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Representing preferences using intervals

ARTIFICIAL INTELLIGENCE 2011年第7-8期175卷 1194-1222页

作者： Oeztuerk, Meltem Pirlot, Marc Tsoukias, Alexis Univ Artois CRIL CNRS F-62307 Lens France Univ Paris 09 CNRS Lamsade Paris France

In this paper we present a general framework for the comparison of intervals when preference relations have to established. The use of intervals in order to take into account imprecision and vagueness in handling preferences is well known in the literature, but a general theory on how such models behave is lacking. In the paper we generalize the concept of interval (allowing the presence of more than two points). We then introduce the structure of the framework based on the concept of relative position and component set. We provide an exhaustive study of 2-point and 3-point intervals comparison and show the way to generalize such results to n-point intervals. (C) 2010 Elsevier B.V. All rights reserved.

关键词： preference modeling Interval representation Intransitivity Thresholds

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A Conjugate Class of Utility Functions for Sequential Decision Problems

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RISK ANALYSIS 2015年第9期35卷 1611-1622页

作者： Houlding, Brett Coolen, Frank P. A. Bolger, Donnacha Univ Dublin Trinity Coll Discipline Stat Dublin 2 Ireland Univ Durham Dept Math Sci Durham England

The use of the conjugacy property for members of the exponential family of distributions is commonplace within Bayesian statistical analysis, allowing for tractable and simple solutions to problems of inference. However, despite a shared motivation, there has been little previous development of a similar property for using utility functions within a Bayesian decision analysis. As such, this article explores a class of utility functions that appear to be reasonable for modeling the preferences of a decisionmaker in many real-life situations, but that also permit a tractable and simple analysis within sequential decision problems.

关键词： Decision analysis matched updating normative choice theory preference modeling risk analysis utility theory

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modeling project preferences in multiattribute portfolio decision analysis

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期263卷 225-239页

作者： Tervonen, Tommi Liesio, Juuso Salo, Ahti Evidera London England Aalto Univ Sch Business Dept Informat & Serv Econ Espoo Finland Aalto Univ Sch Sci Dept Math & Syst Anal Syst Anal Lab Espoo Finland

When choosing a portfolio of projects with a multi-attribute weighting model, it is necessary to elicit trade-off statements about how important these attributes are relative to each other. Such statements correspond to weight constraints, and thus impact on which project portfolios are potentially optimal or non-dominated in view of the resulting set of feasible attribute weights. In this paper, we extend earlier preference elicitation approaches by allowing the decision maker to make direct statements about the selection and rejection of individual projects. We convert such project preference statements to weight information by determining the weights for which (i) the selected project is included in all potentially optimal or non-dominated portfolios, or (ii) the rejected project is not included in any potentially optimal or non-dominated portfolio. We prove that the two complementary selection rules will exclude exactly the same set of weights. However, analyses that apply the dominance structure often lead to multiple, mutually exclusive feasible weight sets, and therefore the approach based on potential optimality is more relevant for practical decision analysis. We also propose ex ante value of information measures to guide the elicitation of project preference statements, and illustrate our results by analyzing a real case on the selection of infrastructure maintenance projects. (C) 2017 The Authors. Published by Elsevier B.V.

关键词： Multiple criteria analysis Project portfolio selection Multi-attribute value theory preference modeling

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A METHOD FOR ESTIMATING FOREST LANDOWNERS LANDSCAPE preferenceS

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SCANDINAVIAN JOURNAL OF FOREST RESEARCH 1993年第3期8卷 408-417页

作者： KANGAS, J LAASONEN, L PUKKALA, T UNIV JOENSUU FAC FORESTRYSF-80101 JOENSUUFINLAND

A simple and usubtle method is presented for estimating the landscape preferences of a private non-industrial forest landowner. Scenic beauties of forest landscapes were compared pairwise: verbal comparisons were converted into numerical values using the same techniques as applied in the Analytic Hierarchy Process. Using the eigenvalue method and a scaling method, scenic beauty indices for forest stands, expressed on a ratio scale, were computed. Regression models that predict the scenic beauty of forest stands according to the preferences of the person in question were estimated, using mensurational forest stand parameters as predictors. Encouraging results on the applicability of the method were obtained in practical tests: the method proved to be worth developing further.

