Editorial: Challenges in multicriteria decision methods

Editorial: Challenges in multicriteria decision methods 1. Multiple criteria decision making or multiple criteria decision aiding or analysis for mathematical modelling of decisions Multiple Criteria Decision Making (MCDM) and Multiple Criteria Decision Aiding or Analysis (MCDA) are fields of study that have their roots in Operational Research (OR) and the modelling of the decision process with multiple criteria (or multi-attributes) therein (Roy, 1996; Polmerol & Barba-Romero, 2000; Belton & Stewart, 2002; Figueira et al., 2016). The acronym MCDM/A is used to represent a number of approaches associated with MCDM and MCDA, that is, decision making, decision aiding and decision analysis (de Almeida et al., 2015a). MCDM/A involves a wide range of methods that establish the preference structure of the Decision-Maker (DM), analyse the environment of the DM and evaluate alternatives (Roy, 1996; Belton & Stewart, 2002), thereby aiming to find the most preferred alternative while considering several, but normally contradictory, points of view. It does so by building mathematical models that are rational and efficient (Vincke, 1992). These methods aim to give a better understanding of how the DM thinks of decision situations (Keeney & Raiffa, 1976; Belton & Stewart, 2002; de Almeida et al., 2015a; Figueira et al., 2016). The MCDM/A community is very active all over the world and is well represented by the International Society on Multi-Criteria Decision Making (http://www.mcdmsociety.org/). This organization promotes biennial international conferences and also Summer Schools in order to disseminate the MCDM/A research. This Special Issue (SI) of the IMA Journal of Management Mathematics relates to the International Conference, which, since it was first published in 1975, has had a strong and continuous influence on the academic community. This SI reminds us that MCDM/A methods have been applied extensively by researchers, managers and analysts to solve complex decision problems that arise in different organizations, business units and systems, and in different areas of application such as evaluating social issues while taking Sustainability into account (Munda, 2008), Risk, Reliability and Maintenance (de Almeida et al., 2015a; de Almeida et al., 2015b; de Almeida et al., 2017), Vehicle Routing and scheduling problems (Geiger, 2017a; Geiger, 2017b; Huber & Geiger, 2017) and many others. The MCDM/A community also has links to several forums and OR Societies, including International Federation of Operational Research Societies (http://ifors.org/), EURO (namely, the Euro Working Group on MCDA: http://www.cs.put.poznan.pl/ewgmcda/) and INFORMS (i.e. the INFORMS Section on MCDM: http://connect.informs.org/multiple-criteria-decision-making). An important difference between MCDM/A and classical techniques of OR is that in MCDM/A the DM’s preferences are considered and formalized in preference theory, which is based on rigorous axioms that characterize an individual’s choice behavior. These preference axioms are essential for establishing preference representation functions, and provide the rationale for the quantitative analysis of preference (Keeney & Raiffa, 1976; Roy, 1996; Belton & Stewart, 2002; Figueira et al., 2016). Imprecise preferences can also be considered by using fuzzy approaches (Pedrycz et al., 2011). MCDM/A methods can be classified in different ways. The traditional classification given in the literature (Roy, 1996; Vincke, 1992; Belton & Stewart, 2002; Pardalos et al., 1995) considers the following three types of methods: unique criterion of synthesis methods (most of which have an additive aggregation), outranking methods, interactive methods (mathematical programming models). Another classification can be by the way that the criteria are analyzed, using either a compensatory or a non-compensatory rationality (de Almeida et al., 2015a). A preference relation is compensatory if there are trade-offs amongst criteria and non-compensatory otherwise (Bouyssou et al., 2006). In non-compensatory rationality, weights represent the relative importance among criteria (Roy, 1996; Vincke, 1992), whereas in compensatory methods, such