A visual interactive approach for multiple criteria decision making with monotone utility functions

We consider the problem of choosing the best of a set of alternatives where each alternative is evaluated on multiple criteria. We develop a visual interactive approach assuming that the decision maker (DM) has a general monotone utility function. The approach partitions the criteria space into nonoverlapping cells. The DM uses various graphical aids to move between cells and to further manipulate selected cells with the goal of creating cells that have ideal points less preferred than an alternative. When the DM identifies such cells, all alternatives in those cells are eliminated from further consideration. The DM may also compare pairs of alternatives. The approach terminates with the most preferred alternative of the DM.     

A multiple criteria decision making approach to manure management systems in the Netherlands

The intensification of livestock operations in the last few decades has resulted in an increased social concern over the environmental impacts of livestock operations and thus making appropriate manure management decisions increasingly important. A socially acceptable manure management system that simultaneously achieves the pressing environmental objectives while balancing the socio-economic welfare of farmers and society at large is needed. Manure management decisions involve a number of decision makers with different and conflicting views of what is acceptable in the context of sustainable development. This paper developed a decision-making tool based on a multiple criteria decision making (MCDM) approach to address the manure management problems in the Netherlands. This paper has demonstrated the application of compromise programming and goal programming to evaluate key trade-offs between socio-economic benefits and environmental sustainability of manure management systems while taking decision makers’ conflicting views of the different criteria into account. The proposed methodology is a useful tool in assisting decision makers and policy makers in designing policies that enhance the introduction of economically, socially and environmentally sustainable manure management systems.     

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.     

A multiple criteria decision making approach for electricity planning in Spain: economic versus environmental objectives

Growing social concern about the environmental impact of economic development has drawn attention to the need to integrate environmental criteria into energy decision-making problems. This has made electricity planning issues more complex given the multiplicity of objectives and decision-makers involved in the decision making process. This paper proposes a methodology that combines several multi-criteria methods to address electricity planning problems within a realistic context. The method is applied to an electricity planning exercise in Spain with a planning horizon set for the year 2030. The model includes the following objectives: (1) total cost; (2) C0₂; (3) SO₂; and (4) NO _x emissions as well as the amount of radioactive waste produced. An efficient social compromise between these conflicting objectives is obtained, which shows the advantages of using this model for policy-making purposes.     

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.     

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.     

Systemic decision making in AHP: a Bayesian approach

Systemic decision making is a new approach for dealing with complex multiactor decision making problems in which the actors’ individual preferences on a fixed set of alternatives are incorporated in a holistic view in accordance with the “principle of tolerance”. The new approach integrates all the preferences, even if they are encapsulated in different individual theoretical models or approaches; the only requirement is that they must be expressed as some kind of probability distribution. In this paper, assuming the analytic hierarchy process (AHP) is the multicriteria technique employed to rank alternatives, the authors present a new methodology based on a Bayesian analysis for dealing with AHP systemic decision making in a local context (a single criterion). The approach integrates the individual visions of reality into a collective one by means of a tolerance distribution, which is defined as the weighted geometric mean of the individual preferences expressed as probability distributions. A mathematical justification of this distribution, a study of its statistical properties and a Monte Carlo method for drawing samples are also provided. The paper further presents a number of decisional tools for the evaluation of the acceptance of the tolerance distribution, the construction of tolerance paths that increase representativeness and the extraction of the relevant knowledge of the subjacent multiactor decisional process from a cognitive perspective. Finally, the proposed methodology is applied to the AHP-multiplicative model with lognormal errors and a case study related to a real-life experience in local participatory budgets for the Zaragoza City Council (Spain).     

On the problem of weights in multiple criteria decision making (the noncompensatory approach)

This paper shows how the notion of ‘relative importance of attributes’ can be defined within the framework of the noncompensatory approach to multiple criteria decision making. The problem of weights then appears as a problem of functional representation of relations. We state some theoretical results concerning this problem and outline a practical decision-aid (Tactic) based on the ideas introduced in the paper.     

A Bayesian priorization procedure for AHP-group decision making

This paper proposes a new priorization procedure for Analytic Hierarchy Process Group Decision Making (AHP-GDM). Unlike the methods normally employed in AHP-GDM, this process does not require intermediate filters for the actors’ initial judgements. The procedure is based on a Bayesian analysis of the problem and in general, it provides more efficient estimates than the techniques conventionally applied in the literature for AHP-GDM: aggregation of individual judgements (AIJ) and aggregation of individual priorities (AIP). The proposed procedure naturally extends to the analysis of incomplete and/or imprecise pairwise comparison matrices, enhancing realism, practicality and scope. The methodology has been illustrated by the analysis of a case study.     

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.     

A new method for multiple criteria group decision making with incomplete weight information under linguistic environment

A new method is proposed to solve multiple criteria group decision making (MCGDM) problems, in which both the criteria values and criteria weights take the form of linguistic information, and the information about linguistic criteria weights is partly known or completely unknown. Firstly, to get reasonable decision result, instead of assigning the same weight to the decision maker (DM) for all criteria, we propose a method to determine the weight of DM with respect to each criterion under linguistic environment by calculating the similarity degree between individual 2-tuple linguistic evaluation value and the mean given by all decision makers (DMs). Secondly, for the situations where the information about the criteria weights is partly known or completely unknown, we establish optimization models to determine the criteria weights by defining 2-tuple linguistic positive ideal solution (TL-PIS), 2-tuple linguistic right negative ideal solution (TL-RNIS) and 2-tuple linguistic left negative ideal solution (TL-LNIS) of the collective 2-tuple linguistic decision matrix. Thirdly, we propose a new method to solve MCGDM problems with partly known or completely unknown linguistic weight information. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method.     

