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Roman Slowinski - One of the best experts on this subject based on the ideXlab platform.
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robust ordinal regression and stochastic multiobjective acceptability analysis in multiple criteria hierarchy process for the choquet integral Preference Model
Omega-international Journal of Management Science, 2016Co-Authors: Silvia Angilella, Salvatore Greco, Salvatore Corrente, Roman SlowinskiAbstract:The paper deals with two important issues of Multiple Criteria Decision Aiding: interaction between criteria and hierarchical structure of criteria. To handle interactions, we apply the Choquet integral as a Preference Model, and to handle the hierarchy of criteria, we apply the recently proposed methodology called Multiple Criteria Hierarchy Process. In addition to dealing with the above issues, we suppose that the Preference information provided by the Decision Maker is indirect and has the form of pairwise comparisons of criteria with respect to their importance and pairwise Preference comparisons of some pairs of alternatives with respect to some criteria. In consequence, many instances of the Choquet integral are usually compatible with this Preference information. These instances are identified and exploited by Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis. To illustrate the whole approach, we show its application to a real world decision problem concerning the ranking of universities for a hypothetical Decision Maker.
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using choquet integral as Preference Model in interactive evolutionary multiobjective optimization
European Journal of Operational Research, 2016Co-Authors: Juergen Branke, Salvatore Greco, Salvatore Corrente, Roman Slowinski, Piotr ZielniewiczAbstract:We propose an interactive multiobjective evolutionary algorithm that attempts to discover the most preferred part of the Pareto-optimal set. Preference information is elicited by asking the user to compare some solutions pairwise. This information is then used to curb the set of compatible user’s value functions, and the multiobjective evolutionary algorithm is run to simultaneously search for all solutions that could potentially be the most preferred. Compared to previous similar approaches, we implement a much more efficient way of determining potentially preferred solutions, that is, solutions that are best for at least one value function compatible with the Preference information provided by the decision maker. For the first time in the context of evolutionary computation, we apply the Choquet integral as a user’s Preference Model, allowing us to capture interactions between objectives. As there is a trade-off between the flexibility of the value function Model and the complexity of learning a faithful Model of user’s Preferences, we propose to start the interactive process with a simple linear Model but then to switch to the Choquet integral as soon as the Preference information can no longer be represented using the linear Model. An experimental analysis demonstrates the effectiveness of the approach.
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selection of a representative value function for robust ordinal regression in group decision making
Group Decision and Negotiation, 2013Co-Authors: Milosz Kadzinski, Salvatore Greco, Roman SlowinskiAbstract:In this paper, we introduce the concept of a representative value function in a group decision context. We extend recently proposed methods UTAGMS-GROUP and UTADISGMS-GROUP with selection of a compromise and collective Preference Model which aggregates Preferences of several decision makers (DMs) and represents all instances of Preference Models compatible with Preference information elicited from DMs. The representative value function is built on results of robust ordinal regression, so its representativeness can be interpreted in terms of robustness concern. We propose a few procedures designed for multiple criteria ranking, choice, and sorting problems. The use of these procedures is conditioned by both satisfying different degrees of consistency of the Preference information provided by all DMs, as well as by some properties of particular decision making situations. The representative value function is intended to help the DMs to understand the robust results, and to provide them with a compromise result in case of conflict between the DMs.
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multi criteria classification a new scheme for application of dominance based decision rules
European Journal of Operational Research, 2007Co-Authors: Jerzy Blaszczynski, Salvatore Greco, Roman SlowinskiAbstract:Abstract We are considering the problem of multi-criteria classification. In this problem, a set of “if … then …” decision rules is used as a Preference Model to classify objects evaluated by a set of criteria and regular attributes. Given a sample of classification examples, called learning data set, the rules are induced from dominance-based rough approximations of Preference-ordered decision classes, according to the Variable Consistency Dominance-based Rough Set Approach (VC-DRSA). The main question to be answered in this paper is how to classify an object using decision rules in situation where it is covered by (i) no rule, (ii) exactly one rule, (iii) several rules. The proposed classification scheme can be applied to both, learning data set (to restore the classification known from examples) and testing data set (to predict classification of new objects). A hypothetical example from the area of telecommunications is used for illustration of the proposed classification method and for a comparison with some previous proposals.
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axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough set decision rules
European Journal of Operational Research, 2004Co-Authors: Salvatore Greco, Roman Slowinski, Benedetto MatarazzoAbstract:Abstract Utility or value functions play an important role of Preference Models in multiple-criteria decision making. We investigate the relationships between these Models and the decision-rule Preference Model obtained from the Dominance-based Rough Set Approach. The relationships are established by means of special “cancellation properties” used in conjoint measurement as axioms for representation of aggregation procedures. We are considering a general utility function and three of its important special cases: associative operator, Sugeno integral and ordered weighted maximum. For each of these aggregation functions we give a representation theorem establishing equivalence between a very weak cancellation property, the specific utility function and a set of rough-set decision rules. Each result is illustrated by a simple example of multiple-criteria decision making. The results show that the decision rule Model we propose has clear advantages over a general utility function and its particular cases.
