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The pseudo-transitivity of preference relations: Strict and weak (m, n)-Ferrers properties

JOURNAL OF MATHEMATICAL PSYCHOLOGY 2014年第1期58卷 45-54页

作者： Giarlotta, Alfio Watson, Stephen Univ Catania Dept Econ & Business I-95129 Catania Italy York Univ Dept Math & Stat Toronto ON M3J 1P3 Canada

Traditionally, a preference on a set A of alternatives is modeled by a binary relation R on A satisfying suitable axioms of pseudo-transitivity, such as the Ferrers condition (aRb and cRd imply and or cRb) or the semitransitivity property (aRb and bRc imply and or dRc). In this paper we study (m, n)-Ferrers properties, which naturally generalize these axioms by requiring that a(1)R ... Ra-m and b(1)R ... Rb-n imply a(1)Rb(n) or b(1)Ra(m). We identify two versions of (m, n)-Ferrers properties: weak, related to a reflexive relation, and strict, related to its asymmetric part. We determine the relationship between these two versions of (m, n)-Ferrers properties, which coincide whenever m + n = 4 (i.e., for the classical Ferrers condition and for semitransitivity), otherwise displaying an almost dual behavior. In fact, as m and n increase, weak (m, n)-Ferrers properties become stronger and stronger, whereas strict (m, n)-Ferrers properties become somehow weaker and weaker (despite failing to display a monotonic behavior). We give a detailed description of the finite poset of weak (m, n)-Ferrers properties, ordered by the relation of implication. This poset depicts a discrete evolution of the transitivity of a preference, starting from its absence and ending with its full satisfaction. (C) 2014 Elsevier Inc. All rights reserved.

关键词： preference modeling Transitivity Ferrers property Semitransitivity Interval order Semiorder Strong interval order Strong semiorder NaP-preference

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Discriminating thresholds as a tool to cope with imperfect knowledge in multiple criteria decision aiding: Theoretical results and practical issues

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2014年 43卷 9-20页

作者： Roy, B. Figueira, J. R. Almeida-Dias, J. Univ Paris 09 LAMSADE Paris France Univ Tecn Lisboa Inst Super Tecn CEG IST Av Rovisco Pais P-1049001 Lisbon Portugal

This paper deals with preference modeling. It concerns the concepts of discriminating thresholds as a tool to cope with the imperfect nature of knowledge in decision aiding. Such imperfect knowledge is related with the definition of each criterion as well as with the data we have to take into account. On the one hand, we shall present a useful theoretical synthesis for the analyst in his/her decision aiding activity, and, on the other hand, we shall provide some practical instructions concerning the approach to follow for assigning the values to these discriminating thresholds. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Decision aiding process preference modeling Imperfect knowledge Pseudo-criteria Multi-criteria analysis/decision support

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Ontology-Based Query Answering with Group preferences

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ACM TRANSACTIONS ON INTERNET TECHNOLOGY 2014年第4期14卷 25-25页

作者： Lukasiewicz, Thomas Martinez, Maria Vanina Simari, Gerardo I. Tifrea-Marciuska, Oana Univ Oxford Dept Comp Sci Oxford OX1 3QD England

The Web has recently been evolving into a system that is in many ways centered on social interactions and is now more and more becoming what is called the Social Semantic Web. One of the many implications of such an evolution is that the ranking of search results no longer depends solely on the structure of the interconnections amongWeb pages-instead, the social components must also come into play. In this article, we argue that such rankings can be based on ontological background knowledge and on user preferences. Another aspect that has become increasingly important in recent times is that of uncertainty management, since uncertainty can arise due to many uncontrollable factors. To combine these two aspects, we propose extensions of the Datalog+/- family of ontology languages that both allow for the management of partially ordered preferences of groups of users as well as uncertainty, which is represented via a probabilistic model. We focus on answering k-rank queries in this context, presenting different strategies to compute group preferences as an aggregation of the preferences of a collection of single users. We also study merging operators that are useful for combining the preferences of the users with those induced by the values obtained from the probabilistic model. We then provide algorithms to answer k-rank queries for DAQs (disjunctions of atomic queries) under these group preferences and uncertainty that generalizes top-k queries based on the iterative computation of classical skyline answers. We show that such DAQ answering in Datalog+/- can be done in polynomial time in the data complexity, under certain reasonable conditions, as long as query answering can also be done in polynomial time (in the data complexity) in the underlying classical ontology. Finally, we present a prototype implementation of the query answering system, as well as experimental results (on the running time of our algorithms and the quality of their results) obtained from real-wo

关键词： Theory Algorithms Design Languages Datalog plus /- knowledge representation preference modeling group preferences social semantic web social choice ranking

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Risk preference modeling with conditional average: an application to portfolio optimization

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ANNALS OF OPERATIONS RESEARCH 2009年第1期165卷 67-95页

作者： Krzemienowski, Adam Warsaw Univ Technol Inst Control & Computat Engn PL-00665 Warsaw Poland

The paper introduces a new risk measure called Conditional Average (CAVG), which was designed to cover typical attitudes towards risk for any type of distribution. It can be viewed as a generalization of Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), two commonly used risk measures. The preference structure induced by CAVG has the interpretation in Yaari's dual theory of choice under risk and relates to Tversky and Kahneman's cumulative prospect theory. The measure is based on the new stochastic ordering called dual prospect stochastic dominance, which can be considered as a dual stochastic ordering to recently developed prospect stochastic dominance. In general, CAVG translates into a nonconvex quadratic programming problem, but in the case of a finite probability space it can also be expressed as a mixed-integer program. The paper also presents the results of computational studies designed to assess the preference modeling capabilities of the measure. The experimental analysis was performed on the asset allocation problem built on historical values of S&P 500 sub-industry indexes.

关键词： preference modeling Stochastic dominance Quantile risk measures Portfolio optimization Experimental analysis

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Robust ordinal regression in preference learning and ranking

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MACHINE LEARNING 2013年第2-3期93卷 381-422页

作者： Corrente, Salvatore Greco, Salvatore Kadzinski, Milosz Slowinski, Roman Univ Catania Dept Econ & Business I-95129 Catania Italy Univ Portsmouth Portsmouth PO1 3DE Hants England Poznan Univ Tech Inst Comp Sci PL-60965 Poznan Poland Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland

Multiple Criteria Decision Aiding (MCDA) offers a diversity of approaches designed for providing the decision maker (DM) with a recommendation concerning a set of alternatives (items, actions) evaluated from multiple points of view, called criteria. This paper aims at drawing attention of the Machine Learning (ML) community upon recent advances in a representative MCDA methodology, called Robust Ordinal Regression (ROR). ROR learns by examples in order to rank a set of alternatives, thus considering a similar problem as preference Learning (ML-PL) does. However, ROR implements the interactive preference construction paradigm, which should be perceived as a mutual learning of the model and the DM. The paper clarifies the specific interpretation of the concept of preference learning adopted in ROR and MCDA, comparing it to the usual concept of preference learning considered within ML. This comparison concerns a structure of the considered problem, types of admitted preference information, a character of the employed preference models, ways of exploiting them, and techniques to arrive at a final ranking.

关键词： Robust ordinal regression Ranking preference learning Multiple criteria decision aiding Comparison preference modeling preference construction

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Scientific impact assessment cannot be fair

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JOURNAL OF INFORMETRICS 2013年第4期7卷 792-802页

作者： Gagolewski, Marek Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland Warsaw Univ Technol Fac Math & Informat Sci PL-00662 Warsaw Poland

In this paper we deal with the problem of aggregating numeric sequences of arbitrary length that represent e.g. citation records of scientists. Impact functions are the aggregation operators that express as a single number not only the quality of individual publications, but also their author's productivity. We examine some fundamental properties of these aggregation tools. It turns out that each impact function which always gives indisputable valuations must necessarily be trivial. Moreover, it is shown that for any set of citation records in which none is dominated by the other, we may construct an impact function that gives any a priori-established authors' ordering. Theoretically then, there is considerable room for manipulation in the hands of decision makers. We also discuss the differences between the impact function-based and the multicriteria decision making-based approach to scientific quality management, and study how the introduction of new properties of impact functions affects the assessment process. We argue that simple mathematical tools like the h- or g-index (as well as other bibliometric impact indices) may not necessarily be a good choice when it comes to assess scientific achievements. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Impact functions Aggregation Decision making preference modeling Hirsch's h-index Scientometrics Bibliometrics

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On-line dynamic adaptation of fuzzy preferences

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INFORMATION SCIENCES 2013年 220卷 5-21页

作者： Marin, Lucas Isern, David Moreno, Antonio Valls, Aida Univ Rovira & Virgili Dept Engn Informat & Matemat Tarragona 43007 Spain

Recommender systems are very useful in domains in which a large amount of continuous information needs to be evaluated before a decision is made. Systems that permanently interact with users need to be adapted to changes in their interests. This paper proposes an algorithm that takes advantage of the preference information implicit in the actions of the user to dynamically adapt the user profile, in which user preferences are represented as fuzzy sets. The algorithm has been tested with real data extracted from the New York Times and has shown promising results. This paper presents the adaptation algorithm and discusses the influence of its basic parameters. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Fuzzy systems preference modeling Dynamic preference adaptation

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A Multi-criteria Recommendation Method for Interval Scaled Ratings

A Multi-criteria Recommendation Method for Interval Scaled R...

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12th IEEE/WIC/ACM International Joint Conferences on Web Intelligence and Intelligent Agent Technology (WI-IAT)

作者： Mikeli, Angeliki Apostolou, Dimitris Despotis, Dimitris Univ Piraeus Piraeus 18534 Greece

ISBN: (纸本)9781479929023

An increasing number of websites, such as Trip Advisor, reflecting the multilateral nature of their products, provide visitors with the possibility to evaluate each item on more than one criterion. The rating scale used usually is represented by a lexical or symbolic scale, such as the five-star rating system. Such scales can be regarded as interval because the symbolic or lexical semantics convey information about the strength of user preferences in addition to their order. In this paper we present I-Rec, a new multi-criteria, model-based recommender system tailored to interval scale ratings, which provides improved results over similar state of the art multi-criteria methods.

关键词： Recommender Systems Multiple Criteria Decision Analysis preference modeling Linear Programming

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Priority-Based Human Resource Allocation in Business Processes

Priority-Based Human Resource Allocation in Business Process...

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11th International Conference on Service Oriented Computing (ICSOC)

作者： Cabanillas, Cristina Garcia, Jose Maria Resinas, Manuel Ruiz, David Mendling, Jan Ruiz-Cortes, Antonio Vienna Univ Econ & Business Vienna Austria Univ Innsbruck STI Innsbruck Innsbruck Austria Univ Seville Seville Spain

ISBN: (纸本)9783642450051;9783642450044

In Business Process Management Systems, human resource management typically covers two steps: resource assignment at design time and resource allocation at run time. Although concepts like role-based assignment often yield several potential performers for an activity, there is a lack of mechanisms for prioritizing them, e. g., according to their skills or current workload. In this paper, we address this research gap. More specifically, we introduce an approach to define resource preferences grounded on a validated, generic user preference model initially developed for semantic web services. Furthermore, we show an implementation of the approach demonstrating its feasibility.

关键词： preference modeling preference resolution priority-based allocation priority ranking RAL resource allocation SOUP

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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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