Table 1 Four different TRMs

\(\left [ {\begin {array}{cccc} {0.3}&{0.2}&{0.1}&{0.4}\\ {0.3}&{0.2}&{0.3}&{0.2}\\ {0.1}&{0.5}&{0.3}&{0.1}\\ {0.2}&{0.2}&{0.1}&{0.5} \end {array}} \right ]\)

\(\left [ {\begin {array}{cccc} {0.3}&{0.2}&{{{\hat {\lambda }}_{13}}}&{{{\hat {\lambda }}_{14}}}\\ {{{\hat {\lambda }}_{21}}}&{{{\hat {\lambda }}_{22}}}&{{{\hat {\lambda }}_{23}}}&{{{\hat {\lambda }}_{24}}}\\ {{{\tilde {\lambda }}_{31}}}&{{{\hat {\lambda }}_{32}}}&{{{\tilde {\lambda }}_{33}}}&{{{\hat {\lambda }}_{34}}}\\ {{{\hat {\lambda }}_{41}}}&{{{\hat {\lambda }}_{42}}}&{0.1}&{0.5} \end {array}} \right ]\)

Case 3: partly known TRM

Case4: completely unknown TRM

\( \left [ {\begin {array}{cccc} {0.3}&{0.2}&{{{\hat {\lambda }}_{13}}}&{{{\hat {\lambda }}_{14}}}\\ {{{\hat {\lambda }}_{21}}}&{{{\hat {\lambda }}_{22}}}&{0.3}&{{{\hat {\lambda }}_{24}}}\\ {{{\hat {\lambda }}_{31}}}&{{{\hat {\lambda }}_{32}}}&{{{\hat {\lambda }}_{33}}}&{{{\hat {\lambda }}_{34}}}\\ {{{\hat {\lambda }}_{41}}}&{{{\hat {\lambda }}_{42}}}&{0.1}&{0.5} \end {array}} \right ] \)

\(\left [ {\begin {array}{*{20}{c}} {{{\hat {\lambda }}_{11}}}&{{{\hat {\lambda }}_{12}}}&{{{\hat {\lambda }}_{13}}}&{{{\hat {\lambda }}_{14}}}\\ {{{\hat {\lambda }}_{21}}}&{{{\hat {\lambda }}_{22}}}&{{{\hat {\lambda }}_{23}}}&{{{\hat {\lambda }}_{24}}}\\ {{{\hat {\lambda }}_{31}}}&{{{\hat {\lambda }}_{32}}}&{{{\hat {\lambda }}_{33}}}&{{{\hat {\lambda }}_{34}}}\\ {{{\hat {\lambda }}_{41}}}&{{{\hat {\lambda }}_{42}}}&{{{\hat {\lambda }}_{43}}}&{{{\hat {\lambda }}_{44}}} \end {array}} \right ] \)