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The article comments on the paper "Mindsets, Rationality and Emotion in Multi-Criteria Decision Analysis," by Fred Wenstøp. One specific point cited by the author concerning the paper is subjectivity. He said that Wenstøp seem to make a usual error mentioning that Pareto solutions correspond to an objective solution while the search of a compromise is subjective. The author also observed that Wenstøp compares MCDA to several different concepts and definitions of rationality. He also added that a large part of the paper is dedicated to the importance of considering emotions in decision theory.

Presents remarks on the article "On the Measurement of Preferences in the Analytic Hierarchy Process," by A. A. Salo and R. P. Hämäläinen. Information on multiattribute value theory (MAVT), a key concept in helping decision makers to come up with optimal decision; Questions answered by MAVT; Factors to consider in order to successfully use MAVT in a prescriptive way.

The aim of this paper is to highlight the role of the Decision Support System within the field of multi-criteria decision aid (MCDA). The MCDA tools have been incorporated into systems to create Multi-Criteria Decision Support Systems (MCDSSs). In our literature review, we noticed that more than 100 papers have been written over a 20-year period in which MCDSS was used as a decision-making tool. The present paper describes some real applications of MCDSS in different fields, harmoniously combined with decision-making methods such as analytic hierarchy process, Utility Additive, and Goal Programming. The present study proposes an integrative MCDSS evaluation through guidance on the tools most useful for a specific user with a particular decision problem. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The author reflects on Howard Raiffa's paper "Preferences for Multi-Attributed Alternatives," published as a RAND Corp. Research Memorandum. He observes that many of the ideas that permeate decision theory and the modern practice of decision analysis are present in the paper. He expresses disappointment for the little discussion of group decision making issues. He comments on the quantitative aspects of the report.

ABSTRACT This paper highlights the omnipresence of the philosophy, theory, methodology and deployment of multiple criteria decision making (MCDM) in essentially every aspect of our lives. It also highlights the specific philosophical, theoretical, methodological, and deployment perspectives that MCDM has influenced, and how MCDM has thus shaped the decision-making process. The following five themes demonstrate the universality of multiple objectives and their impact on the complex decision-making process: (i) the centrality of the states of the system in MCDM; (ii) the centrality of trade-offs in MCDM and the !-constraint method; (iii) the centrality of the time frame in MCDM; (iv) the centrality of risk and uncertainty in MCDM; and (v) the contributions of MCDM to decision analysis. An epilogue concludes the paper. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The author presents views on Howard Raiffa's paper "Preferences for Multi-Attributed Alternatives," published as a RAND Corp. Research Memorandum. He discusses two fundamentally important preference concepts introduced in the paper. He summarizes key issues for implementing multiattribute utility in the memorandum. He comments on the importance of interpreting and applying multiattribute utility theory.

In this paper a decision-making process is applied to a Chilean forestry firm that must deal with a host of environmental variables as well as profit making. At the core of this process is a ‘dynamic objective–subjective structure’ founded on the approach that decision making is about comprehending the preferences of the various parties involved and expanding the set of alternatives open to the decision makers. This is in contrast to many models that aim at finding the ‘best alternative’ and to decision analysis approaches that focus on presenting preferences via value functions. The paper describes in chronological order, following the sessions of a decision-making process, how the various components of the structure emerged. In doing so it demonstrates how the process led to an understanding of the real effects of dealing with the environment and how comprehending the preferences led to the introduction of new decision variables. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The editor discusses the paper which is the focus of this issue, "RAND Memorandum--5868," written by Howard Raiffa and appeared in 1969. She claims that it is the first formal exposition of what came to be known as multiattribute utility theory (MAUT). She explains that the 1976 book "Decision Making With Multiple Objectives" further developed the ideas of the memorandum. She cites the significant impact of those ideas on her career.

The decision maker (DM) can modify the evaluation of an object on one criterion in exchange for a cost depending on the object and the criterion. Recent years have seen a flourishing interest in I multiple criteria sorting models i , that is, models for assigning alternatives to predefined ordered categories while respecting the preference order on the criteria scales. In this issue, Colorni and Tsoukiàs (2021) argue that the term "rating" would be more adequate and would favour recognition by the large community of researchers who elaborate rating methods and users who apply them. [Extracted from the article]

The article discusses some techniques a decision maker might employ if he wants to assess a utility function over complex consequences. It examines the problem where each complex alternative can be described by a series of attributes which are interdependent in various ways. A hierarchical structuring procedure for obtaining a relevant list of attributes is described and examples are cited from Northeast Corridor transportation problems and from medical treatment problems. This paper also presents sufficient conditions in terms of strong conditional utility independence for obtaining a quasi-additive representation.

