Weight approximations in multi‐attribute decision models

The use of surrogate weights based on rankings has been proposed as a method for avoiding difficulties associated with the elicitation of weights in multi‐attribute decision analysis. When the simple multiattribute rating technique using swings (SMARTS) method is being employed it has been suggested that rank order centroid (ROC) weights are the best surrogate weights to use. This study shows that ROC weights are appropriate to use as a substitute for original weights that are constrained to sum to a fixed total (usually 1 or 100) as used in the point allocation method. If, however, the original weights are determined without any initial restrictions, as in the direct rating method, and are then normalized, which is the common procedure in SMARTS analysis, then the ROC weights do not provide the best approximations to the original weights. This paper shows how to obtain rank order distribution (ROD) weights that provide a better approximation than the ROC approach to unrestricted original weights. The paper also shows that, as the number of attributes in a decision problem increases, the ROD weights approximate to the more easily calculated rank sum weights. Copyright © 2003 John Wiley & Sons, Ltd.     

Note on lexicographic‐order preservation and stochastic dominance

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 judgements emerge as matrices that premultiply utility vectors in expected utility sums. First, a generalization of the ‘Conjecture Σ’, 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. Copyright © 1999 John Wiley & Sons, Ltd.     

Evolution of multi‐criteria analysis: a scientometric analysis

The field of multi‐criteria analysis has known very important developments during the last 20 years, if one considers the very large amount of activities that it has generated and continues to generate (papers in journals, a dedicated journal, books, meetings, applications, …). Even if multi‐criteria analysis has reached some maturity, its future is subject to questions and debate among its researchers: what is the evolution of the field? What is its structure? Is it integrating new topics? In order to answer such questions at least partially, we have studied multi‐criteria analysis literature by means of the method of associated words (scientometric analysis) and the software ‘Leximappe’. All the abstracts of the papers which are relative to multi‐criteria analysis and are included in the bibliographic ABI‐INFORM database from 1985 to 1996 have been analysed. In this paper, we will present some results of this study. Copyright © 1999 John Wiley & Sons, Ltd.     

Simulation and multi‐attribute utility modelling of life cycle profit

Investments on capital goods are assessed with respect to the life cycle profit as well as the economic lifetime of the investment. The outcome of an investment with respect to these economic criteria is generally non‐deterministic. An assessment of different investment options thus requires probabilistic modelling to explicitly account for the uncertainties. A process for the assessment of life cycle profit and the evaluation of the adequacy of the assessment is developed. The primary goal of the assessment process is to aid the decision‐maker in structuring and quantifying investment decision problems characterized by multiple criteria and uncertainty. The adequacy of the assessment process can be evaluated by probabilistic criteria indicating the degree of uncertainty in the assessment. Bayesian inference is used to re‐evaluate the initial assessment, as evidence of the system performance becomes available. Thus authentication of contracts of guarantee is supported. Numerical examples are given to demonstrate features of the described life cycle profit assessment process. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

An investigation of the role of scale values in the DS/AHP method of multi‐criteria decision making

DS/AHP is a method of multi‐criteria decision making based on the Dempster–Shafer theory of evidence and the analytic hierarchy process. Central to the utilization of DS/AHP is the composing of preference judgements on identified groups of decision alternatives (DA) across a number of criteria against all the DA present in the problem in question. This paper exposits a series of results whose objectives are to aid in the development of an effective set of preference scale values for use within DS/AHP. These results relate directly to the concomitant level of ignorance (uncertainty) with the judgements made on a single criterion. Two particular directions of investigation are undertaken, firstly in determining the necessary number of scale values available and secondly finding the necessary differences between scale values, dependent on whether an arithmetic or geometric progression is the basis for the scale values. Through an example, the implications and utilization of these results within DS/AHP are illustrated. Copyright © 2003 John Wiley & Sons, Ltd.     

Model and interactive algorithm of bi‐level multi‐objective decision‐making with multiple interconnected decision makers

Furthering a prior research on two‐person bi‐level multi‐objective decision‐making problems of the leader‐follower Stackelberg game, we present an extended model of bi‐level multi‐objective decision‐making with multiple interconnected decision makers at the lower level. In the model, the upper level decision maker acts as a leader and the lower level decision makers behave as the followers, and inter‐connections and interactions exist among these followers in decision‐making scenarios. Following the rules of leader‐follower Stackelberg game, we develop an interactive algorithm of the model for solving multi‐objective decision‐making problems and reflecting the interactive natures among the decision makers. Finally, the authors exemplify the model and algorithm, and draw a conclusion on points of contributions and the significance of this study in decision‐making and support. Copyright © 2001 John Wiley & Sons, Ltd.     

