Trade‐off ranking method for multi‐criteria decision analysis

Multi‐criteria decision analysis presumes trade‐off between different criteria. As a result, the optimal solution is not unique and can be represented by the Pareto frontier in the objective space. Each Pareto solution is a compromise between different objectives. Despite a limited number of Pareto optimal solutions, the decision‐maker eventually has to choose only one option. Such a choice has to be made with the use of additional preferences not included in the original formulation of the optimization problem. The paper represents a new approach to an automatic ranking that can help the decision‐maker. In contrast to the other methodologies, the proposed method is based on the minimization of trade‐off between different Pareto solutions. To be realized, the approach presumes the existence of a well‐distributed Pareto set representing the entire Pareto frontier. In the paper, such a set is generated with the use of the directed search domain algorithm. The method is applied to a number of test cases and compared against two existing alternative approaches.     

Comparing graphic and symbolic classification in interactive multiobjective optimization

In interactive multiobjective optimization systems, the classification of objective functions is a convenient way to direct the solution process in order to search for new, more satisfactory, solutions in the set of Pareto optimal solutions. Classification means that the decision maker assigns the objective functions into classes depending on what kind of changes in their values (in relation to the current values) are desirable. Here we study the role of user interfaces in implementing classification in multiobjective optimization software and how classification should be realized. In this way, we want to pay attention to the usability of multiobjective optimization software. Typically, this topic has not been of interest in the multiobjective optimization literature. However, usability aspect is important because in interactive classification‐based multiobjective optimization methods, the classification is the core of the solution process. We can say that the more convenient the classification is, the more efficient the system or the method is and the better it supports the work of the decision maker. We report experiments with two classification options, graphic and symbolic ones, which are used in connection with an interactive multiobjective optimization system WWW‐NIMBUS. The ideas and conclusions given are applicable for other interactive classification‐based method, as well. Copyright © 2005 John Wiley & Sons, Ltd.     

Robustness of Additive Value Function Methods in MCDM

A simulation model is constructed of choice between a discrete number of non-dominated alternatives. The long-run goals of the decision maker are assumed to be consistent with a hypothetical preference structure which satisfies assumptions of completeness, transitivity and additive independence for an ideal set of criteria. The use of additive value functions to aid the decision maker in this choice is simulated for a variety of contexts and under a number of non-idealities such as the omission of criteria, confounding of criteria and inconsistent responses. It is found that ideal preference orderings are well identified by additive value functions provided that the non-idealities are moderate and that sufficient effort is put into modelling changing marginal values for different levels of performance. One of the potentially most sensitive areas is that of shifts in the decision maker's reference points as a result of the types of preference information asked.     

How Self‐Regulation Creates Distinct Values: The Case of Promotion and Prevention Decision Making

I propose that different relations among basic components of self‐regulation produce distinct types of decision value: (a) Outcome value is produced when the consequences of a decision are relevant to the regulatory orientation of the decision maker, (b) value from fit is produced when goal pursuit means suit the regulatory orientation of the decision maker, and (c) value from proper means is produced when goal pursuit means are in agreement with established rules and normative principles. I use the regulatory focus distinction between promotion focus concerns with aspirations and accomplishments and prevention focus concerns with safety and responsibilities (Higgins, 1997, 1998) to illustrate outcome value and value from fit. Justification of a decision is used to illustrate value from proper means. I propose that decision makers are unlikely to distinguish among their experiences of these 3 types of value, and thus value from fit and value from proper means can be transferred to outcome value. I present evidence of such value transfer and consider its implications for value to the customer. I also reconsider sunk costs and the endowment effect in light of there being value beyond outcome value.     

Navigation in multiobjective optimization methods

Building on previous work of the authors, this paper formally defines and reviews the first approach, referred to as navigation , towards a common understanding of search and decision‐making strategies to identify the most preferred solution among the Pareto set for a multiobjective optimization problem. In navigation methods, the decision maker interactively learns about the problem, whereas the decision support system learns about the preferences of the decision maker. This work introduces a detailed view on navigation leading to the identification of integral components and features. A number of different existing navigation methods are reviewed and characterized. Finally, an overview of applications involving navigation is given, and promising future research direction are discussed.     

Unstable Interaction in Multiple Criteria Decision Problems

In this paper, we present a decision‐aid method with interacting criteria. The fuzzy measures used to aggregate the criteria depend on the considered alternatives. Pairwise comparisons on the importance of criteria and some levels of veto (or favor) degrees, specified by the decision maker, are taken into consideration. For each alternative, we search for the fuzzy measure that makes it the best. The orness degrees of the resulting fuzzy measures are compared and the alternative associated with the minimum orness degree is selected. Copyright © 2014 John Wiley & Sons, Ltd.     

