An action learning evaluation procedure for multiple criteria decision making problems

In this paper we focus on an extension of the Analytic Hierarchy Process (AHP) that accommodates ambiguity on the part of the decision maker (DM), and facilitates the exploration of the decision domain. We propose a systematic action learning process that builds confidence as it converges from numeric interval estimates to numeric point estimates. Our Multiple Criteria Decision Making (MCDM) problem procedure structures the problem as a hierarchy, evaluates all objects using pairwise comparisons that accommodate vagueness and ambiguity, uses interval prioritization techniques, and does synthesis using the linear additive value function. This action learning process facilitates the understanding of key stakeholders, which is imperative for the successful implementation of the subsequent decision.     

DIS-CARD: a new method of multiple criteria sorting to classes with desired cardinality

In this paper, we present a new preference disaggregation method for multiple criteria sorting problems, called DIS-CARD. Real-life experience indicates the need of considering decision making situations in which a decision maker (DM) specifies a desired number of alternatives to be assigned to single classes or to unions of some classes. These situations require special methods for multiple criteria sorting subject to desired cardinalities of classes. DIS-CARD deals with such a problem, using the ordinal regression approach to construct a model of DM’s preferences from preference information provided in terms of exemplary assignments of some reference alternatives, together with the above desired cardinalities. We develop a mathematical model for incorporating such preference information via mixed integer linear programming (MILP). Then, we adapt the MILP model to two types of preference models: an additive value function and an outranking relation. Illustrative example is solved to illustrate the methodology.     

A data model for algorithmic multiple criteria decision analysis

Various software tools implementing multiple criteria decision analysis (MCDA) methods have appeared over the last decades. Although MCDA methods share common features, most of the implementing software have been developed independently from scratch. Majority of the tools have a proprietary storage format and exchanging data among software is cumbersome. Common data exchange standard would be useful for an analyst wanting to apply different methods on the same problem. The Decision Deck project has proposed to build components implementing MCDA methods in a reusable and interchangeable manner. A key element in this scheme is the XMCDA standard, a proposal that aims to standardize an XML encoding of common structures appearing in MCDA models, such as criteria and performance evaluations. Although XMCDA allows to present most data structures for MCDA models, it almost completely lacks data integrity checks. In this paper we present a new comprehensive data model for MCDA problems, implemented as an XML schema. The data model includes types that are sufficient to represent multi-attribute value/utility models, ELECTRE III/TRI models, and their stochastic extensions, and AHP. We also discuss use of the data model in algorithmic MCDA.     

Robustness and information levels in case-based multiple criteria sorting

Case-based preference elicitation methods for multiple criteria sorting problems have the advantage of posing rather small cognitive demands on a decision maker, but they may lead to ambiguous results when preference parameters are not uniquely determined. We use a simulation approach to determine the extent of this problem and to study the impact of additional case information on the quality of results. Our experiments compare two decision analysis tools, case-based distance sorting and the simple additive weighting method, in terms of the effects of additional case information on sorting performance, depending on problem dimension – number of groups, number of criteria, etc. Our results confirm the expected benefit of additional case information on the precision of estimates of the decision maker’s preferences. Problem dimension, however, has some unexpected effects.     

Dealing with inconsistent judgments in multiple criteria sorting models

Sorting models consist in assigning alternatives evaluated on several criteria to ordered categories. To implement such models it is necessary to set the values of the preference parameters used in the model. Rather than fixing the values of these parameters directly, a usual approach is to infer these values from assignment examples provided by the decision maker (DM), i.e., alternatives for which (s)he specifies a required category. However, assignment examples provided by DMs can be inconsistent, i.e., may not match the sorting model. In such situations, it is necessary to support the DMs in the resolution of this inconsistency. In this paper, we extend algorithms from mous5ejor03 that calculate different ways to remove assignment examples so that the information can be represented in the sorting model. The extension concerns the possibility to relax (rather than to delete) assignment examples. These algorithms incorporate information about the confidence attached to each assignment example, hence providing inconsistency resolutions that the DMs are most likely to accept. Received: September 2004, Revised: June 2005 AMS classification: 90B50, 91B08, 90C05     

