Least-square method to priority of the fuzzy preference relations with incomplete information

The priority problem of incomplete preference relations is investigated. Using the transformation relation between multiplicative preference relation and fuzzy preference relation, we develop a least-square model to obtain the collective priority vector of the incomplete preference relations presented by multiple decision makers, with the existence condition of the solution being developed. Meanwhile, we extend this model to the cases of the fuzzy preference relations with complete information presented by multiple decision makers and the fuzzy preference relation with complete information presented by one decision maker. Finally, it is illustrated by a numerical example that the method proposed is feasible and effective.