A Note on the Power of Multiattribute One‐switch Utility Functions

One‐switch utility functions model situations in which the preference between two alternatives switches only once as the outcome of one attribute of both alternatives changes from low to high. Recent research cites evidence that the sum of exponential functions (sumex) is the most convincing type for modelling one‐switch utility functions. Sumex functions allow to model exactly one preferential switch and they are convenient for estimating one‐switch utility functions. However, it is unclear so far if sumex functions are suitable to model preferential switches that are perceivable by a decision maker. This paper first analyses how different the utility of two alternatives before and after a preferential can be modelled with sumex functions given that the preferential switch is caused by a particular attribute outcome improvement. It thereafter investigates how accurately decision makers perceive such utility differences. Copyright © 2015 John Wiley & Sons, Ltd.     

An Approach to Multi‐Criteria Decision Problems Under Severe Uncertainty

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.     

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.     

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 approach to and computational results on testing the form of a decision maker's utility function

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.     

Multi‐Criteria Evaluation for Collaborative Circulating Farming with Collective Operations Between Arable and Cattle Farmers

Tokachi sub‐prefecture in Hokkaido is one of the most famous dairy and crop farming regions in Japan. It is known that Tokachi is faced with various difficult problems such as soil degradation, water contamination and unpleasant odours because of the excessive use of chemical fertilizers and inappropriate treatment of livestock excretion. In this paper, we focus on Shihoro town where agricultural outputs are relatively large in Tokachi, and propose collaborative circulating farming with collective operations between arable and cattle farmers. Under the assumption that the decision‐maker in this problem is a representative of a farming organization who hopes for sustainable agricultural development and values the intentions of local residents including arable and cattle farmers in this region, we employ multi‐attribute utility theory in order to evaluate multiple alternatives of the farming management problem. Copyright © 2012 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.     

An Interactive Approach for Multicriteria Decision Making Using a Tchebycheff Utility Function Approximation

Multicriteria decision making (MCDM) can provide an efficient mean for considering various and conflicting objectives to reveal the alternative that maximizes the decision maker's (DM) utility. In this paper, we propose a new interactive MCDM method for implicit alternatives to help a DM obtain a most preferred solution. We employ a Tchebycheff function to generate weights for objectives consistent with the DM's responses to pairwise comparisons between alternatives and present a mixed integer linear programming formulation to generate these weights. Thus, we approximate the DM's utility function by a Tchebycheff function and generate weights consistent with the DM's responses. We test our approach with different true utility functions on various sized multiple criteria linear programming problems. The computational results show that even with non‐Tchebycheff true utility functions, our method can generate alternatives very close to the optimal solution with few questions. The comparison of our results with other methods reveals its advantages. Copyright © 2013 John Wiley & Sons, Ltd.     

Decision Support System and Multi‐Criteria Decision Aid: A State of the Art and Perspectives

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.     

A Comprehensive Literature Review of the Rank Reversal Phenomenon in the Analytic Hierarchy Process

During the last few decades, several multi‐criteria decision analysis methods have been proposed to help in selecting the best compromise alternatives. Among them, analytic hierarchy process (AHP) and its applications have attracted much attention from academics and practitioners. However, since the early 1980s, critics have raised questions regarding its proper use. One of them concerns the unacceptable changes in the ranks of the alternatives, called rank reversal, upon changing the structure of the decision. Several modifications were suggested to preserve ranks. In this paper, a classification scheme and a comprehensive literature review are presented in order to uncover, classify and interpret the current research on AHP methodologies and rank reversals. On the basis of the scheme, 61 scholarly papers from 18 journals are categorized into specific areas. The specific areas include the papers on the topics of adding/deleting alternatives and the papers published in adding/deleting criteria. The scholarly papers are also classified by (1) year of publication, (2) journal of publication, (3) authors' geographic location and (4) using the AHP in association with other methods. It is hoped that the paper can meet the needs of researchers and practitioners for convenient references of AHP methodologies and rank reversals and hence promote the future of rank reversal research. Copyright © 2012 John Wiley & Sons, Ltd.     

Much ado about nothing: The zero effect in life‐saving decisions

Zero is a special value in our daily lives, and previous research on how zero values affect decision making leaves many questions to be explored. The present research examined the zero effect in life‐saving decisions and found that people expressed strong preferences for options offering a possibility that no one will die, even when the expected loss was relatively high. The prominence effect (the notion that the option with possibly zero deaths is easy to defend and justify) was proposed as one possible explanation. Furthermore, we also found that the zero effect in these life‐saving decisions occurs only in loss framing rather than gain framing. We discuss the relationships between the zero effect, framing, and evaluation mode in life saving and other domains.     