This paper gives a brief overview on new tendencies in environmental policy regarding electronic democracy, with two examples of environmental directives. The European Commission proposed Internet technology for the first time for the dissemination of the Solvent Directive (1999/13/EC), in order to display available information for the numerous affected sectors. Moreover, the possibility of an information exchange between the Commission, the Member States and approximately 400 000 companies concerned by the Directive was created. Another major topic of European Environmental Policy is the IPPC-Directive (96/61/EC), which requires an information exchange on and determination of the best available techniques for most industrial sectors in Europe. The decision making process is described in this paper, with special emphasis on the possibilities of electronic democracy. Based on these considerations, aspects of decision-making behaviour, in the context of integrated decision support for complex issues in the environmental domain, are analysed and put forth for discussion. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Order structures such as linear orders, semiorders and interval orders are often used to model preferences in decision-making problems. In this paper we introduce a family of preference structures where the mutual indifference threshold belongs to a specific family parametrized by extended reals a. This family includes interval orders (α = 1), tangent circle orders (α = 0) and a new preference structure called 'diamond order' (α = ∞). All these preference relations present an asymmetric part which is shown to be always quasi-transitive and to be transitive for α &ge: 1. Diamond orders present 'forbidden configurations' which can occur in the case of tangent circle orders. [ABSTRACT FROM AUTHOR]

In this paper we consider decision problems that can be described as linear decision models. These models have been traditionally solved using linear programming, fuzzy linear programming, multiple-objective linear programming or 'what-if' analysis. Using these approaches, one encounters a number of difficulties. We propose an 'evolutionary approach' to overcome these difficulties. In the proposed approach the decision maker does not have to precisely specify the model (i.e. the objective functions, the RHS values, etc.) at the beginning of the solution procedure. In fact, the model evolves as the solution procedure proceeds. [ABSTRACT FROM AUTHOR]

Most medium- and long-term decision making in industry and government can be viewed as dynamic multi-criteria decision making (MCDM), in which the decision makers are free to alter the emphasis placed on each objective in the light of developing circumstances. In this paper the problem of time-dependent weights in MCDM is discussed and an analysis of empirical data associated with dynamic decision making is presented. [ABSTRACT FROM AUTHOR]

This note concerns two issues left unresolved in our study of lexicographic-order preservation and stochastic dominance in settings where preferences are represented by utility vectors, ordered lexicographically, and judgments emerge as matrices that premultiply utility vectors in expected utility sums. First, a generalization of the 'Conjecture ∑', which implied transitivity of a stochastic dominance relation under non-vacuous resolution-level information, is proved. Second, this paper comments on using resolution-level information in higher as well as in first degree stochastic dominance analysis. [ABSTRACT FROM AUTHOR]

ABSTRACT The reciprocal pairwise comparison matrix is a well-established technique and widely used in multiple criteria decision making methods. However, some entries in a pairwise comparison matrix may not be available in many real-world decision problems. The goal of this paper is to propose a new method for estimating missing elements of an incomplete pairwise comparison matrix. A bias induced matrix model (BIMM), which combines the matrix multiplication and the properties of the original reciprocal pairwise comparison matrix, is used to calculate the missing entries in an incomplete pairwise comparison matrix. The proposed BIMM minimizes all bias values of the bias induced matrix to keep the global consistency. The missing value(s) can be estimated by solving the system of equations from the bias induced matrix. The theorems of the BIMM and the related corollaries are developed, and three numerical examples are introduced to illustrate the proposed model. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Proper scoring rules serve to measure subjective degrees of belief. Traditional proper scoring rules are based on the assumption of expected value maximization. There are, however, many deviations from expected value, primarily due to risk aversion. Correcting techniques have been proposed in the literature for deviations due to nonlinear utility. These techniques still assumed expected utility maximization. More recently, corrections for deviations from expected utility have been proposed. The latter concerned, however, only the quadratic scoring rule, and could handle only half of the domain of subjective beliefs. Further, beliefs close to 0.5 could not be discriminated. This paper generalizes the correcting techniques to all bounded binary proper scoring rules, covers the whole domain of beliefs and, in particular, can discriminate between all degrees of belief. Thus, we fully extend the properness requirement (in the sense of identifying all degrees of subjective beliefs) to virtually all models that deviate from expected value. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Stochastic multicriteria acceptability analysis (SMAA) comprises a family of multiple criteria decision-aiding (MCDA) methods for problems including incomplete, imprecise, and uncertain information. Methods of the family allow solving MCDA problems of various types. Even though the methods have been applied in the past in various real-life decision-making situations, the structure of a unified SMAA framework has not been studied. In this paper we describe the methods of the family and define a unified SMAA framework. We also point out the key points in the methodology for future research. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The author comments on the practical significance of Howard Raiffa's paper "Preference for Multi-Attributed Alternatives," published as a RAND Corp. Research Memorandum. He considers the document as a major turning point in the evolution of prescriptive decision analysis (PDA). He explores the impact of multiattribute utility analysis (MUA) on decision aiding practice. He stresses the need for substantial complementary research to realize the full potential of MUA.

