Dempster–Shafer Fusion of Evidential Pairwise Markov Chains

Fire Safety Evaluation for Scenic Spots: An Evidential Best-Worst Method

“…DSET has two unique characteristics: one is to assign belief values to multi-subset propositions and the other is to fuse bodies of evidence. However, DSET still has some unresolved issues, like conflict management [36][37][38][39], dependence evidence combination [40][41][42], and belief entropy [43][44][45]. Considering its superiority under uncertain environment and its practicability in engineering [46][47][48], DSET has a broad application in many areas, such as risk assessment [49][50][51][52], fault diagnosis [53][54][55], and classification and clustering [56][57][58].…”

Non-stationary data segmentation with hidden evidential semi-Markov chains

“…evidential semi-Markov chain" (HESMC) simultaneously extends HEMCs [41], [44] and HSMCs [13], [16]. As HEMCs and HSMCs showed their interest, our aim is thus to study whether the proposed new model can still simultaneously improve the efficiency of both of them.…”

“…We can still model such situations with a triplet (𝑋 𝑁 , 𝑈 𝑁 , 𝑌 𝑁 ) as above; however, for 𝑈 𝑁 taking its values in a continuous set like ℝ, analytical estimation of (𝑥 𝑁 , 𝑢 𝑁 ) from 𝑦 𝑁 is no longer computable in general. As recalled in subsection 2.4 below, one can deal with such situations using the so-called "hidden evidential Markov chains", see [41] and references therein. On the contrary to the switching non-stationarity above, interpreting 𝑈 𝑁 is not immediate, and the reason why it allows improving non-stationary HMC segmentation is not clearly established.…”

“…It is based on "plausibility" notion that can be seen, in some sense, as extension of probability. TE can be used in a Markovian context [38], [39], and in some situations introducing TE in the Markov chain framework results in a TMC, which turns out to be particularly interesting when dealing with non-stationary data [40] , [41], [42]. We call the related model "hidden evidential Markov chain" (HEMC).…”

“…The deep reasons of the interest of these evidential models are not easy to understand and there is no theoretical results, at our knowledge, until now. There is only a partial result obtained in the simple case of independent variables given in [41], that we recall in paragraph 2.4.…”