Soft consensus model for the group fuzzy AHP decision making

Abstract

The fuzzy analytic hierarchy process (AHP) is an extension to the classical AHP that enables dealing with the impreciseness and vagueness of judgments. It has been frequently used for handling complex decision making problems that demand a group rather than a single decision maker. Group decision making aggregates the judgments of individuals into a joint decision. Although consensus is the desired result in group decision making, it is difficult to achieve due to the diversity of opinions, knowledge and experiences of the decision makers. Therefore, the concept of soft consensus can be applied. We propose a new soft consensus based model for fuzzy AHP group decision making. The judgments in the model are presented as triangular fuzzy numbers. The closeness between judgments of two decision makers is measured by the individual fuzzy consensus index which in turn is based on the compatibility index from classical AHP. In each iteration, two decision makers with the most dissimilar opinions are identified and their judgments are adapted. The process is repeated until the desired consensus level is reached. The model can also take into account the weights of importance of individual decision makers. A fuzzy extension of the geometric mean method is employed for deriving fuzzy weights from a group fuzzy pairwise comparison matrix. The application of the model is provided in an example from the literature.