Employees need to acquire new qualifications throughout their lives in order to deal with the multiple changes in the labour market. This knowledge and competences (formally or non-formally acquired) must be identified and evaluated. For that reason, an integrated approach to the evaluation of Information and Communication Technology knowledge and skills is proposed. The multicriteria method that has been developed refers to professionals who wish to be accredited in a particular specialization through the evaluation of their professional experience, studies and vocational training. The aim of this paper is to present the multicriteria decision support system, Skills Evaluator, which brings into effect the aforementioned method. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The integrated use of scenario planning and multi-criteria decision analysis (MCDA) has been advocated as a powerful combination for providing decision support in strategic decisions. Scenario planning helps decision makers in devising strategies and thinking about possible future scenarios; while MCDA can support an in-depth performance evaluation of each strategy, as well as in the design of more robust and better options. One of the frameworks proposed recently, by Goodwin & Wright, suggests the use of scenario planning with multi-attribute value theory, a mathematically simple, yet extensively researched and widely employed multi-criteria method. However, so far, such framework has been presented only using hypothetical problems. In this paper, we describe two case studies where this approach was used to support real-world strategic decisions. We discuss the challenges and limitations we encountered in applying it and suggest some possible improvements that could be made to such framework. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we compare the ‘vision’ of e-democracy presented by the European Scientific Foundation programme Towards e-democracy (TED) with our practice of MCDA. On the basis of a recent real-world case, we try to analyse the potential for electronic tools. In our opinion, the first steps towards e-democracy are to be made in the direction of the external legitimization (exchange of information with actors not involved directly in the decision process). The relationship with the external actors could be dramatically improved if an Extranet site was used to gather and publish relevant information about the project. It remains to be seen if the introduction of e-democracy at the heart of the decision process—done at face-to-face meetings for the time being—is possible and useful. There are many issues to address, dealing for instance with the balance of legitimacy and power and the changing role of the actors. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The field of e-democracy has approached the problem of improving democratic decision making by emphasizing encouraging broad participation. This is due to a perceived lack of credibility on part of politicians, indicated by decline in both turnout in elections and recruitment to political parties. Experiences so far show that while in local contexts use of electronic tools in combination with redesigned democratic processes have indeed affected participation positively, both scaling and quality requires more sophisticated technical tools of at least two kinds. One kind, recognized by the e-democracy community, are tools supporting cooperative work for facilitating communication among humans. Another kind, this paper argues, is tools for more formal problem modelling. The e-democracy field has so far almost exclusively been concerned with encouraging and—at best—modelling, moderating, and reviewing discussions. Experiences from e.g. citizen juries point to the importance of expert participation. Decision Support Systems could provide—mediated—expert participation in virtual groups and in communication with the public. To achieve this, there is a need to carefully consider both the usability of Decision Support Systems and their role in the overall democratic system. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes a decision support system based on an additive multi-attribute utility model for identifying the optimal strategy in complex decision-making problems. The system allows for incomplete information on the component utility function and weight assessment, which leads to classes of utility functions and weight intervals, respectively. This makes the system suitable for group decision support, because individual conflicting views or judgements in a group of decision-makers can be captured through imprecise responses in the respective assessment methods. Moreover, the system admits uncertainty about the multi-attribute strategy consequences, which can be defined in term of ranges for each attribute instead of single values. The system computes non-dominance and potential optimality to identify the most preferred strategy. We also propose an approach based on Monte Carlo simulation techniques for group decision-making problems, which could be specially useful for e-democracy, where several decision-makers or groups of decision-makers elicit their own preferences separately, which are then compared to try to reach a consensus on their respective preferences. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper introduces a method for finding the non-dominated set in criterion space of an MOLP problem based on Fourier–Motzkin Elimination. The method incorporates a procedure that eliminates decision variables from constraints and transforms a feasible region from decision space to criterion space. While avoiding characterization of the efficient set in decision space, it finds the non-dominated set in criterion space. After the decision maker's most preferred criterion vector has been identified, the corresponding efficient solutions can be found by backward substitution. The method was implemented in MATLAB using a tabular form and computational experiments were conducted. The results indicate that although the method performs well for relatively small problems, it can be computationally intensive for larger problems. Nonetheless, the method is intuitively appealing and it provides useful insights into the geometry and theory of MOLP. As such it makes it a valuable educational tool for students of multi-criteria decision analysis. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Numerical decision analysis (NDA), derived from statistical decision theory, is very well known. Verbal decision analysis (VDA), oriented towards so-called unstructured problems, where the qualitative and uncertain factors dominate, is a newer direction in decision theory and practice. Verbal and numerical decision analyses (DAs) have been compared in an experimental setting, with groups of students. This paper presents the results of a comparison in the context of live practical tasks. Both approaches were attempted on two comparable choices, facing both Russian and US government agencies, involving a choice between oil and gas transportation options. The resulting methodological insights are generalized into a systematic comparison of the strong and weak features of each approach. [ABSTRACT FROM AUTHOR]

