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Random fuzzy multi-objective linear programming: Optimization of possibilistic value at risk (pVaR)

EXPERT SYSTEMS WITH APPLICATIONS 2013年第2期40卷 563-574页

作者： Katagiri, Hideki Uno, Takeshi Kato, Kosuke Tsuda, Hiroshi Tsubaki, Hiroe Hiroshima Univ Fac Engn Higashihiroshima Hiroshima 7398527 Japan Univ Tokushima Inst Socioarts & Sci Tokushima 7708502 Japan Hiroshima Inst Technol Fac Appl Informat Sci Saeki Ku Hiroshima 7315193 Japan Doshisya Univ Fac Sci & Engn Kyotanabe 6100394 Japan Inst Stat Math Dept Data Sci Tachikawa Tokyo 1908562 Japan

This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are transformed into deterministic problems. An interactive algorithm is presented to derive a satisficing solution for a decision maker (DM) from among a set of Pareto optimal solutions. Each Pareto optimal solution that is a candidate of the satisficing solution is exactly obtained by using convex programming techniques. A simple numerical example is provided to show the applicability of the proposed methodology to real-world problems with multiple objectives in uncertain environments. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Multiobjective linear programming Random fuzzy variable Possibility Necessity Possibilistic value at risk (pVaR) Pareto optimal solution interactive algorithm

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Solution approaches for equitable multiobjective integer programming problems

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ANNALS OF OPERATIONS RESEARCH 2022年第2期311卷 967-995页

作者： Bashir, Bashir Karsu, Ozlem Bilkent Univ Dept Ind Engn Ankara Turkey

We consider multi-objective optimization problems where the decision maker (DM) has equity concerns. We assume that the preference model of the DM satisfies properties related to inequity-aversion, hence we focus on finding nondominated solutions in line with the properties of inequity-averse preferences, namely the equitably nondominated solutions. We discuss two algorithms for finding good subsets of equitably nondominated solutions. The first approach is an extension of an interactive approach developed for finding the most preferred nondominated solution when the utility function is assumed to be quasiconcave. We find the most preferred equitably nondominated solution when the utility function is assumed to be symmetric quasiconcave. In the second approach we generate an evenly distributed subset of the set of equitably nondominated solutions to be considered further by the DM. We show the computational feasibility of the two algorithms on equitable multi-objective knapsack problem, in which projects in different categories are to be funded subject to a limited budget. We perform experiments to show and discuss the performances of the algorithms.

关键词： Equitable preferences Equitable efficiency Equitable dominance Generalized Lorenz dominance Multi-objective knapsack problem Convex cones Fairness Multiobjective integer programming interactive algorithm

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A decomposition based minimax regret approach for inverse multiple criteria sorting problem

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4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 2023年第1期21卷 125-149页

作者： Ozpeynirci, Ozgur Ozpeynirci, Selin Mousseau, Vincent Izmir Univ Econ Dept Logist Management Izmir Turkey Univ Paris Saclay Cent Supelec MICS Math & Informat Complex Syst Gif Sur Yvette France Izmir Univ Econ Ind Engn Dept Izmir Turkey

Multiple criteria sorting problem aims to assign objects evaluated on multiple criteria to ordered classes. In inverse multiple criteria sorting problem, the class assignments of objects are known and the decision maker can manipulate the scores of objects on criteria by implementing actions. Selected actions enable the improvement of objects' final classification. As the decision maker chooses to implement more actions, better classifications may be obtained. The contribution of this paper is under two-folds. First, we decompose inverse multiple criteria sorting problem into two phases, where phase one is a pre-process that computes the minimum cost required for each feasible object-class pair considering the underlying sorting model. Phase two interacts with the decision maker to analyze the classification and budget related trade-offs, through an assignment model generated with the outputs of phase one. The second contribution is using a modified version of a regret-based approach available in the literature. This modification includes a tighter formulation of the regret model, and an interactive solution approach using a mixed integer program for computing the minimax regret value rather than a branch-and-bound approach. We present an example instance to illustrate the developed ideas and conduct computational tests on randomly generated instances. The simultaneous use of the decomposition approach, tighter formulation and the interactive algorithm reduces the computation time significantly.