关键词： FOREST MANAGEMENT PLANNING LANDSCAPE modeling preference modeling SCENIC BEAUTY AMENITY VALUES

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A Structured Approach for Rapidly Mapping Multilevel System Measures via Simulation Metamodeling

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SYSTEMS ENGINEERING 2015年第1期18卷 87-101页

作者： Rosen, Scott L. Saunders, Christopher P. Guharay, Samar K. Mitre Corp Mclean VA 22102 USA

With increasing complexity of real-world systems, especially for continuously evolving scenarios, systems analysts encounter a major challenge with the modeling techniques that capture detailed system characteristics defining input-output relationships. The models become very complex and require long time of execution. In this situation, techniques to construct approximations of the simulation model by metamodeling alleviate long run times and the need for large computational resources;it also provides a means to aggregate a simulation's multiple outputs of interest and derives a single decision-making metric. The method described here leverages simulation metamodeling to map the three basic SE metrics, namely, measures of performance to measures of effectiveness to a single figure of merit. This enables using metamodels to map multilevel system measures supports rapid decision making. The results from a case study demonstrate the merit of the method. Several metamodeling techniques are compared and bootstrap error analysis and predicted residual sums of squares statistic are discussed to evaluate the standard error and error due to bias.

关键词： quantitative systems engineering simulation metamodeling preference modeling

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Multiple Criteria Hierarchy Process in Robust Ordinal Regression

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DECISION SUPPORT SYSTEMS 2012年第3期53卷 660-674页

作者： Corrente, Salvatore Greco, Salvatore Slowinski, Roman Poznan Univ Tech Inst Comp Sci PL-60965 Poznan Poland Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland Univ Catania Dept Econ & Business I-95129 Catania Italy

A great majority of methods designed for Multiple Criteria Decision Aiding (MCDA) assume that all evaluation criteria are considered at the same level, however, it is often the case that a practical application is imposing a hierarchical structure of criteria. The hierarchy helps decomposing complex decision making problems into smaller and manageable subtasks, and thus, it is very attractive for users. To handle the hierarchy of criteria in MCDA, we propose a methodology called Multiple Criteria Hierarchy Process (MCHP) which permits consideration of preference relations with respect to a subset of criteria at any level of the hierarchy. MCHP can be applied to any MCDA method. In this paper, we apply MCHP to Robust Ordinal Regression (ROR) being a family of MCDA methods that takes into account all sets of parameters of an assumed preference model, which are compatible with preference information elicited by a Decision Maker (DM). As a result of ROR, one gets necessary and possible preference relations in the set of alternatives, which hold for all compatible sets of parameters or for at least one compatible set of parameters, respectively. Applying MCHP to ROR one gets to know not only necessary and possible preference relations with respect to the whole set of criteria, but also necessary and possible preference relations related to subsets of criteria at different levels of the hierarchy. We also show how MCHP can be extended to handle group decision and interactions among criteria. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Multiple Criteria Decision Aiding Hierarchy of criteria Multiple Criteria Hierarchy Process Robust Ordinal Regression preference modeling

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Self-dual operators and a general framework for weighted nilpotent operators

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2017年 81卷 115-127页

作者： Dombi, J. Csiszar, O. Univ Szeged Inst Informat Szeged Hungary Obuda Univ Inst Appl Math Budapest Hungary

The main purpose of this paper is to consider generated nilpotent operators in an integrative frame and to examine the nilpotent aggregative operator. As a starting point, instead of associativity, we focus on the necessary and sufficient condition of the self dual property. A parametric form of the generated operator o(nu) is given by using a shifting transformation of the generator function. The parameter has an important semantical meaning as a threshold of expectancy (decision level). Nilpotent conjunctive, disjunctive, aggregative and negation operators can be obtained by changing the parameter value. The properties (De Morgan property, commutativity, self-duality, fulfillment of the boundary conditions, bisymmetry) of the weighted general operator are examined and the formula of the commutative self-dual generated operator, the so-called weighted aggregative operator is given. It is proved that the two-variable operator with weights w(1) = w(2) = 1 (SIC)i is conjunctive for low input values, disjunctive for high ones, and averaging otherwise;i.e. a high input can compensate for a lower one. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Nilpotent operators Bounded system Aggregative operator Weighted aggregation Uninorm preference modeling