Multiple-criteria decision aid almost always requires the use of weights, importance coefficients or even a hierarchy of criteria, veto thresholds, etc. These are importance parameters that are used to differentiate the role devoted to each criterion in the construction of comprehensive preferences. Many researchers have studied the problem of how to assign values to such parameters, but few of them have tried to analyse in detail what underlies the notion of importance of criteria and to give a clear formal definition of it. In this paper our purpose is to define a theoretical framework so as to analyse the notion of the importance of criteria under very general conditions. Within this framework it clearly appears that the importance of criteria is taken into account in very different ways in various aggregation procedures. This framework also allows us to shed new light on fundamental questions such as: Under what conditions is it possible to state that one criterion is more important than another? Are importance parameters of the various aggregation procedures dependent on or independent of the encoding of criteria? What are the links between the two concepts of the importance of criteria and the compensatoriness of preferences? This theoretical framework seems to us sufficiently general to ground further research in order to define theoretically valid elicitation methods for importance parameters. [ABSTRACT FROM AUTHOR]

Issues of the cognitive validity of prescriptive decision-aiding methods are discussed in this paper. In view of the difficulty of external validation, the focus is on internal validation of the user interface. The following criteria are applied to a variety of decision aid designs: (1) psychologically valid measurement of features impacted by the decision; (2) psychologically valid elicitation of decision maker's preferences incorporated into a decision rule which processes those features; (3) possibility of checking for decision maker's consistency; (4) possibility of providing him/her with an explanation of the aids findings. [ABSTRACT FROM AUTHOR]

Preferences are often represented in terms of a function, in the deterministic case as well as in the probabilistic case. In the present paper we develop a new numerical representation of preference structures for which the strict preference relation (P) is without circuit but not necessarily transitive. Moreover, we investigate the consequences of the representation for the usual preference structures. In particular, we propose new formulations for the numerical representation of the interval order structure. [ABSTRACT FROM AUTHOR]

In the analytic hierarchy process, it is often thought that rank reversals cannot occur in a single-criterion problem. This paper demonstrates that if it is necessary to cluster items under a single criterion, such reversals are possible. The reversals occur prior to aggregating across clusters and are caused by a failure to make reference to the alternatives when performing criteria comparisons. Rank reversals, however, are only a symptom of the problem. The real problem is a failure to calibrate global weights to a common scale which spans different clusters. Even in the absence of reversals, aggregated weights from the AHP's relative mode of measurement can fail to maintain composite ratio relationships. [ABSTRACT FROM AUTHOR]

Research indicates that selecting a strategy to best exploit a new technology is a complex decision-making process. The task involves making a series of decisions with multiple alternatives, each to be evaluated by multiple criteria whose values have high levels of uncertainty. This paper presents a methodology for modelling a new technology decision using decision trees and an optimizing algorithm. A problem of a mining company considering the adoption of new technology is used to illustrate the decision-making task and modelling methodology. A numerical solution to the case demonstrates the potential of the optimizing technique in strategy selection. [ABSTRACT FROM AUTHOR]

It is well known that the lexicographic aggregation of complete preorders gives a complete preorder. Unfortunately, this property is no longer true when the lexicographic rule is applied to semiorders. In this paper we study some ways of defining a lexicographic aggregation of semiorders and the properties of the resulting structures. [ABSTRACT FROM AUTHOR]