as those using additive aggregation, weights represent substitution rates (Keeney & Raiffa, 1976; Belton & Stewart, 2002). The latter classification is an important starting point for preference modelling and also for choosing a MCDM/A method. There is some correspondence between these classifications. A unique criterion of synthesis consists of using compensatory rationality. Two theories underlying this are Multi-attribute Value Theory, for deterministic consequences, and Multi-attribute Utility Theory, for probabilistic consequences (Keeney & Raiffa, 1976; Belton & Stewart, 2002). Both are based on strong axiomatic structures. There are very many methods that perform additive aggregation, among which are the following: Simple Multi-attribute Rating Technique with Swing, Even Swaps, Utility Additive methods, Analytic Hierarchy Process, Measuring Attractiveness by a Categorical Based Evaluation Technique (Figueira et al., 2016). Outranking methods use non-compensatory rationality. Although some of these methods may be referred to as semi-compensatory, this is arguable because there is no compensation or trade-offs between criteria. These methods explore the outranking preference relation and allow the presence of incomparability relations and partial results in the recommendations. The most used outranking methods are those from the Elimination and Choice Reflecting Reality, in translation from French, family of methods and Preference Ranking Organization Methods for Enrichment Evaluations. Normally, in these methods there is no global score for alternatives (Roy, 1996; Belton & Stewart, 2002; Figueira et al., 2016). Finally, interactive methods cover discrete or continuous problems and include Multi-Objective Linear Programming methods (Karasakal & Köksalan, 2009; Allmendinger et al., 2017). These methods can be compensatory (additive models, for instance) or non-compensatory (lexicographical, for instance). Interactive methods allow the analyst to specify gradually or revise preference information, alternating between computation steps and interaction steps (Lee & Olson, 1999). When the mathematical programming models contain integer variables, they become harder to solve, and Multi-Objective Combinatorial Optimization methods can be applied (Ehrgott & Gandibleux, 2002). There is also a wide range of other methods and tools to support decisions (Figueira et al., 2016), such as Decision Rule approaches and partial information methods. The basic assumption of the Decision Rule approach is that the DM accepts that he/she can give preference information in terms of examples of decisions and to do so, he/she looks for simple rules justifying his/her decisions. An important advantage of this approach is the possibility of handling inconsistencies in the preference information, resulting from the DM’s hesitations. These methods use a non-compensatory rationality. Regarding methods with partial information, they are especially important when a DM is without a well-defined preference structure, and thus unable to specify preferences in the high level of detail required for complete information approaches (Weber, 1987). Examples of partial information methods are the Preference Assessment by Imprecise Ratio Statements method (Salo & Hämäläinen, 1992), Variable Independent Parameters (Dias & Clímaco, 2000), the Flexible and Interactive Tradeoff method (de Almeida et al., 2016). A particular case of partial information is the surrogate weights approach. In the Simple Multi-attribute Rating Technique Exploiting Ranks method (Edwards & Barron, 1994), criteria weights are ranked based on the swing procedure according to the DM’s preferences, and then surrogate weights are calculated based on the Rank Ordered Centroid. These methods focus on the partial information of the DM’s preferences so as to achieve the recommendation without compromising its quality, thus making the use of MCDM/A methods easier (Morais et al., 2015; Danielson & Ekenberg, 2017). It is notable that there are many methodologies for multicriteria decision. However, there are no better or worse techniques, but rather there are techniques that are better suited than others to particular cases. Some interesting applications of MCDM/A methods are discussed in the following section. 