关键词： Inverse multiple criteria sorting Minimax regret interactive algorithm

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AN algorithm FOR SELECTING MAIN POINTS ON A LINE

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COMPUTERS & GEOSCIENCES 1982年第1期8卷 3-10页

作者： DETTORI, G FALCIDIENO, B Istituto per la Matematica Applicata del C.N.R. Via L. B. Alberti 4 16132 Genova Italy

We describe a new method for selecting the main points in a set of points which describe a line based on an assigned tolerance. This method is precise, fast and local. We also present a FORTRAN implementation of the a... 详细信息

关键词： interactive algorithm Data processing Point selection Automated cartography Plotting

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Group decision making based on consistency and consensus analysis of dual multiplicative linguistic preference relations

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INFORMATION SCIENCES 2021年 572卷 590-610页

作者： Meng, Fanyong Chen, Shyi-Ming Fu, Linxian Nanjing Univ Informat Sci & Technol Sch Management Sci & Engn Nanjing 210044 Peoples R China Natl Taiwan Univ Sci & Technol Dept Comp Sci & Informat Engn Taipei Taiwan Cent South Univ Sch Business Changsha 410083 Peoples R China

This paper proposes a new group decision making (GDM) method based on the consistency and the consensus analysis of dual multiplicative linguistic preference relations (DMLPRs). A new type of linguistic variables, called dual multiplicative linguistic variables (DMLVs), is presented, which is defined on the multiplicative linguistic scale. DMLVs are used to rep-resent asymmetrical qualitative hesitancy judgments of decision makers (DMs). A maximum-consistency-based interactive algorithm to derive multiplicative linguistic intu-itionistic preference relations (MLIPRs) is presented, by which the consistency concept for DMLPRs is obtained. Then, we define the concept of inconsistent DMLPRs and propose an optimal-model-based method for deriving consistent DMLPRs. Furthermore, incomplete DMLPRs also can be dealt with by the proposed maximum-consistency-based interactive algorithm. For GDM, the weights of DMs are determined by the cosine-based correlation coefficient between individual DMLPRs. Moreover, we propose a consensus measure to cal-culate the agreement degree of DMLPRs and build an optimal model to increase the con -sensus level of individual DMLPRs. Finally, a new GDM method (call algorithm III) is offered and an application example is used to illustrate the proposed GDM method. The proposed GDM method outperforms the former GDM methods for GDM in the environ-ments of DMLPRs. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Decision analysis Dual multiplicative linguistic variable Preference relation interactive algorithm Consistency and consensus

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An interactive Satisficing Method for Multiobjective Random Fuzzy Programming Problems through the Possibility-Based Probability Model

An Interactive Satisficing Method for Multiobjective Random ...

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IEEE International Conference on Fuzzy Systems (FUZZ 2011)

作者： Katagiri, Hideki Sakawa, Masatoshi Matsui, Takeshi Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

ISBN: (纸本)9781424473175

This paper considers multiobjective linear programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. A new decision making model is proposed in order to maximize both of possibility and probability with respect to the objective function values. An interactive algorithm is constructed to obtain a satisficing solution for a decision maker from among a set of Pareto optimal solutions.

关键词： random fuzzy variable multiobjective programming interactive algorithm possibility measure probability maximization

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interactive Multiobjective Random Fuzzy Programming Problems through the Possibility-Based Fractile Model

Interactive Multiobjective Random Fuzzy Programming Problems...

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IEEE International Conference on Systems, Man and Cybernetics (SMC)

作者： Katagiri, Hideki Sakawa, Masatoshi Matsui, Takeshi Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

ISBN: (纸本)9781457706530

This paper considers multiobjective linear programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. A new decision making model is proposed by incorporating the concept of fractile optimization into a possibilistic programming model in order to maximize both of possibility and probability with respect to the objective function values. An interactive algorithm is constructed to obtain a satisficing solution for a decision maker from among a set of Pareto optimal solutions.

