The concept of grade of membership
Fuzzy Sets and Systems - Interpretations of Grades on Membership
A utility-valued logic for decision making
International Journal of Approximate Reasoning
The uncertain reasoner's companion: a mathematical perspective
The uncertain reasoner's companion: a mathematical perspective
Comparison of rough-set and interval-set models for uncertain reasoning
Fundamenta Informaticae - Special issue: rough sets
Elements of intuitionistic fuzzy logic. Part I
Fuzzy Sets and Systems
Uncertain Reasoning with Interval-Set Algebra
RSKD '93 Proceedings of the International Workshop on Rough Sets and Knowledge Discovery: Rough Sets, Fuzzy Sets and Knowledge Discovery
A framework for linguistic modelling
Artificial Intelligence
An introduction to bipolar representations of information and preference
International Journal of Intelligent Systems
Generalised Label Semantics as a Model of Epistemic Vagueness
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Fuzzy Sets and Systems
Imprecise bipolar belief measures based on partial knowledge from agent dialogues
SUM'10 Proceedings of the 4th international conference on Scalable uncertainty management
Relating De Morgan triples with Atanassov's intuitionistic De Morgan triples via automorphisms
International Journal of Approximate Reasoning
A bipolar model of vague concepts based on random set and prototype theory
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
On truth-gaps, bipolar belief and the assertability of vague propositions
Artificial Intelligence
Conditional beliefs in a bipolar framework
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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Valuation pairs are introduced as a bipolar model of the assertability of propositions. These correspond to a pair of dual valuation functions, respectively, representing the strong property of definite assertability and the dual weaker property of acceptable assertability. In the case where there is uncertainty about the correct valuation pair for a language then a probability distribution is defined on possible valuation pairs. This results in two measures, @m^+ giving the probability that a sentence is definitely assertable, and @m^- giving the probability that a sentence is acceptable to assert. It is shown that @m^+ and @m^- can be determined directly from a two dimensional mass function m defined on pairs of sets of propositional variables. Certain natural properties of @m^+ and @m^- are easily expressed in terms of m, and in particular we introduce certain consonance or nestedness assumptions. These capture qualitative information in the form of assertability orderings for both the propositional variables and the negated propositional variables. On the basis of these consonance assumptions we show that label semantics, intuitionistic fuzzy logic and max-min fuzzy logic can all be viewed as special cases of this bipolar model. We also show that bipolar belief measures can be interpreted within an interval-set model.