Sensitivity of multi-criteria decision making to linguistic quantifiers and aggregation means

Developments in Multi-Criteria (MCDM) and Multi-Expert decision-making allow for using linguistic quantifiers such as ‘all’, ‘most’, ‘at least half’ and similar terms as quantifiers for the decision. Additionally, new methods of aggregating the various opinions have been developed, giving the decision maker an increasingly large variety of options. This paper presents the concept of linguistic quantifiers and presents a collection of quantifiers with their associated weight functions. This paper explores the effect that the type of linguistic quantifier and the aggregation method used have on the ranking of alternatives. This study utilizes eleven linguistic quantifiers and four aggregation means using four well-documented MCDM problems. The results show that the effect of the linguistic quantifiers varies and some quantifiers have more impact on ranking of the alternatives then others. Additionally, the sensitivity of the decision made to the aggregation method is found to be relatively small. The study finds that the weighted harmonic mean is the most sensitive aggregation function to the changes of linguistic quantifiers. The results of this research allow the decision maker to choose the linguistic quantifier and aggregation method based on subjective belief without impeding the resulting decision.