Comparison Among the Three Classes

Abstract

For level-1 and level-3 results with the T 3 aggregator, \({R_{{d_1}/|A{ \cup _{{S_3}}}B|}}\) is the only R compatibility measure that performed as well as the better set-theoretic similarity measures in the majority of cases. In the ph and hp cases, the set-theoretic measures outperformed \({R_{{d_1}/|A{ \cup _{{S_3}}}B|}}\). It should be noted that \({R_{{d_1}/|A{ \cup _{{S_3}}}B|}}\) is also a set-theoretic measure since it is equivalent to \({S_{1/D_{{T_1}}^ - /{S_3}/rel}}\). Kcosθ and \({K_{bhat{t_{\bmod }}}}\) performed as well as or better (mm, mh, hh) than all the set-theoretic measures except for the ph and hp case. For these two cases, the results are comparable to the inclusion indices based on relative cardinality and the \({S_{1/D_{{T_1}}^ - /{S_3}/rel}}\) and \({S_{3/{I_{{S_1}}}/rel/{T_3}}}\) measures. \({G_{{D_*}/\operatorname{supp} }}\) and \({G_{{D_@}/\operatorname{supp} }}\) level-1 results are comparable to \({S_{3/{I_{{S_1}}}/rel/{T_3}}}\) and \({S_{3/{I_{{S_2}}}/rel/{T_3}}}\) similarity measures except for mp, mm, mh, and hp where \({S_{3/{I_{{S_1}}}/rel/{T_3}}}\) and \({S_{3/{I_{{S_2}}}/rel/{T_3}}}\) perform 10 to 20 per cent better. For level-3 results, however, these two G compatibility measures perform 10 to 20 per cent better with the precise domain knowledge base than those two similarity measures. With the high domain imprecision, they perform 10 to 20 per cent worse than those two similarity measures. When the evidential fuzzy set is the reference and the domain information is precise, L Evid/ sup is able to identify the target as well as any of the set-theoretic measures using T3. Similarly when the domain fuzzy set is the reference and the evidence is precise, L Attr/ sup is able to identify the target as well as any of the set-theoretic measures except for \({S_{3/{I_{S1}}/rel/{T_3}}},\) which performs about 20 per cent better for the mp case.