Salvatore Greco - One of the best experts on this subject based on the ideXlab platform.
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on the choquet multiple criteria Preference aggregation Model theoretical and practical insights from a real world application
European Journal of Operational Research, 2018Co-Authors: Marta Carla Bottero, Salvatore Greco, Valentina Ferretti, José Rui FigueiraAbstract:Abstract We consider the use of the Choquet integral for evaluating projects or actions in a real-world application starting from the case of the re-qualification of an abandoned quarry. Despite the Choquet integral being a very well-known Preference Model for which there is a rich and well developed theory, its application in a multiple criteria decision aiding perspective requires some specific methodological developments. This led us to work out and implement in practice two new procedures: a first procedure to build interval scales with the objective of assigning utility values on a common scale to the criteria performances, and a second one to construct a ratio scale for assigning numerical values to the capacities of the Choquet integral. This article discusses the strengths and weaknesses of the Choquet integral as appearing in the case study, proposing as well insights related to the interaction of the experts within a focus group.
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robust ordinal regression and stochastic multiobjective acceptability analysis in multiple criteria hierarchy process for the choquet integral Preference Model
Omega-international Journal of Management Science, 2016Co-Authors: Silvia Angilella, Salvatore Greco, Salvatore Corrente, Roman SlowinskiAbstract:The paper deals with two important issues of Multiple Criteria Decision Aiding: interaction between criteria and hierarchical structure of criteria. To handle interactions, we apply the Choquet integral as a Preference Model, and to handle the hierarchy of criteria, we apply the recently proposed methodology called Multiple Criteria Hierarchy Process. In addition to dealing with the above issues, we suppose that the Preference information provided by the Decision Maker is indirect and has the form of pairwise comparisons of criteria with respect to their importance and pairwise Preference comparisons of some pairs of alternatives with respect to some criteria. In consequence, many instances of the Choquet integral are usually compatible with this Preference information. These instances are identified and exploited by Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis. To illustrate the whole approach, we show its application to a real world decision problem concerning the ranking of universities for a hypothetical Decision Maker.
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using choquet integral as Preference Model in interactive evolutionary multiobjective optimization
European Journal of Operational Research, 2016Co-Authors: Juergen Branke, Salvatore Greco, Salvatore Corrente, Roman Slowinski, Piotr ZielniewiczAbstract:We propose an interactive multiobjective evolutionary algorithm that attempts to discover the most preferred part of the Pareto-optimal set. Preference information is elicited by asking the user to compare some solutions pairwise. This information is then used to curb the set of compatible user’s value functions, and the multiobjective evolutionary algorithm is run to simultaneously search for all solutions that could potentially be the most preferred. Compared to previous similar approaches, we implement a much more efficient way of determining potentially preferred solutions, that is, solutions that are best for at least one value function compatible with the Preference information provided by the decision maker. For the first time in the context of evolutionary computation, we apply the Choquet integral as a user’s Preference Model, allowing us to capture interactions between objectives. As there is a trade-off between the flexibility of the value function Model and the complexity of learning a faithful Model of user’s Preferences, we propose to start the interactive process with a simple linear Model but then to switch to the Choquet integral as soon as the Preference information can no longer be represented using the linear Model. An experimental analysis demonstrates the effectiveness of the approach.
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stochastic multiobjective acceptability analysis for the choquet integral Preference Model and the scale construction problem
European Journal of Operational Research, 2015Co-Authors: Silvia Angilella, Salvatore Greco, Salvatore CorrenteAbstract:Abstract The Choquet integral Preference Model is adopted in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria, while the Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology considered to take into account uncertainty or imprecision on the considered data and Preference parameters. In this paper, we propose to combine the Choquet integral Preference Model with the SMAA methodology in order to get robust recommendations taking into account all parameters compatible with the Preference information provided by the Decision Maker (DM). In case the criteria are on a common scale, one has to elicit only a set of non-additive weights, technically a capacity, compatible with the DM’s Preference information. Instead, if the criteria are on different scales, besides the capacity, one has to elicit also a common scale compatible with the Preferences given by the DM. Our approach permits to explore the whole space of capacities and common scales compatible with the DM’s Preference information.