关键词： random fuzzy variable multiobjective programming interactive algorithm possibility measure fractile criterion optimization

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An interactive approach for inverse multiple criteria sorting problem

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JOURNAL OF MULTI-CRITERIA DECISION ANALYSIS 2021年第3-4期28卷 160-169页

作者： Ozpeynirci, Ozgur Ozpeynirci, Selin Mousseau, Vincent Izmir Univ Econ Dept Logist Management Izmir Turkey Univ Paris Saclay MICS CentraleSupelec Mathemat & Informat Complexite Syst Gif Sur Yvette France Izmir Univ Econ Dept Ind Engn Izmir Turkey

Multiple criteria sorting is the problem of assigning objects that are evaluated on multiple criteria to ordered classes. In inverse multiple criteria sorting problem, the assignment of objects to classes is known. The decision maker (DM) can implement actions to improve the scores of objects on criteria, thus enabling the assignment of objects to better classes. In inverse multiple criteria sorting problems, two types of questions arise: (1) What is the set of actions that will result in the desired classification with minimum cost? and 2) What is the set of actions to obtain the best classification without exceeding a predetermined budget? There exist two versions for each question: (i) Simple version, where the parameters of the sorting method are known and (ii) Robust version, where the parameters are not fully known. In this article, we focus on the case where the DM does not provide any budget limitation or desired classifications a priori. By implementing more actions, that is, by spending more money, better classifications may be obtained. We aim to analyse the trade-off between cost and classification, and determine the set of actions that will result in the most preferred cost-classification compromise by the DM. We develop an approach that proceeds interactively with the DM, and determines such most preferred set of actions. The developed approach assumes the simple version and uses MR-Sort as sorting model. We provide a detailed illustrative example on a real life problem and present the progress of the interactive algorithm.

关键词： interactive algorithm inverse multiple criteria sorting MR-Sort multiple criteria sorting

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A Hybrid algorithm for Learning Causal Networks using Uncertain Experts' Knowledge 11

A Hybrid Algorithm for Learning Causal Networks using Uncert...

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International Conference on Probabilistic Graphical Models

作者： Gonzales, Christophe Journe, Axel Mabrouk, Ahmed Univ Toulon & Var Aix Marseille Univ LIS CNRS Marseille France CSAI Engie Lab Stains France

Bayesian networks (BN) have become one of the most popular frameworks in causal studies. The causal relations between variables are encoded by the structure of the model, which is a directed acyclic graph (DAG). Unfortunately, despite the significant advances in algorithm development, learning the causal structure from data remains a very challenging task, especially for cases with a large number of variables. When the learning algorithm fails to identify the causal orientation of some edges, the human expert can provide some rough guidelines to complete the causal discovery. In many application domains, the expert knowledge might be uncertain about the right orientation of the edge. Worst, it may contradict the orientations learned from observational data, hence leading to conflicting situations. This paper presents a new hybrid algorithm combining a constraint-based approach with a greedy search, that includes specific rules to cope with uncertain domain/expert knowledge at different steps of the learning process. Experiments show the robustness of our method compared to other state-of-the-art algorithms.

关键词： Causal Bayesian Network Expert's Knowledge Constraint-Based algorithm Score-Based algorithm Uncertainty interactive algorithm

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Discovering and leveraging communities in dark multi-layered networks for network disruption 10

Discovering and leveraging communities in dark multi-layered...

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IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM)

作者： Miller, Ryan Gera, Ralucca Saxena, Akrati Chakraborty, Tanmoy Naval Postgrad Sch Dept Appl Math Monterey CA 93943 USA Indian Inst Technol Dept CSE Ropar India IIIT Delhi Dept CSE New Delhi India

ISBN: (纸本)9781538660515

In this paper we introduce a methodology to identify communities in dark multilayered networks, taking into account that the main challenges of these networks are incompleteness, fuzzy boundaries, and dynamic behavior. To account for these characteristics, we create knowledge sharing communities (KSC) that determine the community detection. KSC is driven by weighing the edge attributes as desired for the application that the communities are used. We provide an interactive algorithm that allows the operator to decide on the weights and the thresholds applied to create the communities. By choosing these variables, our results quantitatively outperform community detection on the collapsed monoplex network.

关键词： community detection multi-layered network dark networks interactive algorithm

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