# Bayesian Uncertainty Inferencing for Fault Diagnosis of Intelligent Instruments in IoT Systems
## 6 BN Model Example for IPT in an IoT Network
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**xi** & **Weighted TrIFN** & **Expected Value** & **xi** & **Weighted TrIFN** & **Expected Value** \\ \hline x1 & (0.190,0.279,0.367,0.456);(0.441,0.453) & 0.160 & x18 & (0.274,0.351,0.428,0.506);(0.550,0.360) & 0.232 \\ x2 & (0.221,0.321,0.421,0.521);(0.459,0.415) & 0.193 & x19 & (0.182,0.282,0.382,0.482);(0.448,0.446) & 0.166 \\ x3 & (0.291,0.391,0.491,0.591);(0.521,0.350) & 0.258 & x20 & (0.042,0.131,0.219,0.308);(0.280,0.651) & 0.055 \\ x4 & (0.172,0.261,0.349,0.438);(0.426,0.473) & 0.145 & x21 & (0.237,0.279,0.320,0.362);(0.490,0.439) & 0.157 \\ x5 & (0.122,0.222,0.322,0.422);(0.367,0.525) & 0.115 & x22 & (0.104,0.204,0.304,0.404);(0.352,0.547) & 0.102 \\ x6 & (0.122,0.222,0.322,0.422);(0.365,0.527) & 0.114 & x23 & (0.230,0.319,0.407,0.496);(0.440,0.423) & 0.185 \\ x7 & (0.282,0.382,0.482,0.582);(0.551,0.343) & 0.261 & x24 & (0.276,0.365,0.454,0.543);(0.503,0.371) & 0.232 \\ x8 & (0.377,0.454,0.530,0.607);(0.697,0.260) & 0.353 & x25 & (0.299,0.364,0.430,0.495);(0.629,0.332) & 0.257 \\ x9 & (0.310,0.386,0.463,0.540);(0.643,0.314) & 0.282 & x26 & (0.401,0.501,0.601,0.701);(0.654,0.247) & 0.388 \\ x10 & (0.363,0.429,0.494,0.500);(0.713,0.270) & 0.333 & x27 & (0.297,0.397,0.497,0.597);(0.600,0.312) & 0.287 \\ x11 & (0.438,0.538,0.638,0.738);(0.670,0.227) & 0.424 & x28 & (0.314,0.414,0.511,0.614);(0.580,0.313) & 0.294 \\ x12 & (0.182,0.271,0.360,0.449);(0.437,0.459) & 0.154 & x29 & (0.396,0.496,0.596,0.696);(0.640,0.255) & 0.379 \\ x13 & (0.237,0.337,0.437,0.537);(0.547,0.370) & 0.228 & x30 & (0.237,0.326,0.415,0.503);(0.532,0.390) & 0.211 \\ x14 & (0.252,0.270,0.288,0.307);(0.568,0.419) & 0.160 & x31 & (0.102,0.166,0.231,0.295);(0.305,0.603) & 0.070 \\ x15 & (0.260,0.336,0.411,0.487);(0.562,0.364) & 0.224 & x32 & (0.287,0.387,0.487,0.587);(0.572,0.334) & 0.270 \\ x16 & (0.252,0.270,0.288,0.307);(0.568,0.419) & 0.160 & x33 & (0.203,0.280,0.358,0.435);(0.448,0.447) & 0.160 \\ x17 & (0.092,0.157,0.221,0.286);(0.324,0.608) & 0.068 & & & \\ \hline \end{tabular}
\end{table} 
Table 6: Weighted TrIFN and the expected value. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**x1** & & **T** & & & & **F** & \\ \hline x2 & T & & F & T & & F \\ x3 & T & F & T & F & T & F \\ T & 0.501 & 0.328 & 0.382 & 0.167 & 0.407 & 0.201 & 0.265 & 0.010 \\ F & 0.499 & 0.672 & 0.618 & 0.833 & 0.593 & 0.799 & 0.735 & 0.990 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: CPT of node M11. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experts** & ** \begin{tabular}{c} **Aggregated** \\ **IntIFN with** \\ **Initial Weights** \\ \end{tabular}  & **Cross Entropy** & **\ \begin{tabular}{c} **Intuitionistic** \\ **Fuzzy Entropy** \\ \end{tabular}  & ** \begin{tabular}{c} **Final Expert** \\ **Weights** \\ \end{tabular}  \\ \hline E1 & (0.7631,0.1805) & 0.0570 & 0.2890 & 0.23 \\ E2 & (0.4261,0.4567) & 0.0095 & 0.9467 & 0.18 \\ E3 & (0.6292,0.3085) & 0.0077 & 0.5362 & 0.11 \\ E4 & (0.3341,0.5707) & 0.0423 & 0.6446 & 0.24 \\ E5 & (0.3463 Figure 8: BN model when IPT is in failure state. Figure 7: BN model with fault probability.