2. Challenges and future developments in MCDM/A One of the main challenges for applying MCDM/A is related to building decision models and choosing the most appropriate method. Although a few procedures or frameworks are available building multicriteria models (Polmerol & Barba-Romero, 2000; Belton & Stewart, 2002; de Almeida et al., 2015a) for this issue is still a challenging one. Flexibility when applying them seems to be relevant for resolving MCDM/A problems. One of the most recent enhancements to MCDM/A mathematical models deals with using partial information (or imprecise/incomplete information) about the DM preferences. This may include the use of surrogate weights (Edwards & Barron, 1994; Morais et al., 2015; Danielson & Ekenberg, 2017) or methods using decision rules, simulation or linear programing in order to reduce the space of criteria weights, while analysing the set of alternatives (Weber, 1987; Salo & Hämäläinen, 1992; Dias & Clímaco, 2000; de Almeida et al., 2016; Gusmão & Medeiros, 2016). Using mathematical models for aggregating multiple objectives based on the preferences of an individual is a considerable challenge. However, aggregating the preferences of multiple DMs is even more complex (Kilgour & Eden, 2010; Morais et al., 2014, Urtiga et al., 2017). Therefore, Multi Criteria Group Decision Making throws down multiple challenges for the MCDM/A area. Knowledge of the mathematical structure of these MCDM/A methods is essential, since using any of them inappropriately may lead to unsatisfactory results. We therefore encourage readers to keep themselves fully up-to-date in this field, which we believe is not only at the forefront of best management practice with mathematical support but also has a key role to play in helping organizations to find consistent mathematical models that best fit their context, thereby contributing positively to the rapid progress of society today. 3. An SI from MCDM community This SI arose from the $${23}\textrm{rd}$$ International Conference on MCDM 2015 (Hamburg, Germany, 3–7 August, 2015), and the open call-for-papers that followed. After rigorous review, we selected four papers for publication. We believe that these papers will have a significant impact on the theory and practice of business, management and policy making, using Decision Analysis and Multicriteria Decision Methods. These four papers are related to elicitation process for multicriteria decision models: Munier discusses the engineering behind eliciting experiences. The author states that DMs would like to see their preferences based on their experience and also argues that the standard way of eliciting tolerance to risk and attribute selection has become obsolete. The paper presents a complete set of non-parametric methods that avoid the evoked biases and objections, and suggests several fields of application. Niroomand, Mosallaeipour, Vizvari and Mahmoodirad deal with the supplier-material selection problem using a robust multi-objective method. They consider three different scaled objectives, using a weighted global criterion approach to find Pareto optimal solutions. Uncertain costs and demands are considered and used to analyse the sensitivity of the Pareto optimal solutions. Krejcí presents formulae based on the proper fuzzy approach for obtaining priorities from additive-fuzzy-pairwise-comparison matrices. The proposition is illustrated in numerical examples throughout the paper. Nishizaki, Hayashida and Sekizaki propose a method to generate scaling constants properly for the multi-attribute utility function, which incorporate the preferences of group members, by asking questions that are relatively easy to answer compared to indifference questions. They also develop a method for selecting an alternative that is consistent with the group preference. The trade-off between attributes is evaluated by using a large population of neural networks elicited from the interested individuals. The authors demonstrate the effectiveness of this method for the problem of selecting an environmental policy. Acknowledgement We would like to thank the authors for their contributions to this SI and the cooperation