Dempster-Shafer fusion in triplet partially Markov chains

Hidden Markov Chains (HMC), Pairwise Markov Chains (PMC), and Triplet Markov Chains (TMC), allow one to estimate a hidden process X from an observed process Y. More recently, TMC have been generalized to Triplet Partially Markov chain (TPMC), where the estimation of X from Y remains workable. Otherwise, when introducing a Dempster-Shafer mass function instead of prior Markov distribution in classical HMC, the result of its Dempster-Shafer fusion with a distribution provided Y = y, which generalizes the posterior distribution of X, is a TMC. The aim of this Note is to generalize the latter result replacing HMC with multisensor TPMC.