Assessing risky public investments with MUSTARD

This paper presents a practical implementation of multicriteria methodologies based on the UTA model by Jacquet‐Lagrèze and Siskos and Quasi‐UTA model by Beuthe and Scannella, which are specified with a non‐linear, but piecewise linear, additive utility function. In contrast with the general UTA model, the Quasi‐UTA specification structures the partial utilities as recursive exponential functions of only one curvature parameter. This allows for a reduction of the quantity of information necessary to build the utility function. The software MUSTARD implements different variants of these models. Firstly, it offers the basic deterministic UTA model of disaggregation, but also its first programmed stochastic version. In both cases, the software proceeds stepwise and interactively helping the decision maker to formulate the problem and state preferences between projects; in the stochastic case, the decision maker is even helped to build the criteria distributions. The Quasi‐UTA specification can be introduced in this disaggregation model. Secondly, the software offers an aggregation model whereby the Quasi‐UTA partial utility functions are built separately through specific questioning processes. The questions relating to deterministic criteria are of the ‘direct rating type’, while those of the stochastic criteria are either of the ‘variable probability’ or the ‘variable outcome’ type. The criteria weights can be assessed by the ‘swing weight’ method or by a UTA‐II side‐program. As an example as well as a test of the Quasi‐UTA aggregation approach, the paper presents its application to a real problem of selecting road investment projects in Belgium. Several experts and civil servants were interviewed, and their individual utility functions derived. The projects are ranked according to their rate of return, which is computed on the basis of the projects certain equivalent money value. Copyright © 2002 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.     

Ordering the alternatives of a strategic plan for Valencia (Spain)

In this article we present an evaluation of the initiatives involved in a Strategic Plan for Valencia City (Spain) by applying a method to assist Multi‐Criteria Decision‐Making. The complexity of the case lies in the size of the problem, 47 alternatives and 10 criteria, as well as the need to reach a consensus on the final result. The method followed, which has been named PRES Multi‐expert, can be generalized and applied to other complex cases. Thirteen experts have participated in the process, representing different political and social groups of the City, a group of analysts, formed by three lecturers from the Polytechnic University of Valencia, and a consultant, representing the City Hall of Valencia. The PRES algorithm was used to order the alternatives developed in 1992 by Gómez‐Senent at this University. In this article we highlight the advantages of applying the Multi‐Criteria Decision‐Making Aid techniques and the importance of following a procedure to select the criteria, pondering on them and evaluating the alternatives. This procedure ensures that the parties interested in or affected by the decision take part in deciding what measures to adopt. The Multi‐expert PRES method facilitates this participation and can be adapted to different types of problems. Copyright © 2001 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.     

The Characteristic Objects Method: A New Distance‐based Approach to Multicriteria Decision‐making Problems

Multicriteria decision‐making (MCDM) methods are concerned with the ranking of alternatives based on expert judgements made using a number of criteria. In the MCDM field, the distance‐based approach is one popular method for obtaining a final ranking. The technique for order preference by similarity to the ideal solution (TOPSIS) is a commonly used example of this kind of MCDM method. The TOPSIS ranks the alternatives with respect to their geometric distance from the positive and negative ideal solutions. Unfortunately, two reference points are often insufficient, especially for nonlinear problems. As a consequence of this situation, the final result ranking is prone to errors, including the rank reversals phenomenon. This study proposes a new distance‐based MCDM method: the characteristic objects method. In this approach, the preferences of each alternative are obtained on the basis of the distance from the nearest characteristic objects and their values. For this purpose, we have determined the domain and Fuzzy number set for all the considered criteria. The characteristic objects are obtained as the combination of the crisp values of all the Fuzzy numbers. The preference values of all the characteristic object are determined on the basis of the tournament method and the principle of indifference. Finally, the Fuzzy model is constructed and is used to calculate preference values of the alternatives, making it a multicriteria model that is free of rank reversal. The numerical example is used to illustrate the efficiency of the proposed method with respect to results from the TOPSIS method. The characteristic objects method results are more realistic than the TOPSIS results. Copyright © 2014 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.     

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.