and assistance of many reviewers, whose helpful feedback did much to improve the quality of the papers submitted. References Allmendinger , R. , Ehrgott , M. , Gandibleux , X. , Geiger , M. J. , Klamroth , K. & Luque , M. ( 2017 ) Navigation in multi-objective optimization methods . J. Multi-Criteria Decis. Anal. , 24 , 57 -- 70 . Google Scholar CrossRef Search ADS Belton , V. & Stewart , T. ( 2002 ) Multiple Criteria Decision Analysis . Springer, Boston, MA : Kluwer Academic Publisher . Google Scholar CrossRef Search ADS Bouyssou , D. , Marchant , T. , Pirlot , M. , Tsoukis , A. & Vincke , P. ( 2006 ) Evaluation and Decisions Models with Multiple Criteria . Springer, Boston, MA : Springer . Danielson , M. & Ekenberg , L. ( 2017 ) A robustness study of state-of-the-art surrogate weights for MCDM . Group Decis. Negot. , 26 , 677 -- 691 . Google Scholar CrossRef Search ADS de Almeida , A. T ., Cavalcante , C. A. V ., Alencar , M. H ., Ferreira , R. J. P. , de Almeida-Filho , A. T . & Garcez , T. V. ( 2015a ) Multicriteria and multi-objective models for risk, reliability and maintenance decision analysis . International Series in Operations Research & Management Science , vol. 231 , 1st edn . New York : Springer , p. 416 . de Almeida , A. T. , Ferreira , R. J. P. & Cavalcante , C. A. V. ( 2015b ) A review of the use of multicriteria and multi-objective models in maintenance and reliability . IMA J. Manag. Math. , 26 , 249 -- 271 . Google Scholar CrossRef Search ADS de Almeida , A. T. , de Almeida , J. A. , Costa , A. P. C. S. & de Almeida-Filho , A. T. ( 2016 ) A new method for elicitation of criteria weights in additive models: flexible and interactive tradeoff . Eur. J. Oper. Res. , 250 , 179 -- 191 . Google Scholar CrossRef Search ADS de Almeida , A. T. , Alencar , M. H. , Garcez , T. V. & Ferreira , R. J. P. ( 2017 ) A systematic literature review of multicriteria and multi-objective models applied in risk management . IMA J. Manag. Math. , 28 , 153 -- 184 . Google Scholar CrossRef Search ADS Dias , L. C. & Clímaco , J. N. ( 2000 ) Additive aggregation with variable interdependent parameters: the VIP analysis software . J. Oper. Res. Soc. , 51 , 1070 -- 1082 . Google Scholar CrossRef Search ADS Edwards , W. & Barron , F. H. ( 1994 ) SMARTS and SMARTER: improved simple methods for multi-attribute utility measurement . Organ. Behav. Hum. Decis. Processes , 60 , 306 -- 325 . Google Scholar CrossRef Search ADS Ehrgott , M. & Gandibleux , X. ( eds .) ( 2002 ) Multiple Criteria Optimization: State-of-the-Art Annotated Bibliographic Surveys . Boston : Kluwer Academic Publishers . Figueira , J. R ., Greco , S . & Ehrgott , M. ( 2016 ) Multiple Criteria Decision Analysis: State-of-the-Art Surveys , vol. 1 and 2, 2nd edn. New York : Springer . Gal , T. , Stewart , T. J. & Hanne , T . ( eds .) ( 1999 ) Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications . Boston : Kluwer Academic Publishers. Geiger , M. J. ( 2017a ) A multi-threaded local search algorithm and computer implementation for the multi-mode, resource-constrained multi-project scheduling problem . Eur. J. Oper. Res. , 256 , 729 -- 741 . Google Scholar CrossRef Search ADS Geiger , M. J. ( 2017b ) On an effective approach for the coach trip with shuttle service problem of the VeRoLog solver challenge 2015 . Networks , 69 , 329 -- 345 . Google Scholar CrossRef Search ADS Gusmão , A. P. H . & Medeiros , C. P. ( 2016 ) A model for selecting a strategic information system using the FITradeoff . Math. Probl. Eng.; ID 7850960 Huber , S. & Geiger , M. J. ( 2017 ) Order matters—a variable neighborhood search for the swap-body vehicle routing problem . Eur. J. Oper. Res. , 263 , 419 -- 445 . Google Scholar CrossRef Search ADS Karasakal , E. K. & Köksalan , M. ( 2009 ) Generating a representative subset of the efficient frontier in multiple criteria decision making . Oper. Res ., 57 , 187 -- 199 . Google Scholar CrossRef Search ADS Keeney , R. L . & Raiffa , H . ( 1976 ) Decisions with Multiple Objectives: Preferences and Value Trade-Offs . New York : John Wiley . Kilgour , D. M. & Eden , C. ( 2010 ) Handbook of Group Decision and Negotiation . Advances in Group Decision and Negotiation, vol. 4 . Dordrecht : Springer . Lee , S. M. & Olson , D. L. ( 1999 ) Goal Programming . In Gal T, Stewart TJ and Hanne T (eds.) Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications . Springer, Boston, MA : Kluwer Academic Publishers . Morais , D. C. , de Almeida , A. T. & Figueira J. R . ( 2014 ) A sorting model for group decision making: a case study of water losses in brazil . Group Decis. Negot. , 23 , 937 -- 960 . Morais , D. C. , de Almeida , A. T. , Alencar , L. H. , Clemente , T. R. N. & Cavalcanti , C. Z. B . ( 2015 ) PROMETHEE-ROC model for assessing the readiness of technology for generating energy . Math. Probl. Eng. , 2015 , 1 -- 11 . Google Scholar CrossRef Search ADS Munda , G. ( 2008 ) Social Multi-Criteria Evaluation for a Sustainable Economy . Berlin, Heidelberg : Springer . Google Scholar CrossRef Search ADS Pardalos , P. M. , Siskos , Y. & Zopounidis , C. ( eds ) ( 1995 ) Advances in Multicriteria Analysis . Dordrecht : Kluwer Academic Publishers . Google Scholar CrossRef Search ADS Pedrycz , W. , Ekel , P. & Parreiras , R . ( 2011 ) Fuzzy Multicriteria Decision-Making: Models, Methods, and Applications . Chichester : John Wiley . Polmerol , J-C . & Barba-Romero , S . ( 2000 ) Multicriterion Decision in Management: Principles and Practice . Kluwer . Google Scholar CrossRef Search ADS Roy, B. ( 1996 ) Multicriteria Methodology for Decision Aiding . Springer, Boston, MA : Kluwer Academic Publishers . Google Scholar CrossRef Search ADS Salo , A. A. & Hämäläinen , R. P . ( 1992 ) Preference assessment by imprecise ratio statements . Oper. Res. , 40 , 1053 -- 1061 . Google Scholar CrossRef Search ADS Urtiga , M. M. , Morais , D. C. , Hipel , K. W. & Kilgour , D. M. ( 2017 ) Group decision methodology to support watershed committees in choosing among combinations of alternatives . Group Decis. Negot. , 26 , 729 -- 752 . Google Scholar CrossRef Search ADS Vincke, P. ( 1992 ) Multicriteria Decision-Aid . Bruxelles : John Wiley . Weber , M. ( 1987 ) Decision making with incomplete information . Eur. J. Oper. Res. , 28 , 44 -- 57 . Google Scholar CrossRef Search ADS © The Author(s) 2018. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. 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Editorial: Challenges in multicriteria decision methods

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Abstract

1. Multiple criteria decision making or multiple criteria decision aiding or analysis for mathematical modelling of decisions Multiple Criteria Decision Making (MCDM) and Multiple Criteria Decision Aiding or Analysis (MCDA) are fields of study that have their roots in Operational Research (OR) and the modelling of the decision process with multiple criteria (or multi-attributes) therein (Roy, 1996; Polmerol & Barba-Romero, 2000; Belton & Stewart, 2002; Figueira et al., 2016). The acronym MCDM/A is used to represent a number of approaches associated with MCDM and MCDA, that is, decision making, decision aiding and decision analysis (de Almeida et al., 2015a). MCDM/A involves a wide range of methods that establish the preference structure of the Decision-Maker (DM), analyse the environment of the DM and evaluate alternatives (Roy, 1996; Belton & Stewart, 2002), thereby aiming to find the most preferred alternative while considering several, but normally contradictory, points of view. It does so by building mathematical models that are rational and efficient (Vincke, 1992). These methods aim to give a better understanding of how the DM thinks of decision situations (Keeney & Raiffa, 1976; Belton & Stewart, 2002; de Almeida et al., 2015a; Figueira et al., 2016). The MCDM/A community is very active all over the world and is well represented by the International Society on Multi-Criteria Decision Making (http://www.mcdmsociety.org/). This organization promotes biennial international conferences and also Summer Schools in order to disseminate the MCDM/A research. This Special Issue (SI) of the IMA Journal of Management Mathematics relates to the International Conference, which, since it was first published in 1975, has had a strong and continuous influence on the academic community. This SI reminds us that MCDM/A methods have been applied extensively by researchers, managers and analysts to solve