The design of a system, especially a system architecture, requires the balancing of multiple performance parameters with the system cost and other implementation issues. Multi-attribute utility theory provides a structured, coherent framework for conducting an analysis in which system designs are evaluated on multiple performance parameters. This paper describes the application of multi-attribute utility analysis to the design of the Worldwide Digital Signal Systems Architecture (WWDSA), a telecommunications system, by the United States' Defense Communications Agency (now called the Defense Information Systems Agency). The advantages of using multiattribute utility theory during the system design are highlighted. In addition, we discuss several key analytical issues that led to this application being a success in the eyes of the decision makers. [ABSTRACT FROM AUTHOR]

Despite being in existence for many decades, normative decision theory has not become a commonly used tool for real-world decisions. This paper considers the reasons for this situation and suggestions for circumventing them. The main suggestion involves a two-stage framework in terms of the information available to the decision maker and his/her expectations under the available acts. This framework is well suited for decisions with incomplete structure, which is typical of real decision situations. Within this framework a specific multiplicative model is also discussed. [ABSTRACT FROM AUTHOR]

The article discusses several papers published within the issue including one about the Bayesian Decision Theory and another regarding public policy evaluation.

In this paper we consider the problem of identifying the form of a decision maker's (DM) utility function. We consider a set of alternatives each defined by a number of criteria and we assume that the DM's preferences are consistent with some underlying utility function. We present some theory and develop approaches to test whether the DM's preferences are consistent with a linear, a quasi-concave, a quasi-convex or a general monotonic function. We present our computational experience showing that in almost all cases the approaches correctly identify the form of the underlying utility function and require very little preference information of the DM. [ABSTRACT FROM AUTHOR]

A self-reflecting signed order is a preference relation that compares relative likes and dislikes for items in a set X by jointly ordering X and a disjoint copy of AT. If you would like Jones but not Smith appointed to a committee, and also think it more important to exclude Smith than include Jones, your self-reflecting signed order records this information. We review basic representational theory for signed orders, then examine them when X is multiattributed. Axioms for additive measurement of multiattribute self-reflecting signed orders are specified for several X-structures. [ABSTRACT FROM AUTHOR]

The article discusses various reports published within the issue including one by Silvio Giove and colleagues on a multiple criteria model for the evaluation of the sustainability of projects in Venice, Italy, Amit Kothial and colleagues on the proper scoring rules for the measurement of subjective degrees of beliefs and another by Marta Bottero and colleagues on choosing the best location for a waste incinerator plant in Torino, Italy.

Comments on the article "Rethinking Value Elicitation for Personal Consequential Decisions," by G. Wright and P. Goodwin. Characteristics of the decision problem; Link between uncomparability and a conflict between two different value systems.

ABSTRACT Solving complex decision problems is a demanding task; it requires determining and evaluating the consequences of decision alternatives. To this end, uncertain factors that can only partly be influenced by the decision makers, and their interdependencies need to be considered. Scenarios focus on this part of the decision problem; they enable a systematic exploration of a multitude of possible future developments that are relevant for the decision including external events and decisions made. Scenarios are particularly useful when the problem is pervaded by severe uncertainties that cannot be quantified. For the evaluation of alternatives, multiple objectives and the potentially diverging preferences of the involved actors need to be respected. Multi-criteria decision analysis aims at structuring the problem, evaluating the alternatives and supporting decision makers pursuing multiple goals. We propose an approach integrating scenarios and multi-criteria decision analysis that focuses on the robustness of alternatives in complex, dynamic, uncertain and time-bound situations. In this integrated framework, the scenarios provide the basis for evaluating a set of alternatives. Ideally, the set of scenarios considered captures all possible future developments. To appropriately explore this set, formal or analytical approaches to scenario construction generate a large number of scenarios. This challenges the decision makers' information-processing capacity. To support them in managing the richness of information, a two-fold approach that uses selection and aggregation is presented. By using a selection method, the scenarios that are deemed most relevant are identified, and their evaluations are presented in detail to decision makers. This approach is complemented by an aggregation of scenario evaluations on the basis of the decision makers' preferences. We present two approaches to facilitate the preference elicitation process. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A prescriptive decision model of stakeholder compensation is presented. The supra decision-maker (regulator) may derive the optimal compensation for redefining decision options in a decision context with unevenly distributed, uncertain, consequences in a way that reflects fairness among stakeholders with different representational weight and risk-attitude. The derived compensation is used by the supra decision-maker as a bargaining factor for committing stakeholders in a decision-making process. Expert judgement is utilized for specifying the probability distributions related to the uncertain consequences. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