Invited Review—Survey of Value‐Focused Thinking: Applications,Research Developments and Areas for Future Research

Criteria are the central focus of multi‐criteria decision analysis. Many authors have suggested using our values (or preferences) to define the criteria we use to evaluate alternatives. Value‐focused thinking (VFT) is an important philosophy that advocates a more fundamental view of values in our decision making in our private and professional lives. VFT proponents advocate starting first with our values and then using our values to create decision opportunities, evaluate alternatives and finally develop improved alternatives. It has been 20 years since VFT was first introduced by Ralph Keeney. This paper surveys the VFT literature to provide a comprehensive summary of the significant applications, describe the main research developments and identify areas for future research. We review the scope and magnitude of VFT applications and the key developments in theory since VFT was introduced in 1992 and found 89 papers written in 29 journals from 1992 to 2010. We develop about 20 research questions that include the type of article (application, theory, case study, etc.), the size of the decision space (which, when given, ranged from $200K to billions of dollars), the contribution documented in the article (application benefits) and the research contributions (categorized by preferences, uncertainties and alternatives). After summarizing the answers to these questions, we conclude the paper with suggestions for improving VFT applications and potential future research. We found a large number of significant VFT applications and several useful research contributions. We also found an increasing number of VFT papers written by international authors. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

An evaluation of multi‐criteria methods in integrated assessment of climate policy

Those who conduct integrated assessments (IAs) are aware of the need to explicitly consider multiple criteria and uncertainties when evaluating policies for preventing global warming. MCDM methods are potentially useful for understanding tradeoffs and evaluating risks associated with climate policy alternatives. A difficulty facing potential MCDM users is the wide range of different techniques that have been proposed, each with distinct advantages. Methods differ in terms of validity, ease of use, and appropriateness to the problem. Alternative methods also can yield strikingly different rankings of alternatives. A workshop was held in which climate change experts and policy makers evaluated the usefulness of MCDM for IA. Participants applied several methods in the context of a hypothetical greenhouse gas policy decision. Methods compared include value and utility functions, goal programming, ELECTRE, fuzzy sets, stochastic dominance, min max regret, and several weight selection methods. Ranges, rather than point estimates, were provided for some questions to incorporate imprecision regarding weights. Additionally, several visualization methods for both deterministic and uncertain cases were used and evaluated. Analysis of method results and participant feedback through questionnaires and discussion provide the basis for conclusions regarding the use of MCDM methods for climate change policy and IA analyses. Hypotheses are examined concerning predictive and convergent validity of methods, existence of splitting bias among experts, perceived ability of methods to aid decision‐making, and whether expressing imprecision can change ranking results. Because participants gained from viewing a problem from several perspectives and results from different methods often significantly differed, it appears worthwhile to apply several MCDM methods to increase user confidence and insight. The participants themselves recommended such multimethod approaches for policymaking. Yet they preferred the freedom of unaided decision‐making most of all, challenging the MCDM community to create transparent methods that permit maximum user control. Copyright © 2002 John Wiley & Sons, Ltd.     

The contributions of multi‐criteria decision making to the development of decision support systems subspecialties: an empirical investigation

This study focuses on examining the structure of decision support systems (DSS) research, with a particular emphasis on assessing the contributions of multi‐criteria decision making (MCDM) to the development of each of the DSS subspecialty areas. This study traces how concepts and findings by researchers in the MCDM area have been picked up by DSS researchers to be applied, extended and refined in the development of DSS research subspecialties. In doing so, factor analysis is applied to an author cocitation frequency matrix derived from a large database file of comprehensive DSS literature. This study concludes that researchers in the MCDM area have made crucial contributions to the development of DSS research subspecialties. Copyright © 1999 John Wiley & Sons, Ltd.     

