We study the relationship between a notion of conjunction among conditional events, introduced in recent papers, and the notion of Frank t-norm. By examining different cases, in the setting of coherence, we show each time that the conjunction coincides with a suitable Frank t-norm. In particular, the conjunction may coincide with the Product t-norm, the Minimum t- norm, and Lukasiewicz t-norm. We show by a counterexample, that the prevision assessments obtained by Lukasiewicz t-norm may be not coherent. Then, we give some conditions of coherence when using Lukasiewicz t-norm.

Gilio, A., Sanfilippo G (2019). Triangular norms and conjunction of conditional events. In E-BOOK OF ABSTRACT: 43rd Annual Meeting of the Italian Association for Mathematics Applied to Economic and Social Sciences (AMASES) (pp. 296-296).

Triangular norms and conjunction of conditional events

Sanfilippo G
2019-01-01

Abstract

We study the relationship between a notion of conjunction among conditional events, introduced in recent papers, and the notion of Frank t-norm. By examining different cases, in the setting of coherence, we show each time that the conjunction coincides with a suitable Frank t-norm. In particular, the conjunction may coincide with the Product t-norm, the Minimum t- norm, and Lukasiewicz t-norm. We show by a counterexample, that the prevision assessments obtained by Lukasiewicz t-norm may be not coherent. Then, we give some conditions of coherence when using Lukasiewicz t-norm.
Coherence; Conditional Event; Conditional random quantity; Conjunction; Frank t-norm.
Gilio, A., Sanfilippo G (2019). Triangular norms and conjunction of conditional events. In E-BOOK OF ABSTRACT: 43rd Annual Meeting of the Italian Association for Mathematics Applied to Economic and Social Sciences (AMASES) (pp. 296-296).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/390554
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