complex decision problems that arise in different organizations, business units and systems, and in different areas of application such as evaluating social issues while taking Sustainability into account (Munda, 2008), Risk, Reliability and Maintenance (de Almeida et al., 2015a; de Almeida et al., 2015b; de Almeida et al., 2017), Vehicle Routing and scheduling problems (Geiger, 2017a; Geiger, 2017b; Huber & Geiger, 2017) and many others. The MCDM/A community also has links to several forums and OR Societies, including International Federation of Operational Research Societies (http://ifors.org/), EURO (namely, the Euro Working Group on MCDA: http://www.cs.put.poznan.pl/ewgmcda/) and INFORMS (i.e. the INFORMS Section on MCDM: http://connect.informs.org/multiple-criteria-decision-making). An important difference between MCDM/A and classical techniques of OR is that in MCDM/A the DM’s preferences are considered and formalized in preference theory, which is based on rigorous axioms that characterize an individual’s choice behavior. These preference axioms are essential for establishing preference representation functions, and provide the rationale for the quantitative analysis of preference (Keeney & Raiffa, 1976; Roy, 1996; Belton & Stewart, 2002; Figueira et al., 2016). Imprecise preferences can also be considered by using fuzzy approaches (Pedrycz et al., 2011). MCDM/A methods can be classified in different ways. The traditional classification given in the literature (Roy, 1996; Vincke, 1992; Belton & Stewart, 2002; Pardalos et al., 1995) considers the following three types of methods: unique criterion of synthesis methods (most of which have an additive aggregation), outranking methods, interactive methods (mathematical programming models). Another classification can be by the way that the criteria are analyzed, using either a compensatory or a non-compensatory rationality (de Almeida et al., 2015a). A preference relation is compensatory if there are trade-offs amongst criteria and non-compensatory otherwise (Bouyssou et al., 2006). In non-compensatory rationality, weights represent the relative importance among criteria (Roy, 1996; Vincke, 1992), whereas in compensatory methods, such as those using additive aggregation, weights represent substitution rates (Keeney & Raiffa, 1976; Belton & Stewart, 2002). The latter classification is an important starting point for preference modelling and also for choosing a MCDM/A method. There is some correspondence between these classifications. A unique criterion of synthesis consists of using compensatory rationality. Two theories underlying this are Multi-attribute Value Theory, for deterministic consequences, and Multi-attribute Utility Theory, for probabilistic consequences (Keeney & Raiffa, 1976; Belton & Stewart, 2002). Both are based on strong axiomatic structures. There are very many methods that perform additive aggregation, among which are the following: Simple Multi-attribute Rating Technique with Swing, Even Swaps, Utility Additive methods, Analytic Hierarchy Process, Measuring Attractiveness by a Categorical Based Evaluation Technique (Figueira et al., 2016). Outranking methods use non-compensatory rationality. Although some of these methods may be referred to as semi-compensatory, this is arguable because there is no compensation or trade-offs between criteria. These methods explore the outranking preference relation and allow the presence of incomparability relations and partial results in the recommendations. The most used outranking methods are those from the Elimination and Choice Reflecting Reality, in translation from French, family of methods and Preference Ranking Organization Methods for Enrichment Evaluations. Normally, in these methods there is no global score for alternatives (Roy, 1996; Belton & Stewart, 2002; Figueira et al., 2016). Finally, interactive methods cover discrete or continuous problems and include Multi-Objective Linear Programming methods (Karasakal & Köksalan, 2009; Allmendinger et al., 2017). These methods can be compensatory (additive models, for instance) or non-compensatory (lexicographical, for instance). Interactive methods allow the analyst to specify gradually or revise preference