The Impact of “Display‐Set” Options on Decision‐Making

The way a choice set is constructed can have a significant influence on how individuals perceive and evaluate their options, and make decisions between them. Here, I examine whether a “display set” of visible but unavailable options can exert these same types of influences on whether or not to choose a single (target) item. Across a series of experiments, purchase intent is increased when the display set and target are drawn from the same category, but decreased when the display and target items are mismatched. This effect is shown to depend on perceived similarity, such that increasing display‐target similarity increases purchase intent towards the target. Furthermore, contrary to the predictions made by previous neural and behavioral research on choice sets, the relative value and/or number of display‐only items have no significant impact on these decisions. These findings reveal a novel choice behavior in commonly encountered settings such as online marketplaces. Copyright © 2016 John Wiley & Sons, Ltd.     

On the advancement and software support of decision‐making in focused ultrasound therapy

Focused ultrasound therapy (FUS) is a modern and promising way for minimally invasive cancer treatment. Recent advances in treatment technology, bio‐physical models, and numerical simulation methods have given rise to a significant curative potential. However, clinical routine of FUS still features classical planning approaches, which widely fail in exploiting this potential. The structure of FUS planning problems strongly suggests interactive multi‐criteria decision‐making concepts in order to improve treatment quality. This research work introduces an multi‐criteria decision‐making approach to FUS planning and explains how to bridge the conceptual gap between the clinical state of the art and this new planning paradigm.     

Attribute‐based differentiation of alternatives

An intermediate step is introduced to the dialogue decision process for decision analysis. Alternatives are refined after they have been generated within a strategy table but before they are subject to more detailed evaluation. Two or more judges create a subjective mapping from alternatives to attributes that will later be mapped to criteria. In strategy tables, each of the alternative strategies consists of a coherent set of choices made across several decisions that are to be coordinated. These strategic alternatives are modified so as to increase their differentiation in the attribute space, rather than in the decision space alone. When criteria weights are unknown, the best alternative from the modified set may be superior to the best alternative from the original set. Furthermore, analysis of the resulting alternatives may yield a better mapping of the value response surface for the action space, in the sense that this mapping leads to eventual construction of a higher value alternative. Results are reported for a consulting engagement incorporating the proposed step. Copyright © 2003 John Wiley & Sons, Ltd.     

A Fuzzy Topsis Method for Prioritized Aggregation in Multi‐Criteria Decision Making Problems

Aggregation in a decision making environment requires the fusion of opinions of a group of decision makers. The group of decision makers are required to analyse a set of interrelated criteria that are usually measured on a linguistic scale. This process requires, in many instances, to capture experts experience, intuition and thinking that are traditionally expressed in a linguistic fashion rather than a numerical fashion. Furthermore, the necessity of considering the relationship between the criteria to the overall decision must be considered by the group of decision makers. This paper extends the application of fuzzy numbers, fuzzy relative importance scores (FRIS), fuzzy relative weights (FRW) and the fuzzy technique of order preference by similarity to ideal solution (TOPSIS) in prioritized aggregation. This extension provides a mean to systematically aggregate a group of decision makers' views for a set of interrelated criteria that are measured on a linguistic scale. First, an overview of the application of fuzzy numbers and the characteristics of aggregating fuzzy numbers in multi‐criteria decision making problems are presented. Then, the application of TOPSIS in fuzzy environments is presented. Next, past research is highlighted to present prioritized aggregation and the different aggregation operators' classes. Subsequently, a new prioritized aggregation method is presented. This method utilizes fuzzy TOPSIS with prioritized aggregation in fuzzy environments. Finally, the fuzzy prioritized aggregation method presented in this paper is applied on an actual case study. According to the results, the method presented in this paper provides a systematic approach to capture the uncertainty and imprecision associated with quantifying linguistic measurements in multi‐criteria decision making problems. Furthermore, it considers the relationship between the set of linguistically measured criteria undergoing prioritized aggregation in a fuzzy environment. Lastly, findings, conclusions and future work are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Multiple Criteria Decision‐Making in Management Accounting and Control‐State of the Art and Research Perspectives Based on a Bibliometric Study

As an academic discipline as well as in practice, decision support is one of the most important functions of management accounting and control (MAC). Owing to decision settings' increasing complexity, suitable multiple criteria methods are becoming increasingly important for MAC. We, therefore, examine the extent to which certain multiple criteria decision‐making (MCDM) methods are used in the MAC context. In order to do so, we undertook an extensive bibliometric analysis of the management accounting field during the last three decades. The results indicate an increase in the importance of MCDM. Furthermore, recent research activities were classified into different areas of decision‐making within MAC since the majority of publications deal with the areas of strategic management, budgeting and performance management. More specifically, strategy and performance evaluation, strategic planning and the selection of alternatives are the most prominent MCDM applications. Our analysis reveals that the analytic hierarchy process (AHP) is the most popular analytical tool with which to support management in complex decision‐making situations. The results of the study prove that technical MAC literature does not cover a desirable range of MCDM applications and that the AHP, as well as the analytic network process (ANP) are of increasing importance in respect of the international scope of MAC. Therefore, the area of MCDM continues to be an active part of management science research and application, specifically of MAC. Copyright © 2011 John Wiley & Sons, Ltd.     

