Obtaining the consensus and inconsistency among a set of assertions on a qualitative attribute

The centroid or consensus of a set of objects with qualitative attributes

“…Thus, if for some reason we discard observation d(perhaps because it is the greatest outlier (Guzman-Arenas & Jimenez, 2010), the ''most far away" report), we have, for bag {a, b, c, e}: the total confusion when a is used as candidate for the consensus of {a, b, c, e} is 0 + 0.3 + 0.167 + 0.3 = 0.767; when using b, it is 0.633 + 0 + 0.567 + 0 = 1.2; using c is used as candidate, the total confusion is 0.233 + 0.3 + 0 + 0.3 = 0.833. Finally, using e, it is 0.633 + 0 + 0.567 + 0 = 1.2.…”

“…The inconsistencyof a bag of values is reported elsewhere (Guzman-Arenas & Jimenez, 2010); this section is placed here for completeness, in order to understand Section 2.…”

“…It is not symmetric: conf(r, s) -conf(s, r), in general. The function conf is not a distance function, but it obeys the triangle inequality (Guzman-Arenas & Jimenez, 2010).…”

“…A recent paper (Guzman-Arenas & Jimenez, 2010) finds the centroid or most likely value of a bag of qualitative values, such as {Afghanistan; Beirut; Iraq; Kabul; Middle East; Afghanistan; Syria}.…”

“…The inconsistency r and centroid r* of a collection of values, as well as their theoretical properties, comparisons with similar measures and uses, are dealt elsewhere (Guzman-Arenas & Jimenez, 2010); for that reason, we only list here a short list of their properties.…”