A look to independence under T-conditional possibility

The notion of conditioning is still debated for non-additive uncertainty measures. Referring to the possibilistic framework, we consider different notions of conditioning, focusing on the axiomatic definition of $T$-conditional possibility that can accommodate Dubois and Prade’s conditioning rule. A notion strictly linked to that of conditioning is independence, for which we provide a comparison with respect to the different conditioning rules. In particular, we introduce conditional independence for variables under $T$-conditional possibility, with $T$ a continuous t-norm, by taking as a significant particular case $T_DP$ -conditional possibility (obtained through Dubois and Prade’s minimum specificity principle).