An introduction to bipolar representations of information and preference

Dubois, Didier; Prade, Henri

doi:10.1002/int.20297

Cited by 219 publications

(117 citation statements)

References 30 publications

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“…Indeed the behaviour of lower and upper random set neighbourhoods with regard to these laws is exactly what would be expected from two criteria, one weaker and one stronger, related in a bipolar manner as outlined in [4] , rather than being based on the notion of justifiability as is the case in intuitionistic logic. In particular, lower and upper membership functions would seem to be a special case of what Dubois and Prade [4] refer to as symmetric bivariate unipolarity, whereby judgments are made according to two distinct evaluations on unipolar scales. In the current context, we have a strong and a weak evaluation criterion where the former corresponds to definite appropriateness and the latter to possible appropriateness.…”

Section: Discussionmentioning

confidence: 56%

A Random Set and Prototype Theory Interpretation of Intuitionistic Fuzzy Sets

Lawry

2010

Communications in Computer and Information Science

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract. An interpretation of intuitionistic fuzzy sets is proposed based on random set theory and prototype theory. The extension of fuzzy labels are modelled by lower and upper random set neighbourhoods, identifying those element of the universe within an uncertain distance threshold of a set of prototypical elements. These neighbourhoods are then generalised to compound fuzzy descriptions generated as logical combinations of basic fuzzy labels. The single point coverage functions of these lower and upper random sets are then shown to generate lower and upper membership functions satisfying the min-max combination rules of interval fuzzy set theory, the latter being isomophic to intuitionistic fuzzy set theory.

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Section: Discussionmentioning

confidence: 56%

A Random Set and Prototype Theory Interpretation of Intuitionistic Fuzzy Sets

Lawry

2010

Communications in Computer and Information Science

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“…The issue of bi-polarity returned of interest in the recent years (see [94]) through different contributions where the presence of clearly distinct positive and negative reasons are considered in representing preferences and supporting decisions (see [14], [36], [37]). …”

Section: Beyond Fuzzy Setsmentioning

confidence: 99%

Preferences in artificial intelligence

Pigozzi

Tsoukiàs

Viappiani

2015

Ann Math Artif Intell

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“…Therefore, a linguistic difference value between a pair of 2-tuple linguistic values (s i , α i ) and (s m , α m ), is expressed in the linguistic comparison scale S c , whose granularity is selected according to the knowledge to interpret the difference between pairs of alternatives by using a bipolar scale 16 , due to the presence of the neutral point, separating positive differences from negatives ones. It is noteworthy that, as pointed out by Miller 32 …”

Section: Linguistic Difference Function Between 2-tuple Linguistic Vamentioning

confidence: 99%

Pure linguistic PROMETHEE I and II methods for heterogeneous MCGDM problems

Espinilla¹,

Halouani²,

Chabchoub³

2015

IJCIS

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The PROMETHEE methods basic principle is focused on a pairwise comparison of alternatives for each criterion, selecting a preference function type that often requires parameters in order to obtain a preference value. When a MCGDM problem is defined in an heterogeneous context, an adequate and common approach is to unify the involved information in linguistic values. However, for each criterion, there is a difficulty to select the specific preference function and define its parameters because they are expressed by crisp values in the unit interval, when the information involved in the problem has been unified into linguistic values. In this paper, a methodology for modeling linguistic preference functions in order to facilitate the selecting of each linguistic preference function type and the definition of its parameters is proposed, providing a more realistic definition of the criteria. Therefore, a generic linguistic preference function is proposed whose inputs and outputs are linguistic values. According to the generic linguistic preference function, six basic preference function types are extended for linguistic values. To do so, a linguistic difference function between linguistic values is defined, being its output, the input of the linguistic preference function. Furthermore, the proposed methodology is integrated in linguistic PROMETHEE I and II for heterogeneous MCGDM problems to obtain partial rankings and a full ranking of alternatives. So, the methodology provides pure linguistic PROMETHEE I and II that offer interpretability and understandability. Finally, the feasibility and applicability of pure linguistic PROMETHEE I and II are illustrated in a case study for the selection of a green supplier.

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An introduction to bipolar representations of information and preference

Cited by 219 publications

References 30 publications

A Random Set and Prototype Theory Interpretation of Intuitionistic Fuzzy Sets

A Random Set and Prototype Theory Interpretation of Intuitionistic Fuzzy Sets

Preferences in artificial intelligence

Pure linguistic PROMETHEE I and II methods for heterogeneous MCGDM problems

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