Extending relational algebra to handle bipolarity

Bosc, Patrick; Pivert, Olivier; Mokhtari, Amine; Liétard, Ludovic

doi:10.1145/1774088.1774456

Cited by 36 publications

(43 citation statements)

References 9 publications

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“…2) 'Or Else': The expression 'c 1 or else c 2 ' is used to express a strong, non symmetric disjunction in the sense that c 2 is considered at a less important level as c 1 and therefore is not a full alternative for c 1 . From a slightly different perspective c 1 can be considered as the most demanding criterion which preferably has to be satisfied, but if this is not possible, c 2 is still considered as an acceptable alternative.…”

Section: ) 'And If Possible'mentioning

confidence: 99%

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Bipolarity and Multipolarity in Aggregation Structures

Tré

Dujmović

Zadrożny

2016

Studies in Fuzziness and Soft Computing

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Abstract-In recent years, there has been an increasing interest in handling (heterogeneous) bipolarity in order to deal more adequately with user preferences in information management. Different approaches have been presented. With respect to criteria specification in either flexible database querying or decision support, a main distinction can be made between bipolarity that is specified inside a single criterion and bipolarity that is specified among multiple criteria. Consider criteria that are defined over the values of a given domain. With bipolarity inside a criterion specification, a user might for example state which domain values she likes (positive pole) and which domain values she doesn't like (negative pole). Herewith, both poles do not have to be the complement of each other. With bipolarity among multiple criteria, in general two poles of criteria are given different semantics and handled in a different way. In this paper we survey different forms of bipolarity among multiple criteria from the standpoint of aggregation and try to classify them into two groups: bipolarity based on positive (desirable) and negative (undesirable) criteria and bipolarity based on nonuniform inputdependent annihilators. Moreover, we present canonical forms of aggregators of the two groups.

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Section: ) 'And If Possible'mentioning

confidence: 99%

“…This approach is used amongst others by Dubois and Prade [4], [5] and by Liétard et al [1], [12]- [14], [18].…”

Section: Introductionmentioning

confidence: 99%

Bipolarity and Multipolarity in Aggregation Structures

Tré

Dujmović

Zadrożny

2016

Studies in Fuzziness and Soft Computing

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“…Based on the lexicographical order, the lmin and lmax operators [10,6] are introduced in order to define the conjunction (resp. intersection) and the disjunction (resp.…”

Section: Fuzzy Bipolar Conditionsmentioning

confidence: 99%

“…In order to define a bipolar relational algebra, the algebraic operators (selection, projection, join, union, intersection) have been extended to fuzzy bipolar conditions [11,6]. These operators allow the expression of fuzzy bipolar queries over fuzzy bipolar relations.…”

Section: Introductionmentioning

confidence: 99%

Bipolarity and the relational division

Tamani¹,

Liétard²,

Rocacher³

2011

Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011)

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A fuzzy bipolar relation is a relation defined by a fuzzy bipolar condition, which could be interpreted as an association of a constraint and a wish. In this context, the extension of the relational division operation to bipolarity is studied in this paper. Firstly, we define a bipolar division when the involved relations are crisp. Then, we define, from the semantic point of view, several forms of bipolar division when the involved relations are defined by fuzzy bipolar conditions. These forms of division can be related to the general model of fuzzy bipolar division introduced in [4,5].

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“…On the one hand, the constraint-wish (or mandatory-desired) approach will be presented, used amongst others by Dubois and Prade [16,17] and Bosc et al [10,26,27,29,39], and on the other hand, the satisfied-dissatisfied (or positivenegative) approach will be discussed, used amongst others by Zadrożny et al [47] and De Tré et al [13,30,33]. For both approaches, an overview is given, which consecutively handles the semantics of the actual framework, the evaluation of query conditions within this framework, the ranking of query results and the aggregation of compound query conditions.…”

Section: Introductionmentioning

confidence: 99%

Constraint-Wish and Satisfied-Dissatisfied: An Overview of Two Approaches for Dealing with Bipolar Querying

Matthé

Nielandt

Zadrożny

et al. 2013

Flexible Approaches in Data, Information and Knowledge Management

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In recent years, there has been an increasing interest in dealing with user preferences in flexible database querying, expressing both positive and negative information in a heterogeneous way. This is what is usually referred to as bipolar database querying. Different frameworks have been introduced to deal with such bipolarity. In this chapter, an overview of two approaches is given. The first approach is based on mandatory and desired requirements. Hereby the complement of a mandatory requirement can be considered as a specification of what is not desired at all. So, mandatory requirements indirectly contribute to negative information (expressing what the user does not want to retrieve), whereas desired requirements can be seen as positive information (expressing what the user prefers to retrieve). The second approach is directly based on positive requirements (expressing what the user wants to retrieve), and negative requirements (expressing what the user does not want to retrieve). Both approaches use pairs of satisfaction degrees as the underlying framework but have different semantics, and thus also different operators for criteria evaluation, ranking, aggregation, etc.

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Extending relational algebra to handle bipolarity

Cited by 36 publications

References 9 publications

Bipolarity and Multipolarity in Aggregation Structures

Bipolarity and Multipolarity in Aggregation Structures

Bipolarity and the relational division

Constraint-Wish and Satisfied-Dissatisfied: An Overview of Two Approaches for Dealing with Bipolar Querying

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