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Identifying non-additive multi-attribute value functions based on uncertain indifference statements

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2019年 85卷 49-67页

作者： Haag, Fridolin Lienert, Judit Schuwirth, Nele Reichert, Peter Eawag Swiss Fed Inst Aquat Sci & Technol Uberlandstr 133 CH-8600 Dubendorf Switzerland Swiss Fed Inst Technol Inst Biogeochem & Pollutant Dynam Univ Str 16 CH-8092 Zurich Switzerland

Multi-criteria decision analysis (MCDA) requires an accurate representation of the preferences of decision makers, for instance in the form of a multi-attribute value function. Typically, additivity or other stringent assumptions about the preferences are made to facilitate elicitation by assuming a simple parametric form. When relaxing such assumptions, parameters cannot be elicited easily with standard methods. We present a novel approach for identifying multi-attribute value functions which can have any shape. As preference information indifference statements are used that can be elicited by trade-off questions. Instead of asking one indifference statement for each pair of attributes, we ask for multiple trade-offs at different points in the attribute space. This allows inferring parameters of complex value functions despite the simplicity of the preference statements. Parameters are estimated by taking into account preference and elicitation uncertainty with a probabilistic model. Statistical inference supports identifying the most adequate preference model out of several candidate models through quantifying the uncertainty and assessing the need for non-additivity. The approach is elaborated for determining value functions by hierarchical aggregation. We apply it to an assessment of the ecological state of rivers, which is used to support environmental management decisions in Switzerland. preference models of four experts were quantified, confirming the feasibility of the approach and the relevance of considering non-additive functions. The method suggests a promising direction for improving the representation of preferences. (C) 2018 The Authors. Published by Elsevier Ltd.

关键词： decision making/process preference modeling multi-attribute value theory uncertainty aggregation environmental assessment

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SYNTHETIC DESCRIPTION OF A SEMIORDER

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DISCRETE APPLIED MATHEMATICS 1991年第3期31卷 299-308页

作者： PIRLOT, M UNIV LIBRE BRUXELLES B-1050 BRUSSELSBELGIUM

Recently, in studying minimal representations of semiorders, we introduced a substructure of "noses" and "hollows" essentially describing the frontier between 0's and 1's in the incidence step matrix of a semiorder. We show that the "noses" and "hollows" provide a synthetic description of a semiorder that they determine completely. The results have computational implications.

关键词： SEMIORDER preference modeling NUMERICAL REPRESENTATION VALUED GRAPH

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Interactive and nonparametric modeling of preferences on an ordinal scale using small data

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EXPERT SYSTEMS WITH APPLICATIONS 2016年 65卷 345-360页

作者： Eriskin, Levent Koksal, Gulser Middle East Tech Univ Dept Ind Engn TR-06800 Ankara Turkey

In this study, we consider learning preference structure of a Decision Maker (DM). Many preference modeling problems in a variety of fields such as marketing, quality control and economics involve possibly interacting criteria, and an ordinal scale is used to express preference of objects. In these cases, typically underlying preference structure of the DM and distribution of criteria values are not known, and only a few data can be collected about the preferences of the DM. For developing a preference model under such circumstances, we propose using nonparametric Statistical Learning approaches interactively. In particular, we employ Active Learning by asking a preference question to the DM at each step and try to reach a close approximation to the correct model in a small number of steps. Our experimental analysis proves that the proposed approach outperforms a "naive" approach where subsequent questions are asked randomly. In the study, we also provide algorithmic recommendations for modeling different underlying value functions, if information is available about the form of the preference structure and/or distribution of criteria values. This study can be regarded as a pioneering approach considering that Statistical Learning based approaches in the literature have been developed and tested based on a relatively large preference information and they do not interact with the DM in model developing process while Multi Criteria Decision Aid based approaches typically ignore interactions among the criteria, suffer from generalization ability, and have no concern about predicting equally good everywhere in the criteria domain. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： preference modeling Sorting Active learning Interactive approach Multi criteria decision aid

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