An introduction to bipolar representations of information and preference
International Journal of Intelligent SystemsPublished 20 June 2008
Didier Dubois, Henri Prade
Citations223
SJR quartileQ1
SJR score1.14
SNIP1.40
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
Three forms of bipolarity are laid bare: symmetric univariate, dual bivariate, and asymmetric (or heterogeneous) bipolarity, which can be instrumental in the logical handling of incompleteness and inconsistency, rule representation and extraction, argumentation, learning, and decision analysis.
Abstract
International audience
Keywords
Computer ScienceDecision Sciences
Fuzzy Sets and SystemsIntuitionistic fuzzy sets
16,153 Citations1986Krassimir Atanassov
Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
Journal of Risk and UncertaintyAdvances in prospect theory: Cumulative representation of uncertainty
15,596 Citations1992Amos Tversky, Daniel Kahneman
Rough Sets: Theoretical Aspects of Reasoning about Data
8,416 Citations1991Zdzisław Pawlak
Personality and Social Psychology ReviewBeyond Bipolar Conceptualizations and Measures: The Case of Attitudes and Evaluative Space
1,246 Citations1997John T. Cacioppo, Wendi L. Gardner +1 more
Evidence is reviewed showing that the positive and negative evaluative processes underlying many attitudes are distinguishable, are characterized by distinct activation functions, are related differentially to attitude ambivalence, have distinguishable antecedents, and tend to gravitate from a bivariate toward a bipolar structure when the underlying beliefs are the target of deliberation or a guide for behavior.
Fuzzy Sets and SystemsUninorm aggregation operators
952 Citations1996Ronald R. Yager, Alexander Rybalov
A generalization of the t-norm and t-conorm called the uni-norm is defined and a class of operators called RQ-star aggregation operators which are useful for aggregations guided by imperatives such as “if most of the scores are above the identity take the Max else use the Min” are introduced.
The Journal of Socio-EconomicsRational actors or rational fools: implications of the affect heuristic for behavioral economics
560 Citations2002Paul Slovic, Melissa L. Finucane +2 more
Annals of Mathematics and Artificial IntelligencePossibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification
400 Citations2001Didier Dubois, Henri Prade
This paper clarifies a pervasive confusion between possibility theory axioms and fuzzy set basic connectives by demonstrating that any belief representation where compositionality is taken for granted is bound to at worst collapse to a Boolean truth assignment and at best to a poorly expressive tool.
European Journal of Operational ResearchBasic concepts for a theory of evaluation: The aggregative operator
211 Citations1982József Dombi
Theory of evaluation sheds new light on such well-known concepts as membership, conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications, of human decision making and of multicriteria analysis.
Data Mining and Knowledge DiscoveryA systematic approach to the assessment of fuzzy association rules
187 Citations2006Didier Dubois, Eyke Hüllermeier +1 more
This paper develops a systematic approach to the assessment of fuzzy association rules by partitioning the data stored in a database into examples of a given rule, counterexamples, and irrelevant data, and evaluation measures are derived from the cardinalities of the corresponding subsets.
Information SciencesYinYang bipolar logic and bipolar fuzzy logic
184 Citations2003Wen-Ran Zhang, Lulu Zhang
BCL1, BCLn, and BCLF are bipolar generalizations or fusions of Boolean logic, multiple valued logic, and fuzzy logic, respectively, which provides a unique representation for bipolar knowledge fusion and visualization in an equilibrium world.
Fuzzy Sets and SystemsBi-capacities—I: definition, Möbius transform and interaction
162 Citations2004Michel Grabisch, Christophe Labreuche
Journal of Logic Language and InformationKnowledge-Driven versus Data-Driven Logics
140 Citations2000Didier Dubois, Petr Hájek +1 more
The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data-driven modelling, and a bi-modal logic system is presented which handles both beliefs and observations, and for which a completeness theorem is given.
Information FusionBipolar possibility theory in preference modeling: Representation, fusion and optimal solutions
134 Citations2005Salem Benferhat, Didier Dubois +2 more
The bipolar view in preference modeling distinguishes between negative and positive preferences, which are handled separately and are combined in distinct ways, and the problem of merging multiple-agent preferences in this bipolar framework is discussed.
Logic Journal of IGPLOn Ignorance and Contradiction Considered as Truth-Values
86 Citations2007D. Dubois
A critical view of the alleged significance of Belnap four-valued logic for reasoning under inconsistent and incomplete information is provided and the critique also questions the significance of partial logic.
Discrete MathematicsThe Möbius transform on symmetric ordered structures and its application to capacities on finite sets
73 Citations2004Michel Grabisch
Considering a linearly ordered set, its symmetric version is introduced, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure close to a commutative ring.
European Journal of Operational ResearchGeneralized Choquet-like aggregation functions for handling bipolar scales
71 Citations2005Christophe Labreuche, Michel Grabisch
There is a unique aggregation operator that fits with these axioms based on the notion of {\em bi-capacity} and generalizes both the Choquet integral and the CPT model.
European Journal of Operational ResearchTwo axiomatic approaches to decision making using possibility theory
60 Citations2003Phan H. Giang, Prakash P. Shenoy
A utility theory for decision making under uncertainty that is described by possibility theory is proposed and an expected utility theorem is proved for the generalized axiomatic system based on the newly introduced concept of binary utility.
Fundamenta InformaticaeRough Sets and 3-valued Lukasiewicz Logic
55 Citations1997Mohua Banerjee
The present work establishes a relationship between the finitary fragment of this logic and 3-valued Lukasiewicz logic L3 and it is observed that there is an embedding from L3 into the modal system S 5.
International Journal of Intelligent SystemsA new perspective on reasoning with fuzzy rules
52 Citations2003D. F. DuBois, Henri Prade +1 more
The notion of an “if …, then …” rule is examined in the context of positive and negative information and a new compositional rule of inference adapted to conjunctive rules, specific to positive information, is proposed.