Group decision making methods of the incomplete IFPRs and IPRs

Abstract

We propose optimal priority methods on the incomplete intuitionistic fuzzy preference relation (IFPR) and the incomplete interval preference relation (IPR). The least squares method has been used previously to derive the priority vector of the fuzzy preference relation (FPR). In this paper, we generalize the least squares method to IFPR and IPR based on our proposed multiplicative consistent conditions. We also investigate the relationships between the optimal models of incomplete IFPRs, IPRs and FPRs. We also apply the same method to the case of collective judgment with complete information. We illustrate the feasibility and effectiveness of our proposed methods with three numerical examples.

Consistency-Driven Methodology to Manage Incomplete Linguistic Preference Relation: A Perspective Based on Personalized Individual Semantics

“…𝑉 𝑘 Model (10) provides a novel approach to measure the consistency of incomplete linguistic preference relations by setting the PNSs for linguistic terms. The obtained results will be used in the IPE-CDO model to make sure the optimum consistency of the incomplete linguistic preference relation will not be destroyed.…”

“…Let 𝑂𝐶𝐼(𝐿 𝑘 ) be the consistency index of the incomplete linguistic preference relation 𝐿 𝑘 obtained from Model (10). To guarantee the optimum consistency of 𝐿 𝑘 is not destroyed in the process of estimating missing values, the PNSs of the known linguistic values provided by decision maker 𝑒 𝑘 should belong to the set 𝐴𝑃𝑆, and therefore…”

“…,8) is obtained via the generation of the PNSs for the linguistic terms. As an example, we illustrate this phase with 𝐿 1 by building the consistency-driven optimization model (10) with following Eqs. ( 17)- (24).…”

“…A difficulty in dealing with preference relations in GDM problems is the missing of some of the expected preference information values [10], [15], [22], [32]. Experts may not provide all the expected preference degree between two or more alternatives because the number of alternatives is high or because lack of knowledge on some of the pairwise comparisons.…”

The analytic hierarchy process with personalized individual semantics

“…During the decision making process, preference relations (e.g. [7,28,22]) are very useful tools for decision makers to express their preferences over X .…”