Two integrals and some modified versions-critical remarks
Fuzzy Sets and Systems
Two families of fuzzy integrals
Fuzzy Sets and Systems
Possibility and necessity integrals
Fuzzy Sets and Systems
A first course in fuzzy logic
Measures of uncertainty in expert systems
Artificial Intelligence
Supremum preserving upper probabilities
Information Sciences: an International Journal
Fuzzy Measure Theory
Integration and Conditioning in Numerical Possibility Theory
Annals of Mathematics and Artificial Intelligence
Recent Literature Collected by Didier DUBOIS, Henri PRADE and Salvatore SESSA
Fuzzy Sets and Systems
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In this paper we analyze, mainly in a finitary setting, the consistency properties of fuzzy possibilities, interpreting them as instances of upper previsions and applying the basic notions of avoiding sure loss and coherence from the theory of imprecise probabilities. It ensues that fuzzy possibilities always avoid sure loss, but satisfy the stronger coherence condition only in a special case. Their natural extension, i.e. their least-committal correction to a coherent upper prevision, is determined. The same analysis is then performed when min is replaced in the definition of fuzzy possibility by a T-norm or, more generally, a seminorm, showing that the consistency properties and also the natural extension remain the same. Some "closure" properties are also discussed, which are guaranteed to hold if the T-seminorm is continuous, and are satisfied by (ordinary) possibilities too.