R&D Project Selection: A Decision Process Approach

The fundamental decision problem of an R&D firm is to select projects in which to invest. Most reported models dealing with this subject use sophisticated mathematical models maximizing specific attributes of the projects without dealing with the underlying motivation of the decision maker. This paper summarizes a successful application of a decision-making process involving multicriteria in the selection of R&D projects in the Ecogen Israel Partnership. We emphasize the structure of the decision problem, with the main goal of helping the decision maker to better understand the nature of his problem. We systematically generate the objective hierarchy of the decision maker, including his main criteria, subcriteria attributes and alternatives. The ‘best’ alternative can then be found using most interactive procedures found in the literature. As the decision maker is totally involved in the entire decision-making process he is better able to understand his problem and preferences.     

A parameter analysis method for the weight‐set to satisfy preference orders of alternatives in additive multi‐criteria value models

In the context of the additive multi‐criteria value model, this paper investigates how the set of criteria weights (weight‐set hereafter) can be determined according to the preference orders of alternatives given by the decision maker. A construction method is proposed for the weight‐set for different intervals of β, where β is a differential amount of value between the preference information on two alternatives. The results of this paper are important for sensitivity analysis in multi‐criteria decision making (MCDM) problems and multi‐criteria group decision analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

Sequential decision making: An aggregate scheduling methodology

Recent studies of sequential decision making performance have utilized optimal dynamic programming solutions as the criteria for evaluating the quality of human decisions. The difficulties incumbent in increasing the dimensionality of dynamic programming formulations effectively prohibit their extension beyond the case of a single decision variable. In the following article an alternative optimization formulation for a two-decision-variable case is presented, followed by the development of a corresponding one-decision-variable problem. In addition, related methodological problems limiting the comparability of results among previous studies are presented. It is suggested that the proposed problem formulation and its accompanying interpretation for the decision maker largely eliminate these previous methodological problems. Furthermore, the problem formulation permits quantification of the relative weights that should optimally be placed on future decision periods in the multiple-stage decision problem.     

Effectiveness of the GOFER course in decision making for high school students

The paper describes and evaluates the GOFER course in decision making for high school students (Mann, Harmoni and Power, 1988). The course was based on principles from the conflict theory of decision making (Janis and Mann, 1977) and was designed to provide adolescents with an understanding of factors that produce good and poor decision making as well as knowledge and practice of sound decision skills. Two evaluation studies were conducted to examine effectiveness of the course. Study 1 was conducted with young adolescents (12 year olds). It found a significant difference between students trained in the course and a control group on measures of self-esteem as a decision maker, self reported decision habits and knowledge of decision strategy. Study 2 was conducted with mid-adolescents (15 year olds). It, too, found a significant difference between students who took the course and a control group on measures of self esteem as a decision maker and self-reported decision habits. It is concluded that while the evaluation study fell short of an ideal test, the GOFER course met the criteria of improving student knowledge, raising confidence in decision making and changing self reported decision habits.     

An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems using chance constrained conditions

Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this paper, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using chance constrained programming techniques, the stochastic programming problems are transformed into deterministic ones. As a fusion of stochastic approaches and fuzzy ones, after determining the fuzzy goals of the decision maker, interactive fuzzy satisficing methods to derive a satisficing solution for the decision maker by updating the reference membership levels is presented. Copyright © 2003 John Wiley & Sons, Ltd.     

A new fuzzy multicriteria evaluation method for group site selection in GIS

Multiple criteria group site selection problems involve a group of individuals evaluating a set of alternative sites on the basis of multiple criteria. This paper presents an application of a new fuzzy algorithm for finding and exploring potential solutions to these problems in a raster Geographical Information System (GIS) environment. Linguistic assessments from decision‐makers are represented as triangular fuzzy numbers (TFN's), which are adjusted for uncertainty in the source data and their relationship to suitability by using an approach based on type‐2 fuzzy sets. The first aggregation of inputs is a compensatory one based on fuzzy multiattribute decision‐making (MADM) theory. An adjusted aggregation then factors in conflicts, risks and uncertainties to enable a variety of compensatory and non‐compensatory outcomes to be generated based on decision‐maker preferences. The algorithm was implemented in ArcView GIS as part of an ongoing collaborative project with Brisbane Airport. This paper outlines the fuzzy algorithm and its use in site selection for a recycling facility on the Brisbane Airport site. Copyright © 2005 John Wiley & Sons, Ltd.     

