A new perspective on reasoning with fuzzy rules

Dubois, Didier; Prade, Henri; Ughetto, Laurent

doi:10.1002/int.10103

Cited by 43 publications

(13 citation statements)

References 40 publications

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“…The bipolar view can be exploited for building a typology of fuzzy if-then rules, based on multivalued implications or conjunctions, where each type of fuzzy rule serves a specific purpose. 24 It emphasizes the advantages of using conjointly implicative rules (encoding negative information) and conjunctive rules (encoding positive information) in the same rule-based system. Finally, the bipolar view is instrumental in rigorously extending the support and the confidence degrees to fuzzy association rules.…”

Section: Bipolarity and If-then Rulesmentioning

confidence: 98%

An introduction to bipolar representations of information and preference

Dubois¹,

Prade²

2008

Int. J. Intell. Syst.

219

116

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Bipolarity seems to pervade human understanding of information and preference, and bipolar representations look very useful in the development of intelligent technologies. Bipolarity refers to an explicit handling of positive and negative sides of information. Basic notions and background on bipolar representations are provided. Three forms of bipolarity are laid bare: symmetric univariate, dual bivariate, and asymmetric (or heterogeneous) bipolarity. They can be instrumental in the logical handling of incompleteness and inconsistency, rule representation and extraction, argumentation, learning, and decision analysis. C 2008 Wiley Periodicals, Inc.

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Section: Bipolarity and If-then Rulesmentioning

confidence: 98%

An introduction to bipolar representations of information and preference

Dubois¹,

Prade²

2008

Int. J. Intell. Syst.

219

116

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“…The bipolar view of information based on (δ, π) pairs sheds new light on the debate between conjunctive and implicative representation of rules [88]. Representing a rule as a material implication focuses on counterexamples to rules, while using a conjunction between antecedent and consequent points out examples of the rule and highlights its positive content.…”

Section: Basic Notions Of Possibility Theorymentioning

confidence: 99%

Possibility Theory and Its Applications: Where Do We Stand?

Dubois

Prade

2015

Springer Handbook of Computational Intelligence

148

101

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This paper provides an overview of possibility theory, emphasizing its historical roots and its recent developments. Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory can be cast either in an ordinal or in a numerical setting. Qualitative possibility theory is closely related to belief revision theory, and common-sense reasoning with exception-tainted knowledge in Artificial Intelligence. Possibilistic logic provides a rich representation setting, which enables the handling of lower bounds of possibility theory measures, while remaining close to classical logic. Qualitative possibility theory has been axiomatically justified in a decision-theoretic framework in the style of Savage, thus providing a foundation for qualitative decision theory. Quantitative possibility theory is the simplest framework for statistical reasoning with imprecise probabilities. As such it has close connections with random set theory and confidence intervals, and can provide a tool for uncertainty propagation with limited statistical or subjective information.

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“…which corresponds to the proper inference mode from what is guaranteed to be possible (see [26] for details).…”

Section: A First Dichotomy : Conjunction Vs Implicationmentioning

confidence: 99%

Rules and meta-rules in the framework of possibility theory and possibilistic logic

Dubois¹,

Prade²,

Schockaert³

2011

Scientia Iranica

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Abstract:The contribution of Lotfi Zadeh to the development of fuzzy logic, goes far beyond the introduction of the seminal concept of a fuzzy set and has multiple facets. This article, as a small tribute to the corpus of ideas, notions and results brought together over almost five decades by Zadeh, singles out and illustrates two of his most stimulating, thoughtprovoking and fruitful creations: fuzzy rules on the one hand, and possibility theory on the other hand. Indeed, the modeling of conditional statements of the form "if x is A then y is B" plays a crucial role in any attempt at formalizing human reasoning. Starting from the expression of different forms of fuzzy rules that have been identified in the setting of possibility theory, we study their counterparts in the extensions of possibilistic logic. A distinction between rules and meta-rules is especially emphasized, in the representational setting of possibility theory. It amounts to viewing rules as pieces of knowledge that contribute to the partial specification of a unique epistemic state, while meta-rules characterize constraints between specified epistemic states, as in possibilistic answer set programming.

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A new perspective on reasoning with fuzzy rules

Cited by 43 publications

References 40 publications

An introduction to bipolar representations of information and preference

An introduction to bipolar representations of information and preference

Possibility Theory and Its Applications: Where Do We Stand?

Rules and meta-rules in the framework of possibility theory and possibilistic logic

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