Conjoint measurement in multiple objective decision making: A new approach

A new methodology for estimating the objective function in a multiple objective mathematical programming model is presented. A decision maker is required to provide pairwise preferences, or rank orders, of a set of solutions to the multiple objective problem. Conjoint measurement is then applied to this preference information to estimate parameters of an assumed utility function. Simulation tests support the method as being mathematically tractable, while a laboratory study with human decision makers provides encouraging results for the practicality of the technique.     

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.     

Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting

Multiple criteria group decision making (MCGDM) problems have become a very active research field over the last decade. Many practical problems are often characterized by MCGDM. The aim of this paper is to develop a new approach for MCGDM problems with incomplete weight information in linguistic setting based on the projection method. Firstly, to reflect the reality accurately, a method to determine the weights of decision makers in linguistic setting is proposed by calculating the degree of similarity between 2-tuple linguistic decision matrix given by each decision maker and the average 2-tuple linguistic decision matrix. By using the weights of decision makers, all individual 2-tuple linguistic decision matrices are aggregated into a collective one. Then, to determine the weight vector of criteria, we establish a non-linear optimization model based on the basic ideal of the projection method, i.e., the optimal alternative should have the largest projection on the 2-tuple linguistic positive ideal solution (TLPIS). Calculate the 2-tuple linguistic projection of each alternative on the TLPIS and rank all the alternatives according to the 2-tuple linguistic projection value. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method, and the validity is verified by comparing the evaluation results of the proposed method with that of the technique for order preference by similarity to ideal solution (TOPSIS) method.     

A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations

This paper proposes a method for solving stochastic multiple criteria decision making (MCDM) problems, where evaluations of alternatives on considered criteria are random variables with known probability density functions or probability mass functions. Probabilities on all possible results of pairwise comparisons of alternatives are first calculated using Probability Theory. Then, all possible results of pairwise comparisons are classified into superior, indifferent and inferior ones using a predefined identification rule. Consequently, the probabilities on all possible results of pairwise comparisons are partitioned into superior, indifferent and inferior probabilities. Furthermore, based on the derived probabilities, an algorithm is developed to rank the alternatives. Finally, a numerical example is used to illustrate the feasibility and validity of the proposed method.     

The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making

QUALIFLEX, a generalization of Jacquet-Lagreze’s permutation method, is a useful outranking method in decision analysis because of its flexibility with respect to cardinal and ordinal information. This paper develops an extended QUALIFLEX method for handling multiple criteria decision-making problems in the context of interval type-2 fuzzy sets. Interval type-2 fuzzy sets contain membership values that are crisp intervals, which are the most widely used of the higher order fuzzy sets because of their relative simplicity. Using the linguistic rating system converted into interval type-2 trapezoidal fuzzy numbers, the extended QUALIFLEX method investigates all possible permutations of the alternatives with respect to the level of concordance of the complete preference order. Based on a signed distance-based approach, this paper proposes the concordance/discordance index, the weighted concordance/discordance index, and the comprehensive concordance/discordance index as evaluative criteria of the chosen hypothesis for ranking the alternatives. The feasibility and applicability of the proposed methods are illustrated by a medical decision-making problem concerning acute inflammatory demyelinating disease, and a comparative analysis with another outranking approach is conducted to validate the effectiveness of the proposed methodology.     

The SIR method: A superiority and inferiority ranking method for multiple criteria decision making

In this paper, a superiority and inferiority ranking (SIR) method is proposed. This new method uses two types of information, the superiority and the inferiority information, to derive two types of flows, the superiority flow and the inferiority flow, by which the set of alternatives are ranked partially or completely. Relationships between the SIR method and some of the classical multiple criteria decision making (MCDM) methods (such as SAW, TOPSIS and PROMETHEE) are explored. It is proved that the SIR method is a significant extension of the well-known PROMETHEE method.     

Bayesian enhanced strategic decision making for reliability

Successful strategies for maintenance and replacement require good decisions. We might wish to determine how often to perform preventive maintenance, or the optimal time to replace a system. Alternatively, our interest might be in selecting a threshold to adopt for action under condition monitoring, or in choosing suitable warranty schemes for our products. Stochastic reliability models involving unknown parameters are often used to answer such questions. In common with other problems in operational research, some applications of maintenance and replacement are notorious for their lack of data. We present a general review and some new ideas for improving decisions by adopting Bayesian methodology to allow for the uncertainty of model parameters. These include recommendations for specifying suitable prior distributions using predictive elicitation and simple methods for Bayesian simulation. Practical demonstrations are given to illustrate the potential benefits of this approach.     

Pruning of decision alternatives in multiple criteria decision making,based on the Uta method for estimating utilities

A new interactive method for the progressive elimination of elements from a finite set of decision alternatives is proposed. A sequence of alternatives is presented to the decision maker, who places each new alternative presented in rank order relative to the earlier alternatives evaluated. This ranking of elements in a subset of the decision space is used to eliminate other alternatives from further consideration. The approach is broadly based on the UTA method for utility assessment. The emphasis is not, however, on assessing a utility function as such; instead the class of utility functions is used to eliminate elements of the decision space, when the optimality of such elements is inconsistent with the presumed properties of the utility function and the rank orderings given. In this way, the decision maker need only evaluate a relatively small subset of the decision space, before all remaining alternatives are eliminated. The new procedure is illustrated by two numerical examples.     

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.