Algorithms to Detect and Rectify Multiplicative and Ordinal Inconsistencies of Fuzzy Preference Relations

Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree for an FPR. For inconsistent FPRs, two algorithms devised: 1) find elements 2) detect ordinally elements. An integrated algorithm proposed improve simultaneously ordinal consistencies. Finally, some examples, comparative analysis, simulation experiments provided demonstrate effectiveness methods.