A Multicriteria Decision‐Making Application to the Conceptual Design of Mechanical Components

Early design is crucial for the success of the final product. In the conceptual design phase, several constraints, criteria, objectives and disciplines have to be considered. To this aim, multidisciplinary optimization has proven effective for the solution of engineering design problems, even in the industrial every‐day practice, to improve and simplify the work of designers in a successful quest of the best compromise solution. In this paper, a multicriteria decision‐making (MCDM)‐based design platform for early optimal design of industrial components is proposed. In a group decision‐making context, the selection of the most suitable component among several possible layouts is performed by means of a group Fuzzy Technique for Order of Preference by Similarity to Ideal Solution approach. Hence, a multi‐objective optimization is performed on the selected component by applying a multi‐objective particle swarm optimization for finding optimal component dimensions. An industrial case study is presented for showing the efficiency of the multicriteria decision‐making‐based design platform, regarding an innovative and low‐cost solution to increase the duration of heel tips in women's shoes. Copyright © 2016 John Wiley & Sons, Ltd.     

Endorsement of sexist ideology in Taiwan and the United States: Social dominance orientation,right‐wing authoritarianism,and deferential family norms

Despite close relationships between men and women in daily lives, gender inequality is ubiquitous and often supported by sexist ideology. The understanding of potential bases of sexist ideology is thus important. According to Duckitt's dual‐process model (2001), different worldviews may explain different types of sexist ideology. Individuals who hold a “competitive world” worldview tend to endorse group‐based dominance. This lends itself to the endorsement of hostile sexism, because hostile sexism is an obvious form of male dominance. Conversely, individuals who hold a “dangerous world” worldview tend to adhere to social cohesion, collective security, and social traditions. This lends itself to the endorsement of benevolent sexism, because benevolent sexism values women who conform to gender norms. As predicted by Duckitt's model, research has shown that social dominance orientation, a general orientation towards the endorsement of group‐based dominance, is closely associated with hostile sexism. Furthermore, right‐wing authoritarianism, which measures adherence to social traditions, is closely associated with benevolent sexism. Due to the interdependent nature of gender relationships, the current research proposed that a relationship‐based belief in hierarchy, deferential family norms, and norms depicting proper manners among family members should predict the endorsement of hostile and benevolent sexism, after controlling for social dominance orientation and right‐wing authoritarianism. As predicted, according to student samples collected in Taiwan and the US, the endorsement of deferential family norms predicted the endorsement of hostile sexism and of benevolent sexism, respectively. In addition, among men and women, social dominance orientation predicted hostile sexism more strongly (as opposed to benevolent sexism), whereas right‐wing authoritarianism predicted benevolent sexism more strongly (as opposed to hostile sexism). Implications regarding relationship norms, social dominance orientation, right‐wing authoritarianism, and sexist ideology are discussed.     

Mechanisms of moral disengagement and their differential use by right‐wing authoritarianism and social dominance orientation in support of war

Right‐wing authoritarianism (RWA) and social dominance orientation (SDO) are associated with the approval of war as a political intervention [McFarland, 2005]. We examined whether the effects of RWA and SDO on war support are mediated by moral‐disengagement mechanisms [i.e., responsibility reduction, moral justification, minimizing consequences, and dehumanizing–blaming victims; Bandura, 1999] and whether the ideologies use the mechanisms differently. Our data were consistent with the possibility that minimizing consequences (Study 1) and moral justification (Study 2) mediate the effects of RWA and SDO on approval of war. Both ideologies were positively associated with all moral‐disengagement mechanism though more strongly so for RWA. Comparisons within ideologies suggest that RWA was most strongly associated with moral justification and SDO was most strongly associated with dehumanizing–blaming victims. We discuss implications and limitations. Aggr. Behav. 36:238–250, 2010. © 2010 Wiley‐Liss, Inc.