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). Conjunction of Conditional Events and t-Norms. In G. Kern-Isberner, Z. Ognjanovic (a cura di), Symbolic and Quantitative Approaches to Reasoning with Uncertainty 15th European Conference, ECSQARU 2019 Belgrade, Serbia, September 18–20, 2019 Proceedings (pp. 199-211) [10.1007/978-3-030-29765-7_17].
Conjunction of Conditional Events and t-Norms
Sanfilippo, Giuseppe
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
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