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Finitely maxitive \(T\)-conditional possibility theory: coherence and extension. (English) Zbl 1352.68241
Summary: Starting from the axiomatic definition of finitely maxitive \(T\)-conditional possibility (where \(T\) is a continuous triangular norm), the paper aims at a comprehensive and self-contained treatment of coherence and extension of a possibilistic assessment defined on an arbitrary set of conditional events. Coherence (or consistence with a \(T\)-conditional possibility) is characterized either in terms of existence of a linearly ordered class of finitely maxitive possibility measures (\(T\)-nested class) agreeing with the assessment, or in terms of solvability of a finite sequence of nonlinear systems for every finite subfamily of conditional events. Coherence reveals to be a necessary and sufficient condition for the extendibility of an assessment to any superset of conditional events and, in the case of \(T\) equal to the minimum or a strict t-norm, the set of coherent values for the possibility of a new conditional event can be computed solving two optimization problems over a finite sequence of nonlinear systems for every finite subfamily of conditional events.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
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