Methodology to select solutions for multiobjective optimization problems: Weighted stress function method

The weighted stress function method is proposed here as a new way of identifying the best solution from a set of nondominated solutions according to the decision maker's preferences, expressed in terms of weights. The method was tested using several benchmark problems from the literature, and the results obtained were compared with those of other methods, namely, the reference point evolutionary multiobjective optimization (EMO), the weighted Tchebycheff metric, and a goal programming method. The weighted stress function method can be seen to exhibit a more direct correspondence between the weights set by the decision maker and the final solutions obtained than the other methods tested.     

Reduction of pairwise comparisons in decision making via a duality approach

Although pairwise comparisons have been seen by many as an effective and intuitive way for eliciting qualitative data for multi‐criteria decision making problems, a major drawback is that the number of the required comparisons increases quadratically with the number of the entities to be compared. Thus, often even data for medium size decision problems may be impractical to be elicited via pairwise comparisons. The more the comparisons are, the higher is the likelihood that the decision maker will introduce erroneous data. This paper introduces a dual formulation to a given multi‐criteria decision making problem, which can significantly alleviate the previous problems. Some theoretical results establish that this is possible when the number of alternatives is greater than the number of decision criteria plus one. Copyright © 1999 John Wiley & Sons, Ltd.     

Simulation of Preference Information in an Interactive Reference Point‐Based Method for the Bi‐Objective Inventory Routing Problem

In the research area of multiple criteria decision making, very few publications exist that explicitly design the simulation of a decision maker (DM) in an interactive approach. For this reason, we outline some methods widely used in the literature to identify common assumptions of simulating the DM's responses and the required input preference information. Our paper aims at covering the identified gap by introducing experimental concepts. Such concepts are used for theoretical analyses of a combined search‐and‐decision‐making procedure. Simulating the DM is a fruitful idea because the algorithm can be tested without integrating a human decision maker. Finally, we conduct experiments based on the proposed settings for a multiobjective inventory routing problem, which is a relevant and challenging logistic problem. Copyright © 2014 John Wiley & Sons, Ltd.     

Rethinking value elicitation for personal consequential decisions

The application of multiattribute decision analysis to personal consequential decision problems can be unhelpful particularly where the analysis fails to help the decision maker to discover new values, or where the decision maker is unable to visualize the experience that may result from choosing a particular course of action. We concur with James March that values are best discovered by the act of choosing and experimenting but acknowledge that the act of choice can lead to irreversible consequences. Both of these problems suggest that techniques which assist the decision maker to envisage the consequences of choice need to be developed and incorporated into the modelling process. We suggest some forms that these techniques might take. Copyright © 1999 John Wiley & Sons, Ltd.     

Multicriteria approval: application of approval voting concepts to MCDM problems

Multicriteria decision making (MCDM) methods generally require information that is difficult and expensive to obtain. It is shown in this paper that given an ordering of criteria by importance, and whether each alternative is above the average evaluation of the alternatives for each criterion, considerable information can be extracted concerning the overall rankings of the alternatives. This is done by recognizing the similarity between criteria in MCDM, and voters in social choice theory. Multicriteria approval, proposed in this paper, is an MCDM adaptation of approval voting which can be used to classify decisions into one of several categories, depending on whether, and the manner in which, a superior alternative can be identified. An exhaustive examination of all possible decision situations of tractable size is made to measure the applicability of multicriteria approval, and the approach is demonstrated in an industrial procurement case. In addition to requiring minimal information from a decision maker, multicriteria approval satisfies several desirable criteria for MCDM techniques. © 1998 John Wiley & Sons, Ltd.     

Preference‐based Learning of Ideal Solutions in TOPSIS‐like Decision Models

Combining established modelling techniques from multiple‐criteria decision aiding with recent algorithmic advances in the emerging field of preference learning, we propose a new method that can be seen as an adaptive version of TOPSIS, the technique for order preference by similarity to ideal solution decision model (or at least a simplified variant of this model). On the basis of exemplary preference information in the form of pairwise comparisons between alternatives, our method seeks to induce an ‘ideal solution’ that, in conjunction with a weight factor for each criterion, represents the preferences of the decision maker. To this end, we resort to probabilistic models of discrete choice and make use of maximum likelihood inference. First experimental results on suitable preference data suggest that our approach is not only intuitively appealing and interesting from an interpretation point of view but also competitive to state‐of‐the‐art preference learning methods in terms of prediction accuracy. Copyright © 2014 John Wiley & Sons, Ltd.