information, alternating between computation steps and interaction steps (Lee & Olson, 1999). When the mathematical programming models contain integer variables, they become harder to solve, and Multi-Objective Combinatorial Optimization methods can be applied (Ehrgott & Gandibleux, 2002). There is also a wide range of other methods and tools to support decisions (Figueira et al., 2016), such as Decision Rule approaches and partial information methods. The basic assumption of the Decision Rule approach is that the DM accepts that he/she can give preference information in terms of examples of decisions and to do so, he/she looks for simple rules justifying his/her decisions. An important advantage of this approach is the possibility of handling inconsistencies in the preference information, resulting from the DM’s hesitations. These methods use a non-compensatory rationality. Regarding methods with partial information, they are especially important when a DM is without a well-defined preference structure, and thus unable to specify preferences in the high level of detail required for complete information approaches (Weber, 1987). Examples of partial information methods are the Preference Assessment by Imprecise Ratio Statements method (Salo & Hämäläinen, 1992), Variable Independent Parameters (Dias & Clímaco, 2000), the Flexible and Interactive Tradeoff method (de Almeida et al., 2016). A particular case of partial information is the surrogate weights approach. In the Simple Multi-attribute Rating Technique Exploiting Ranks method (Edwards & Barron, 1994), criteria weights are ranked based on the swing procedure according to the DM’s preferences, and then surrogate weights are calculated based on the Rank Ordered Centroid. These methods focus on the partial information of the DM’s preferences so as to achieve the recommendation without compromising its quality, thus making the use of MCDM/A methods easier (Morais et al., 2015; Danielson & Ekenberg, 2017). It is notable that there are many methodologies for multicriteria decision. However, there are no better or worse techniques, but rather there are techniques that are better suited than others to particular cases. Some interesting applications of MCDM/A methods are discussed in the following section. 2. Challenges and future developments in MCDM/A One of the main challenges for applying MCDM/A is related to building decision models and choosing the most appropriate method. Although a few procedures or frameworks are available building multicriteria models (Polmerol & Barba-Romero, 2000; Belton & Stewart, 2002; de Almeida et al., 2015a) for this issue is still a challenging one. Flexibility when applying them seems to be relevant for resolving MCDM/A problems. One of the most recent enhancements to MCDM/A mathematical models deals with using partial information (or imprecise/incomplete information) about the DM preferences. This may include the use of surrogate weights (Edwards & Barron, 1994; Morais et al., 2015; Danielson & Ekenberg, 2017) or methods using decision rules, simulation or linear programing in order to reduce the space of criteria weights, while analysing the set of alternatives (Weber, 1987; Salo & Hämäläinen, 1992; Dias & Clímaco, 2000; de Almeida et al., 2016; Gusmão & Medeiros, 2016). Using mathematical models for aggregating multiple objectives based on the preferences of an individual is a considerable challenge. However, aggregating the preferences of multiple DMs is even more complex (Kilgour & Eden, 2010; Morais et al., 2014, Urtiga et al., 2017). Therefore, Multi Criteria Group Decision Making throws down multiple challenges for the MCDM/A area. Knowledge of the mathematical structure of these MCDM/A methods is essential, since using any of them inappropriately may lead to unsatisfactory results. We therefore encourage readers to keep themselves fully up-to-date in this field, which we believe is not only at the forefront of best management practice with mathematical support but also has a key role to play in helping organizations to find consistent mathematical models that best fit their context, thereby contributing positively to the rapid progress of society today. 3. An SI from MCDM community This SI arose from the $${23}\textrm{rd}$$ International Conference on MCDM 2015 (Hamburg, Germany, 3–7 August, 2015), and the open call-for-papers that followed. After rigorous review, we selected four papers for publication. We believe that these papers will have a significant impact on the theory and practice of business, management and policy making, using Decision Analysis and Multicriteria Decision Methods. These four papers are related to elicitation process for multicriteria decision models: Munier discusses the engineering behind eliciting experiences. The author states that DMs would like to see their preferences based on their experience and also argues that the standard way of eliciting tolerance to risk and attribute selection has become obsolete. The paper presents a complete set of non-parametric methods that avoid the evoked biases and objections, and suggests several fields of application. Niroomand, Mosallaeipour, Vizvari and Mahmoodirad deal with the supplier-material selection problem using a robust multi-objective method. They consider three different scaled objectives, using a weighted global criterion approach to find Pareto optimal solutions. Uncertain costs and demands are considered and used to analyse the sensitivity of the Pareto optimal solutions. Krejcí presents formulae based on the proper fuzzy approach for obtaining priorities from additive-fuzzy-pairwise-comparison matrices. The proposition is illustrated in numerical examples throughout the paper. Nishizaki, Hayashida and Sekizaki propose a method to generate scaling constants properly for the multi-attribute utility function, which incorporate the preferences of group members, by asking questions that are relatively easy to answer compared to indifference questions. They also develop a method for selecting an alternative that is consistent with the group preference. The trade-off between attributes is evaluated by using a large population of neural networks elicited from the interested individuals. The authors demonstrate the effectiveness of this method for the problem of selecting an environmental policy. Acknowledgement We would like to thank the authors for their contributions to this SI and the cooperation and assistance of many reviewers, whose helpful feedback did much to improve the quality of the papers submitted. References Allmendinger , R. , Ehrgott , M. , Gandibleux , X. , Geiger , M. J. , Klamroth , K. & Luque , M. ( 2017 ) Navigation in multi-objective optimization methods . J. Multi-Criteria Decis. Anal. , 24 , 57 -- 70 . Google Scholar CrossRef Search ADS Belton , V. & Stewart , T. ( 2002 ) Multiple Criteria Decision Analysis . Springer, Boston, MA : Kluwer Academic Publisher . Google Scholar CrossRef Search ADS Bouyssou , D. , Marchant , T. , Pirlot , M. , Tsoukis , A. & Vincke , P. ( 2006 ) Evaluation and Decisions Models with Multiple Criteria . Springer, Boston, MA : Springer . Danielson , M. & Ekenberg , L. ( 2017 ) A robustness study of state-of-the-art surrogate weights for MCDM . Group Decis. Negot. , 26 , 677 -- 691 . Google Scholar CrossRef Search ADS de Almeida , A. T ., Cavalcante , C. A. V ., Alencar , M. H ., Ferreira , R. J. P. , de Almeida-Filho , A. T . & Garcez , T. V. ( 2015a ) Multicriteria and multi-objective models for risk, reliability and maintenance decision analysis . International Series in Operations Research & Management Science , vol. 231 , 1st edn . New York : Springer , p. 416 . de Almeida , A. T. , Ferreira , R. J. P. & Cavalcante , C. A. V. ( 2015b ) A review of the use of multicriteria and multi-objective models in maintenance and reliability . IMA J. Manag. Math. , 26 , 249 -- 271 . Google Scholar CrossRef Search ADS de Almeida , A. T. , de Almeida , J. A. , Costa , A. P. C. S. & de Almeida-Filho , A. T. ( 2016 ) A new method for elicitation of criteria weights in additive models: flexible and interactive tradeoff . Eur. J. Oper. Res. , 250 , 179 -- 191 . Google Scholar CrossRef Search ADS de Almeida , A. T. , Alencar , M. H. , Garcez , T. V. & Ferreira , R. J. P. 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IMA Journal of Management MathematicsOxford University Press

Published: Mar 22, 2018

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