Modeling action-interdependence in multiple criteria decision making

A problem of subset selection when actions are interdependent is formulated within a multiple criteria framework. More specifically, a novel definition and characterization of interdependence of actions applicable to Multiple Criteria Decision Making (MCDM) are presented. The effects of interdependence of actions on the modeling and resolution of a subset choice problem are shown, and the importance of taking interdependence of actions into account is discussed. Most of the discussion is generalized to independence and interdependence of sets of actions, which are then compared to the case of individual actions. A general approach to evaluate a combination of interdependent actions is proposed and the use of the multiple criteria structure to eliminate some difficulties in evaluating a set of interdependent actions is explained.     

Progressive methods in multiple criteria decision analysis

This is a summary of the author’s Ph.D. thesis, defended on 8 October 2007 at the University of Luxembourg and the Faculté Polytechnique de Mons, under the joint supervision of Raymond Bisdorff and Marc Pirlot. The thesis is written in English and is available from the author upon request. The work is situated in the field of multiple criteria decision analysis. It mostly deals with what we call progressive methods, i.e., iterative procedures presenting partial conclusions to the decision maker that can be refined at further steps of the analysis. Such progressive methods have been studied in the context of multiattribute value theory and outranking methods.      

Searching for psychologically stable solutions of multiple criteria decision problems

In interactive decision making, a choice behavior of the decision maker may differ depending on proximity of a current solution to satisfactory values of objectives. An interactive approach proposed in this paper allows the decision maker to use different search principles depending on his/her perception of the achieved values of objectives and trade-offs. While an analysis of the values of objectives may guide the initial search for a final solution, it can be replaced by trade-off evaluations at some later stages. Such an approach allows the decision maker to change search principles, and to identify a psychologically stable solution to the multiple criteria decision problem.     

Regularized estimation for preference disaggregation in multiple criteria decision making

Disaggregation methods have been extensively used in multiple criteria decision making to infer preferential information from reference examples, using linear programming techniques. This paper proposes simple extensions of existing formulations, based on the concept of regularization which has been introduced within the context of the statistical learning theory. The properties of the resulting new formulations are analyzed for both ranking and classification problems and experimental results are presented demonstrating the improved performance of the proposed formulations over the ones traditionally used in preference disaggregation analysis.     

Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis

Models for Multiple Criteria Decision Analysis (MCDA) often separate per-criterion attractiveness evaluation from weighted aggregation of these evaluations across the different criteria. In simulation-based MCDA methods, such as Stochastic Multicriteria Acceptability Analysis, uncertainty in the weights is modeled through a uniform distribution on the feasible weight space defined by a set of linear constraints. Efficient sampling methods have been proposed for special cases, such as the unconstrained weight space or complete ordering of the weights. However, no efficient methods are available for other constraints such as imprecise trade-off ratios, and specialized sampling methods do not allow for flexibility in combining the different constraint types. In this paper, we explore how the Hit-And-Run sampler can be applied as a general approach for sampling from the convex weight space that results from an arbitrary combination of linear weight constraints. We present a technique for transforming the weight space to enable application of Hit-And-Run, and evaluate the sampler’s efficiency through computational tests. Our results show that the thinning factor required to obtain uniform samples can be expressed as a function of the number of criteria n as φ(n) = (n − 1)³. We also find that the technique is reasonably fast with problem sizes encountered in practice and that autocorrelation is an appropriate convergence metric.     

An improved method for ranking alternatives in multiple criteria decision analysis

Scoring rules are an important disputable subject in data envelopment analysis (DEA). Various organizations use voting systems whose main object is to rank alternatives. In these methods, the ranks of alternatives are obtained by their associated weights. The method for determining the ranks of alternatives by their weights is an important issue. This problem has been the subject at hand of some authors. We suggest a three-stage method for the ranking of alternatives. In the first stage, the rank position of each alternative is computed based on the best and worst weights in the optimistic and pessimistic cases, respectively. The vector of weights obtained in the first stage is not a singleton. Hence, to deal with this problem, a secondary goal is used in the second stage. In the third stage of our method, the ranks of the alternatives approach the optimistic or pessimistic case. It is mentionable that the model proposed in the third stage is a multi-criteria decision making (MCDM) model and there are several methods for solving it; we use the weighted sum method in this paper. The model is solved by mixed integer programming. Also, we obtain an interval for the rank of each alternative. We present two models on the basis of the average of ranks in the optimistic and pessimistic cases. The aim of these models is to compute the rank by common weights.     

