The Experts below are selected from a list of 4524 Experts worldwide ranked by ideXlab platform
Salvatore Greco - 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 Corrente, Salvatore Greco, 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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combining analytical hierarchy process and Choquet Integral within non additive robust ordinal regression
Omega-international Journal of Management Science, 2016Co-Authors: Salvatore Corrente, Salvatore Greco, Alessio IshizakaAbstract:We consider multiple criteria decision aiding in the case of interaction between criteria. In this case the usual weighted sum cannot be used to aggregate evaluations on different criteria and other value functions with a more complex formulation have to be considered. The Choquet Integral is the most used technique and also the most widespread in the literature. However, the application of the Choquet Integral presents two main problems being the necessity to determine the capacity, which is the function that assigns a weight not only to all single criteria but also to all subset of criteria, and the necessity to express on the same scale evaluations on different criteria. While with respect to the first problem we adopt the recently introduced Non-Additive Robust Ordinal Regression (NAROR) taking into account all the capacities compatible with the preference information provided by the DM, with respect to the second one we build the common scale for the considered criteria using the Analytic Hierarchy Process (AHP). We propose to use AHP on a set of reference points in the scale of each criterion and to use an interpolation to obtain the other values. This permits to reduce considerably the number of pairwise comparisons usually required by the DM when applying AHP. An illustrative example details the application of the proposed methodology.
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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 Corrente, Salvatore Greco, 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 Corrente, Salvatore GrecoAbstract: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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multiple criteria hierarchy process for the Choquet Integral
International Conference on Evolutionary Multi-criterion Optimization, 2013Co-Authors: Silvia Angilella, Salvatore Corrente, Salvatore Greco, Roman SlowinskiAbstract:Interaction between criteria and hierarchical structure of criteria are nowadays two important issues in Multiple Criteria Decision Analysis (MCDA). Interaction between criteria is often dealt with fuzzy Integrals, especially the Choquet Integral. To handle the hierarchy of criteria in MCDA, a methodology called Multiple Criteria Hierarchy Process (MCHP) has been recently proposed. It permits consideration of preference relations with respect to a subset of criteria at any level of the hierarchy. In this paper, we propose to apply MCHP to the Choquet Integral. In this way, using the Choquet Integral and the MCHP, it is possible to compare two alternatives not only globally, but also partially, taking into account a particular subset of criteria and the possible interaction between them.
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 Corrente, Salvatore Greco, 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 Corrente, Salvatore Greco, 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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multiple criteria hierarchy process for the Choquet Integral
International Conference on Evolutionary Multi-criterion Optimization, 2013Co-Authors: Silvia Angilella, Salvatore Corrente, Salvatore Greco, Roman SlowinskiAbstract:Interaction between criteria and hierarchical structure of criteria are nowadays two important issues in Multiple Criteria Decision Analysis (MCDA). Interaction between criteria is often dealt with fuzzy Integrals, especially the Choquet Integral. To handle the hierarchy of criteria in MCDA, a methodology called Multiple Criteria Hierarchy Process (MCHP) has been recently proposed. It permits consideration of preference relations with respect to a subset of criteria at any level of the hierarchy. In this paper, we propose to apply MCHP to the Choquet Integral. In this way, using the Choquet Integral and the MCHP, it is possible to compare two alternatives not only globally, but also partially, taking into account a particular subset of criteria and the possible interaction between them.
Chunqiao Tan - One of the best experts on this subject based on the ideXlab platform.
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Interval-Valued Intuitionistic Fuzzy Multicriteria Group Decision Making Based on VIKOR and Choquet Integral
2020Co-Authors: Chunqiao Tan, Xiaohong ChenAbstract:An effective decision making approach based on VIKOR and Choquet Integral is developed to solve multicriteria group decision making problem with conflicting criteria and interdependent subjective preference of decision makers in a fuzzy environment where preferences of decision makers with respect to criteria are represented by interval-valued intuitionistic fuzzy sets. First, an intervalvalued intuitionistic fuzzy Choquet Integral operator is given. Some of its properties are investigated in detail. The extended VIKOR decision procedure based on the proposed operator is developed for solving the multicriteria group decision making problem where the interactive criteria weight is measured by Shapley value. An illustrative example is given for demonstrating the applicability of the proposed decision procedure for solving the multi-criteria group decision making problem in interval-valued intuitionistic fuzzy environment
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a multi criteria interval valued intuitionistic fuzzy group decision making with Choquet Integral based topsis
Expert Systems With Applications, 2011Co-Authors: Chunqiao TanAbstract:An extension of TOPSIS, a multi-criteria interval-valued intuitionistic fuzzy decision making technique, to a group decision environment is investigated, where inter-dependent or interactive characteristics among criteria and preference of decision makers are taken into account. To get a broad view of the techniques used, first, some operational laws on interval-valued intuitionistic fuzzy values are introduced. Based on these operational laws, a generalized interval-valued intuitionistic fuzzy geometric aggregation operator is proposed which is used to aggregate decision makers' opinions in group decision making process. In addition, some of its properties are discussed. Then Choquet Integral-based Hamming distance between interval-valued intuitionistic fuzzy values is defined. Combining the interval-valued intuitionistic fuzzy geometric aggregation operator with Choquet Integral-based Hamming distance, an extension of TOPSIS method is developed to deal with a multi-criteria interval-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is used to illustrate the developed procedures.
