As simple as possible but not simpler in Multiple Criteria Decision Aiding: the robust-stochastic level dependent Choquet integral approach |
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| Institution: | 1. Department of Economics and Business, University of Catania, Corso Italia, 55, 95129, Catania, Italy;2. Portsmouth Business School, Centre for Operational Research and Logistics (CORL), University of Portsmouth, Portsmouth, United Kingdom;1. HEC Liège, Management School of the University of Liège, Liège, Belgium;2. School of Business and Economics, Maastricht University, Maastricht, the Netherlands;1. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL 32611, USA;2. Department of Industrial Engineering and Management Systems, University of Central Florida, 12800 Pegasus Dr., Orlando, FL 32816, USA;3. Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, Pittsburgh, PA 15261, USA;1. Department of Mathematics, Technische Universität Kaiserslautern, Kaiserslautern 67663 Germany;2. CEG-IST, Instituto Superior Técnico, Universidade de Lisboa, Lisboa 1049-001, Portugal;1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, People’s Republic of China;2. Logistics Research Centre, Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hong Kong, People’s Republic of China;1. Faculty of Economics and Business Administration, Ghent University, Tweekerkenstraat 2, Gent 9000 Belgium;2. Technology and Operations Management Area, Vlerick Business School, Belgium;3. UCL School of Management, University College, London, UK;1. Isenberg School of Management, University of Massachusetts-Amherst, 90 Campus Center Way, 209A Flint Lab, Amherst, MA 01003, USA;2. Management School, University of Liverpool, L69 7ZH, UK;3. Lancaster University Management School, LA1 4YX, UK |
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| Abstract: | The level dependent Choquet integral has been proposed to handle decision making problems in which the importance and the interaction of criteria may depend on the level of the alternatives’ evaluations. This integral is based on a level dependent capacity, which is a family of single capacities associated to each level of evaluation for the considered criteria. We present two possible formulations of the level dependent capacity where importance and interaction of criteria are constant inside each one of the subintervals in which the interval of evaluations for considered criteria is split or vary with continuity inside the whole interval of evaluations. Since, in general, there is not only one but many level dependent capacities compatible with the preference information provided by the Decision Maker, we propose to take into account all of them by using the Robust Ordinal Regression (ROR) and the Stochastic Multicriteria Acceptability Analysis (SMAA). On one hand, ROR defines a necessary preference relation (if an alternative a is at least as good as an alternative b for all compatible level dependent capacities), and a possible preference relation (if a is at least as good as b for at least one compatible level dependent capacity). On the other hand, considering a random sampling of compatible level dependent capacities, SMAA gives the probability that each alternative reaches a certain ranking position as well as the probability that an alternative is preferred to another. A real-world decision problem on rankings of universities is provided to illustrate the proposed methodology. |
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