A DSS for multiple criteria decision analysis with imprecisely specified trade-offs

The paper describes a decision support system (DSS) for multiple criteria decision analysis (MCDA). It is assumed that the information about the trade-offs is given in the form of lower and upper bounds. The software helps the user to identify candidate solutions from a finite set of decision alternatives and can be used in an interactive decision process. The choice of the software features is based on the author's experience with an environmental case study, which is discussed.     

Decision-aid for discrete multiple criteria decision making problems with imprecise data

We describe ways of aiding decision making with a discrete set of alternatives. In many decision situations, it is not possible to obtain explicit preference information from the decision makers. Instead, useful decision-aid can be provided to the decision makers by describing what kind of weighting of the criteria result in certain choices of the alternatives. The suggested treatment is based on the basic ideas of the ELECTRE III method. The modelling of the preferences by pseudo-criteria is especially helpful in case the data, that is, the criterion values are imprecise. Unlike ELECTRE III, no ranking of the alternatives is produced. Based on a minimum-procedure in the exploitation of the outranking relations, we provide information about the weights of the criteria that make a certain alternative the best. We also present an interactive searching procedure in the weighting space. The auxiliary optimization problems to be solved are nondifferentiable. Cases with both single and multiple decision makers are considered.     

Weight determination for consistently ranking alternatives in multiple criteria decision analysis

One of the most difficult tasks in multiple criteria decision analysis (MCDA) is determining the weights of individual criteria so that all alternatives can be compared based on the aggregate performance of all criteria. This problem can be transformed into the compromise programming of seeking alternatives with a shorter distance to the ideal or a longer distance to the anti-ideal despite the rankings based on the two distance measures possibly not being the same. In order to obtain consistent rankings, this paper proposes a measure of relative distance, which involves the calculation of the relative position of an alternative between the anti-ideal and the ideal for ranking. In this case, minimizing the distance to the ideal is equivalent to maximizing the distance to the anti-ideal, so the rankings obtained from the two criteria are the same. An example is used to discuss the advantages and disadvantages of the proposed method, and the results are compared with those obtained from the TOPSIS method.     

Nonatomic total rewards Markov decision processes with multiple criteria

We consider a Markov decision process with an uncountable state space for which the vector performance functional has the form of expected total rewards. Under the single condition that initial distribution and transition probabilities are nonatomic, we prove that the performance space coincides with that generated by nonrandomized Markov policies. We also provide conditions for the existence of optimal policies when the goal is to maximize one component of the performance vector subject to inequality constraints on other components. We illustrate our results with examples of production and financial problems.     

A multicriteria assignment procedure for a nominal sorting problematic

This paper addresses the problem of the assignment of an action in the particular case where the categories defined a priori are not ordered. In multicriteria literature, it is the nominal sorting problematic. We propose a simple and easy method to understand the procedure of assignment to tackle this problematic. Afterwards, we shall illustrate the proposed method by using an example that is inspired by a research carried out the construction sector of the work accident prevention field.     

A multiple criteria decision analytic approach for evaluating acid rain policy choices

Multi-Attribute Utility Theoretic Approach is adopted to analyze the problem of acid rain policy choices for multiple impacted groups (agents) under two conditions: exact and imprecise preference information. The analysis involves the setting up of attributes and feasible policy alternatives. Estimates of acid rain impacts are obtained from secondary data. The emphasis is more on framework which allows explorations of compromises and the identification of acceptable impact areas than on exact results. The strongest message of this paper is that even without specifying exact cardinal preferences some dominance relationships can be established between policies in a real-world setting.