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intuitionistic fuzzy Choquet Integral operator for multi criteria decision making
Expert Systems With Applications, 2010Co-Authors: Chunqiao Tan, Xiaohong ChenAbstract:For the real decision making problems, most criteria have inter-dependent or interactive characteristics so that it is not suitable for us to aggregate them by traditional aggregation operators based on additive measures. Thus, to approximate the human subjective decision making process, it would be more suitable to apply fuzzy measures, where it is not necessary to assume additivity and independence among decision making criteria. In this paper, an intuitionistic fuzzy Choquet Integral is proposed for multiple criteria decision making, where interactions phenomena among the decision making criteria are considered. First, we introduced two operational laws on intuitionistic fuzzy values. Then, based on these operational laws, intuitionistic fuzzy Choquet Integral operator is proposed. Moreover, some of its properties are investigated. It is shown that the intuitionistic fuzzy Choquet Integral operator can be represented by some special t-norms and t-conorms, and it is also a generalization of the intuitionistic fuzzy OWA operator and intuitionistic fuzzy weighted averaging operator. Further, the procedure and algorithm of multi-criteria decision making based on intuitionistic fuzzy Choquet Integral operator is given under uncertain environment. Finally, a practical example is provided to illustrate the developed approaches.
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 Corrente, Salvatore Greco, 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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combining analytical hierarchy process and Choquet Integral within non additive robust ordinal regression
Omega-international Journal of Management Science, 2016Co-Authors: Salvatore Corrente, Salvatore Greco, Alessio IshizakaAbstract:We consider multiple criteria decision aiding in the case of interaction between criteria. In this case the usual weighted sum cannot be used to aggregate evaluations on different criteria and other value functions with a more complex formulation have to be considered. The Choquet Integral is the most used technique and also the most widespread in the literature. However, the application of the Choquet Integral presents two main problems being the necessity to determine the capacity, which is the function that assigns a weight not only to all single criteria but also to all subset of criteria, and the necessity to express on the same scale evaluations on different criteria. While with respect to the first problem we adopt the recently introduced Non-Additive Robust Ordinal Regression (NAROR) taking into account all the capacities compatible with the preference information provided by the DM, with respect to the second one we build the common scale for the considered criteria using the Analytic Hierarchy Process (AHP). We propose to use AHP on a set of reference points in the scale of each criterion and to use an interpolation to obtain the other values. This permits to reduce considerably the number of pairwise comparisons usually required by the DM when applying AHP. An illustrative example details the application of the proposed methodology.
-
using Choquet Integral as preference model in interactive evolutionary multiobjective optimization
European Journal of Operational Research, 2016Co-Authors: Juergen Branke, Salvatore Corrente, Salvatore Greco, 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.
-
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 Corrente, Salvatore GrecoAbstract: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.
-
multiple criteria hierarchy process for the Choquet Integral
International Conference on Evolutionary Multi-criterion Optimization, 2013Co-Authors: Silvia Angilella, Salvatore Corrente, Salvatore Greco, Roman SlowinskiAbstract:Interaction between criteria and hierarchical structure of criteria are nowadays two important issues in Multiple Criteria Decision Analysis (MCDA). Interaction between criteria is often dealt with fuzzy Integrals, especially the Choquet Integral. To handle the hierarchy of criteria in MCDA, a methodology called Multiple Criteria Hierarchy Process (MCHP) has been recently proposed. It permits consideration of preference relations with respect to a subset of criteria at any level of the hierarchy. In this paper, we propose to apply MCHP to the Choquet Integral. In this way, using the Choquet Integral and the MCHP, it is possible to compare two alternatives not only globally, but also partially, taking into account a particular subset of criteria and the possible interaction between them.
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 Corrente, Salvatore Greco, 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.
-
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 Corrente, Salvatore GrecoAbstract: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.
-
multiple criteria hierarchy process for the Choquet Integral
International Conference on Evolutionary Multi-criterion Optimization, 2013Co-Authors: Silvia Angilella, Salvatore Corrente, Salvatore Greco, Roman SlowinskiAbstract:Interaction between criteria and hierarchical structure of criteria are nowadays two important issues in Multiple Criteria Decision Analysis (MCDA). Interaction between criteria is often dealt with fuzzy Integrals, especially the Choquet Integral. To handle the hierarchy of criteria in MCDA, a methodology called Multiple Criteria Hierarchy Process (MCHP) has been recently proposed. It permits consideration of preference relations with respect to a subset of criteria at any level of the hierarchy. In this paper, we propose to apply MCHP to the Choquet Integral. In this way, using the Choquet Integral and the MCHP, it is possible to compare two alternatives not only globally, but also partially, taking into account a particular subset of criteria and the possible interaction between them.