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selection of a representative value function for robust ordinal regression in group decision making
Group Decision and Negotiation, 2013Co-Authors: Milosz Kadzinski, Salvatore Greco, Roman SlowinskiAbstract:In this paper, we introduce the concept of a representative value function in a group decision context. We extend recently proposed methods UTAGMS-GROUP and UTADISGMS-GROUP with selection of a compromise and collective Preference Model which aggregates Preferences of several decision makers (DMs) and represents all instances of Preference Models compatible with Preference information elicited from DMs. The representative value function is built on results of robust ordinal regression, so its representativeness can be interpreted in terms of robustness concern. We propose a few procedures designed for multiple criteria ranking, choice, and sorting problems. The use of these procedures is conditioned by both satisfying different degrees of consistency of the Preference information provided by all DMs, as well as by some properties of particular decision making situations. The representative value function is intended to help the DMs to understand the robust results, and to provide them with a compromise result in case of conflict between the DMs.
Roman Słowinski - One of the best experts on this subject based on the ideXlab platform.
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extreme ranking analysis in robust ordinal regression
Omega-international Journal of Management Science, 2012Co-Authors: Miłosz Kadziński, Salvatore Greco, Roman SłowinskiAbstract:We extend the principle of robust ordinal regression with an analysis of extreme ranking results. In our proposal, we consider the whole set of instances of a Preference Model that is compatible with Preference information provided by the DM. We refer to both, the well-known UTAGMS method, which builds the set of general additive value functions compatible with DM's Preferences, and newly introduced in this paper PROMETHEEGKS, which constructs the set of compatible outranking Models via robust ordinal regression. Then, we consider all complete rankings that follow the use of the compatible Preference Models, and we determine the best and the worst attained ranks for each alternative. In this way, we are able to assess its position in an overall ranking, and not only in terms of pairwise comparisons, as it is the case in original robust ordinal regression methods. Additionally, we analyze the ranges of possible comprehensive scores (values or net outranking flows). We also discuss extensions of the presented approach on other multiple criteria problems than ranking. Finally, we show how the presented methodology can be applied in practical decision support, reporting results of three illustrative studies.
Silvia Angilella - One of the best experts on this subject based on the ideXlab platform.
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robust ordinal regression and stochastic multiobjective acceptability analysis in multiple criteria hierarchy process for the choquet integral Preference Model
Omega-international Journal of Management Science, 2016Co-Authors: Silvia Angilella, Salvatore Greco, Salvatore Corrente, Roman SlowinskiAbstract:The paper deals with two important issues of Multiple Criteria Decision Aiding: interaction between criteria and hierarchical structure of criteria. To handle interactions, we apply the Choquet integral as a Preference Model, and to handle the hierarchy of criteria, we apply the recently proposed methodology called Multiple Criteria Hierarchy Process. In addition to dealing with the above issues, we suppose that the Preference information provided by the Decision Maker is indirect and has the form of pairwise comparisons of criteria with respect to their importance and pairwise Preference comparisons of some pairs of alternatives with respect to some criteria. In consequence, many instances of the Choquet integral are usually compatible with this Preference information. These instances are identified and exploited by Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis. To illustrate the whole approach, we show its application to a real world decision problem concerning the ranking of universities for a hypothetical Decision Maker.
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stochastic multiobjective acceptability analysis for the choquet integral Preference Model and the scale construction problem
European Journal of Operational Research, 2015Co-Authors: Silvia Angilella, Salvatore Greco, Salvatore CorrenteAbstract:Abstract The Choquet integral Preference Model is adopted in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria, while the Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology considered to take into account uncertainty or imprecision on the considered data and Preference parameters. In this paper, we propose to combine the Choquet integral Preference Model with the SMAA methodology in order to get robust recommendations taking into account all parameters compatible with the Preference information provided by the Decision Maker (DM). In case the criteria are on a common scale, one has to elicit only a set of non-additive weights, technically a capacity, compatible with the DM’s Preference information. Instead, if the criteria are on different scales, besides the capacity, one has to elicit also a common scale compatible with the Preferences given by the DM. Our approach permits to explore the whole space of capacities and common scales compatible with the DM’s Preference information.
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stochastic multiobjective acceptability analysis for the choquet integral Preference Model and the scale construction problem
arXiv: Optimization and Control, 2013Co-Authors: Silvia Angilella, Salvatore Greco, Salvatore CorrenteAbstract:The Choquet integral is a Preference Model used in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria. The Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology used to take into account imprecision or lack of data in the problem at hand. For example, SMAA permits to compute the frequency that an alternative takes the k-th rank in the whole space of the admissible Preference parameters, e.g. in case evaluations on the considered criteria are aggregated through the weighted sum Model, in the space of weights compatible with the Preference information supplied by the Decision Maker (DM). In this paper, we propose to integrate the SMAA methodology with the Choquet integral Preference Model in order to get robust recommendations taking into account the whole space of Preference parameters compatible with the DM's Preference information. In case the alternatives are evaluated by all the criteria on a common scale, the Preference parameters are given by the capacity expressing the non-additive weights, representing the importance of criteria and their interaction. If the criteria are instead evaluated on different scales, besides the capacity, Preference parameters include the common scale on which the evaluations of criteria have to be recoded to be compared. Our approach permits to explore the whole space of Preference parameters being capacities and common scales compatible with the DM's Preference information.
