DMCDM is developed in which three phases are involved: (1) establish priorities among evaluation criteria over different periods; (2) estimate the weight of vectors of different time periods, where the variabilities in the influence of evaluation criteria over the different periods are considered; (3) assess potential alternatives

Heterogeneous group decision making with thermodynamical parameters

There often exist different types of information due to the subjective and objective criteria in practical decision-making problems, thus it is necessary to develop some efficient frameworks to deal with the decision-making problems with heterogeneous information. The paper proposes a framework for group decisionmaking problems with heterogeneous information with thermodynamical parameters consisting of three parts to achieving this goal. The first part builds the rectifications of criteria weights according to decision makers’ confidence in evaluations. The second part adopts thermodynamical parameters to measure the numerical values and the data distribution of heterogeneous information to characterize the heterogeneous information fully. The last part applies the TODIM (an acronym in Portuguese for Interactive and Multicriteria Decision Making) to aggregate the decision-making results based on the characterized heterogeneous information without transforming it into a unified form. By depicting decision makers’ different sensitive attitudes towards uncertainty by several mathematical expressions, experiments are performed to assess the sensitive attitudes’ impacts on decisionmaking results with the proposed framework. Finally, a case study on the selection of a green supplier under the low-carbon economy is provided to illustrate the flexibility and feasibility of the proposed framework

Multicriteria analysis under uncertainty with IANUS - method and empirical results

IANUS is a method for aiding public decision-making that supports efforts towards sustainable development and has a wide range of application. IANUS stands for Integrated Assessment of Decisions uNder Uncertainty for Sustainable Development. This paper introduces the main features of IANUS and illustrates the method using the results of a case study in the Torgau region (eastern Germany). IANUS structures the decision process into four steps: scenario derivation, criteria selection, modeling, evaluation. Its overall aim is to extract the information needed for a sound, responsible decision in a clear, transparent manner. The method is designed for use in conflict situations where environmental and socioeconomic effects need to be considered and so an interdisciplinary approach is required. Special emphasis is placed on a broad perception and consideration of uncertainty. Three types of uncertainty are explicitly taken into account by IANUS: development uncertainty (uncertainty about the social, economic and other developments that affect the consequences of decision), model uncertainty (uncertainty associated with the prediction of the effects of decisions), and weight uncertainty (uncertainty about the appropriate weighting of the criteria). The backbone of IANUS is a multicriteria method with the ability to process uncertain information. In the case study the multicriteria method PROMETHEE is used. Since PROMETHEE in its basic versions is not able to process uncertain information an extension of this method is developed here and described in detail. --

Simplified models for multi-criteria decision analysis under uncertainty

Includes abstract.Includes bibliographical references.When facilitating decisions in which some performance evaluations are uncertain, a decision must be taken about how this uncertainty is to be modelled. This involves, in part, choosing an uncertainty format {a way of representing the possible outcomes that may occur. It seems reasonable to suggest {and is an aim of the thesis to show {that the choice of how uncertain quantities are represented will exert some influence over the decision-making process and the final decision taken. Many models exist for multi-criteria decision analysis (MCDA) under conditions of uncertainty; perhaps the most well-known are those based on multi-attribute utility theory [MAUT, e.g. 147], which uses probability distributions to represent uncertainty. The great strength of MAUT is its axiomatic foundation, but even in its simplest form its practical implementation is formidable, and although there are several practical applications of MAUT reported in the literature [e.g. 39, 270] the number is small relative to its theoretical standing. Practical applications often use simpler decision models to aid decision making under uncertainty, based on uncertainty formats that `simplify' the full probability distributions (e.g. using expected values, variances, quantiles, etc). The aim of this thesis is to identify decision models associated with these `simplified' uncertainty formats and to evaluate the potential usefulness of these models as decision aids for problems involving uncertainty. It is hoped that doing so provides some guidance to practitioners about the types of models that may be used for uncertain decision making. The performance of simplified models is evaluated using three distinct methodological approaches {computer simulation, `laboratory' choice experiments, and real-world applications of decision analysis {in the hope of providing an integrated assessment. Chapter 3 generates a number of hypothetical decision problems by simulation, and within each problem simulates the hypothetical application of MAUT and various simplified decision models. The findings allow one to assess how the simplification of MAUT models might impact results, but do not provide any general conclusions because they are based on hypothetical decision problems and cannot evaluate practical issues like ease-of-use or the ability to generate insight that are critical to good decision aid. Chapter 4 addresses some of these limitations by reporting an experimental study consisting of choice tasks presented to numerate but unfacilitated participants. Tasks involved subjects selecting one from a set of five alternatives with uncertain attribute evaluations, with the format used to represent uncertainty and the number of objectives for the choice varied as part of the experimental design. The study is limited by the focus on descriptive rather than real prescriptive decision making, but has implications for prescriptive decision making practice in that natural tendencies are identified which may need to be overcome in the course of a prescriptive analysis

Pairwise comparison matrices and the error-free property of the decision maker

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal