Binary Relations and Preference Modeling

Bouyssou, Denis; Vincke, Philippe

doi:10.1002/9780470611876.ch2

Cited by 5 publications

(6 citation statements)

References 106 publications

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“…Such statements define actually binary relations, called preference relations: relations (1), (2) and (3) are defined over attribute domains, whereas (4) over the set of attributes. Preference relations are usually required to satisfy some intuitive properties like reflexivity and transitivity, that is to be preorders ( [5], [18], [31]). Note that a preference relation can be expressed over an attribute domain independently of whether the domain is naturally ordered (e.g.…”

Section: A Motivating Examplementioning

confidence: 99%

“…(a) In Section II we rely on preorders ( [5], [14], [31]) to capture preferences over attributes and their domains. By linearizing preorder domains we can then naturally induce block sequences of a preference query result.…”

Section: B Contributionsmentioning

confidence: 99%

“…In this paper we rely on partial preorders ( [5], [18], [31]) to model a preference relation. We write dƒd′ to denote that d′ is at least as preferable as d on a domain D. Thus, the symmetric part of ƒ is essentially an equivalence relation modelling the equal preference relation  (when both dƒd′ and d′ƒd hold), and the asymmetric part of ƒ is a strict partial order capturing strict preference d€d′ (when dƒd′ and ¬d′ƒd).…”

Section: Modelling User Preferencesmentioning

confidence: 99%

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Efficient Rewriting Algorithms for Preference Queries

Georgiadis

Kapantaidakis

Christophides

et al. 2008

2008 IEEE 24th International Conference on Data Engineering

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Abstract-Preference queries are crucial for various applications (e.g. digital libraries) as they allow users to discover and order data of interest in a personalized way. In this paper, we define preferences as preorders over relational attributes and their respective domains. Then, we rely on appropriate linearizations to provide a natural semantics for the block sequence answering a preference query. Moreover, we introduce two novel rewriting algorithms (called LBA and TBA) which exploit the semantics of preference expressions for constructing progressively each block of the answer. We demonstrate experimentally the scalability and performance gains of our algorithms (up to 3 orders of magnitude) for variable database and result sizes, as well as for preference expressions of variable size and structure. To the best of our knowledge, LBA and TBA are the first algorithms for evaluating efficiently arbitrary preference queries over voluminous databases. I. INTRODUCTIONWith the Web explosion, an increasing number of users access large data collections without a precise knowledge of their content, or a clearly identified search goal. Users would rather describe features of data that are potentially useful in some task, or in other words features that best suit their preferences. Modern database systems should then be able to process queries enhanced with preferences, and such queries are called preference queries. The answer to a preference query is a sequence of data blocks, where each block contains data that are more interesting (in terms of the preferences) than the data in the following block. In this way, the user can inspect the blocks one by one and stop inspection at any point at which he feels satisfied by the data already inspected. In this paper, we are interested in the efficient computation of such block sequences when data collections are modeled as relational tables and preferences as binary relations over the table attributes and their respective domains.

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Section: A Motivating Examplementioning

confidence: 99%

Section: B Contributionsmentioning

confidence: 99%

Section: Modelling User Preferencesmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Rewriting Algorithms for Preference Queries

Georgiadis

Kapantaidakis

Christophides

et al. 2008

2008 IEEE 24th International Conference on Data Engineering

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“…That is, when an MCDA method does not take into consideration the incomparability relation, the method usually allows obtaining a total order, i.e., full comparability of all alternatives in the ranking. Otherwise, a partial order is achieved, what means that there may be alternatives which cannot be compared to other ones in the obtained ranking [61].…”

mentioning

confidence: 99%

Inter-Criteria Dependencies-Based Decision Support in the Sustainable wind Energy Management

Ziemba

2019

Energies

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Decision problems related to the wind energy require considering many, often interrelated and dependent on each other, criteria. To solve such problems, decision systems based on Multi-Criteria Decision Analysis (MCDA) methods are usually used. Unfortunately, most methods assume independence between the criteria, therefore, their application in decision problems related to the wind energy is debatable. This paper presents the use of the Analytic Network Process (ANP) method to solve a decision problem consisting in selecting the location and design of a wind farm. The use of the ANP method allows capturing the complexity of the decision problem by taking into consideration dependencies between criteria. As part of the verification of the solution, the results of the ANP method were compared with those of the Analytic Hierarchy Process (AHP) method, which uses only hierarchical dependencies between criteria. The conducted verification showed that the inter-criteria dependencies may have a significant influence on the obtained solution. On the basis of the conducted sensitivity analysis and the research into robustness of the rankings to the rank reversal phenomenon, it has been found out that the ranking obtained with the use of the ANP is characterized by a higher quality than by means of the AHP.

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“…Preference modeling, field where preference relations are studied in details, is a central step for decision aiding but it is also commonly used in other domains such as artificial intelligence, economy, political sciences, psychology and sociology. Interested reader can find more details in [3,10,11,15,16,17] among many others.…”

Section: Introductionmentioning

confidence: 99%

A valued Ferrers relation for interval comparison

Öztürk

Tsoukiàs

2015

Fuzzy Sets and Systems

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The paper deals with the valued comparison of intervals for decision making. Interval orders are classical preference structures where the comparison of intervals is done in an ordinal way. In this paper we focus on valued comparison where more information, especially the distance between end-points of intervals, is used in order to have more sophisticated preference structures. The generalization of an interval order as a valued structure requires the choice of de Morgan triplets. We propose a valued outranking relation for interval comparison and show that it satisfies different definitions of valued interval orders using different de Morgan triplet. The decomposition of our outranking relation into preference and indifference provides a valued preference structure where the preference is T -transitive and monotone.

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Binary Relations and Preference Modeling

Cited by 5 publications

References 106 publications

Efficient Rewriting Algorithms for Preference Queries

Efficient Rewriting Algorithms for Preference Queries

Inter-Criteria Dependencies-Based Decision Support in the Sustainable wind Energy Management

A valued Ferrers relation for interval comparison

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