One approach to evaluate the relative performance of decision alternatives with respect to multiple criteria is provided by the analytic hierarchy process. The method is based on pairwise comparisons between attributes, and several numerical measurement scales for the ratio statements have been proposed. The choice of measurement scale is re-examined, and new arguments supporting the measurement scale of geometric progression are derived. Separately from the measurement scale considerations, the effects of the scale parameter in geometric measurement scale are also studied. By using a regression model for pairwise comparisons data, it is shown that the statistical inference does not depend on the value of the scale parameter in the case of a single pairwise comparison matrix. It is also shown when the scale independence of statistical inference can be achieved in a decision hierarchy. This requires the use of the geometric-mean aggregation rule instead of the traditional arithmetic-mean aggregation. The results of the case study demonstrate that the measurement scale and the aggregation rule have potentially large impacts on decision support. [ABSTRACT FROM AUTHOR]

Given a finite set A of actions evaluated by a set of attributes, preferential information is considered in the form of a pairwise comparison table including pairs of actions from subset B ⊂ A described by stochastic dominance relations on particular attributes and a total order on the decision attribute. Using a rough sets approach for the analysis of the subset of preference relations, a set of decision rules is obtained, and these are applied to a set A\B of potential actions. The rough sets approach of looking for the reduction of the set of attributes gives us the possibility of operating on a multi-attribute stochastic dominance for a reduced number of attributes. [ABSTRACT FROM AUTHOR]

The ELECTRE family of decision aid methods is a well-known approach to help decision makers (DMs) advance in a decision process. Among the most recent methods in the family, ELECTRE IS, III, and TRI compute fuzzy indices for the credibility of a given action outranking some other. We consider the case when the DMs are unsure which values each parameter should take, which may result from insufficient, imprecise or contradictory information, as well as from different preferences among a group of DMs. In the framework of a robustness analysis approach, where DMs provide only partial information on the parameter values (through constraints on acceptable combinations), we study how to find whether an outranking among two actions in an ELECTRE method is robust. In this context, we study the resulting nonlinear problems of optimizing a credibility index (under the type of constraints that we consider to appear in practice) and present some examples. [ABSTRACT FROM AUTHOR]

We propose new measures of consistency of additive and multiplicative pairwise comparison matrices These measures, the relative consistency and relative error, are easy to compute and have clear and simple algebraic and geometric meaning, interpretation and properties. The correspondence between these measures in the additive and multiplicative cases reflects the same correspondence which underpins the algebraic structure of the problem and relates naturally to the corresponding optimization models and axiom systems. The relative consistency and relative error are related to one another by the theorem of Pythagoras through the decomposition of comparison matrices into their consistent and error components. One of the conclusions of our analysis is that inconsistency is not a sufficient reason for revision of judgments. [ABSTRACT FROM AUTHOR]

It is not only people who may disappear, nor one's keys. It may also be the optimum that one was so certain of being able to grasp and that so suddenly reveals itself to be totally elusive. And the situation then becomes dramatic, as with people, or utterly confused, as with the loss of keys: a familiar element is suddenly missing and one does not know how, nor where, to look for it. However, in contrast with the disappearance of a person that provokes action based on rational behaviour--notification of the police, broadcasting of a notice of search--the disappearance of the optimum begets reactions that are unpredictable, irrational or even ideological. Instead of its absence being accepted and action taken accordingly, its absence is denied. Why does the optimum vanish under certain conditions? And why does one not accept to admit that fact? Those are the two questions that we shall examine. We shall start with the second one, which presents a more straightforward approach to the problem. [ABSTRACT FROM AUTHOR]

We describe an interactive procedure, implemented on a PC, for solving multiple-objective non-linear programming (MONP) problems. The procedure is composed of two stages. The first stage consists of modelling decision maker's (DM's) preferences using a fuzzy outranking relation in a sample of non-dominated points. The relation is then translated into a preference cone defining a subset of non-dominated points of greatest interest to the DM. In the second stage the subset of non-dominated points generated by the cone is scanned interactively. A graphical interface enables a visual interaction. The DM can either reduce directly the subset of non-dominaied points to be scanned or retract to the first stage and give finer preference information which results in contraction of the cone and reduction of the subset of non-dominated points scanned in the second stage. Description of the procedure is followed by presentation of its application to a didactic MONP problem. [ABSTRACT FROM AUTHOR]