Salvatore Corrente - One of the best experts on this subject based on the ideXlab platform.
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robust ordinal regression and stochastic multiobjective acceptability analysis in multiple criteria hierarchy process for the choquet integral Preference Model
Omega-international Journal of Management Science, 2016Co-Authors: Silvia Angilella, Salvatore Greco, Salvatore Corrente, Roman SlowinskiAbstract:The paper deals with two important issues of Multiple Criteria Decision Aiding: interaction between criteria and hierarchical structure of criteria. To handle interactions, we apply the Choquet integral as a Preference Model, and to handle the hierarchy of criteria, we apply the recently proposed methodology called Multiple Criteria Hierarchy Process. In addition to dealing with the above issues, we suppose that the Preference information provided by the Decision Maker is indirect and has the form of pairwise comparisons of criteria with respect to their importance and pairwise Preference comparisons of some pairs of alternatives with respect to some criteria. In consequence, many instances of the Choquet integral are usually compatible with this Preference information. These instances are identified and exploited by Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis. To illustrate the whole approach, we show its application to a real world decision problem concerning the ranking of universities for a hypothetical Decision Maker.
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using choquet integral as Preference Model in interactive evolutionary multiobjective optimization
European Journal of Operational Research, 2016Co-Authors: Juergen Branke, Salvatore Greco, Salvatore Corrente, Roman Slowinski, Piotr ZielniewiczAbstract:We propose an interactive multiobjective evolutionary algorithm that attempts to discover the most preferred part of the Pareto-optimal set. Preference information is elicited by asking the user to compare some solutions pairwise. This information is then used to curb the set of compatible user’s value functions, and the multiobjective evolutionary algorithm is run to simultaneously search for all solutions that could potentially be the most preferred. Compared to previous similar approaches, we implement a much more efficient way of determining potentially preferred solutions, that is, solutions that are best for at least one value function compatible with the Preference information provided by the decision maker. For the first time in the context of evolutionary computation, we apply the Choquet integral as a user’s Preference Model, allowing us to capture interactions between objectives. As there is a trade-off between the flexibility of the value function Model and the complexity of learning a faithful Model of user’s Preferences, we propose to start the interactive process with a simple linear Model but then to switch to the Choquet integral as soon as the Preference information can no longer be represented using the linear Model. An experimental analysis demonstrates the effectiveness of the approach.
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stochastic multiobjective acceptability analysis for the choquet integral Preference Model and the scale construction problem
European Journal of Operational Research, 2015Co-Authors: Silvia Angilella, Salvatore Greco, Salvatore CorrenteAbstract:Abstract The Choquet integral Preference Model is adopted in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria, while the Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology considered to take into account uncertainty or imprecision on the considered data and Preference parameters. In this paper, we propose to combine the Choquet integral Preference Model with the SMAA methodology in order to get robust recommendations taking into account all parameters compatible with the Preference information provided by the Decision Maker (DM). In case the criteria are on a common scale, one has to elicit only a set of non-additive weights, technically a capacity, compatible with the DM’s Preference information. Instead, if the criteria are on different scales, besides the capacity, one has to elicit also a common scale compatible with the Preferences given by the DM. Our approach permits to explore the whole space of capacities and common scales compatible with the DM’s Preference information.
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stochastic multiobjective acceptability analysis for the choquet integral Preference Model and the scale construction problem
arXiv: Optimization and Control, 2013Co-Authors: Silvia Angilella, Salvatore Greco, Salvatore CorrenteAbstract:The Choquet integral is a Preference Model used in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria. The Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology used to take into account imprecision or lack of data in the problem at hand. For example, SMAA permits to compute the frequency that an alternative takes the k-th rank in the whole space of the admissible Preference parameters, e.g. in case evaluations on the considered criteria are aggregated through the weighted sum Model, in the space of weights compatible with the Preference information supplied by the Decision Maker (DM). In this paper, we propose to integrate the SMAA methodology with the Choquet integral Preference Model in order to get robust recommendations taking into account the whole space of Preference parameters compatible with the DM's Preference information. In case the alternatives are evaluated by all the criteria on a common scale, the Preference parameters are given by the capacity expressing the non-additive weights, representing the importance of criteria and their interaction. If the criteria are instead evaluated on different scales, besides the capacity, Preference parameters include the common scale on which the evaluations of criteria have to be recoded to be compared. Our approach permits to explore the whole space of Preference parameters being capacities and common scales compatible with the DM's Preference information.
