On the Consistency Model for GDM Using Incomplete Interval-Valued Fuzzy Preference Relations

Abstract

In this thesis work we provided a process grounded on consistency for multi- person decision making when suggestions of experts are presented in the shape of incomplete interval-valued fuzzy preference relations. The presented methodology utilizes Lukasiewicz's triangular norm in conjunction with scaling conditions to obtain the complete interval-valued fuzzy preference relations (IVFPRs) against every expert, the transitive closure formula satisfies Lukasiewicz's consistency. Consistency analysis makes us capable to find the consistency weights of decision makers. Final priority weights are allocated to the decision makers by accumulating consistency weights and predefined weights. The weighted sum of matrices of preference is then contrived as a combined consistency matrix. Procedure of normalization is then utilized to establish complementary matrices after manipulating the degrees of likelihood and the final ranking values of options or alternative(s) are also acquired. Some numerical illustrations verify the effectiveness of the presumed consistency model given in the methodology.