Consistency of hesitant fuzzy linguistic preference relations: An interval consistency index

Abstract

The study of hesitant consistency is very important in decision-making with hesitant fuzzy linguistic preference relations (HFLPRs), and generally the normalization method is used as a tool to measure the consistency degree of a HFLPR. In this paper we propose a new hes- itant consistency measure, called interval consistency index, to estimate the consistency range of a HFLPR. The underlying idea of the interval consistency index consists of measur- ing the worst consistency index and the best consistency index of a HFLPR. Furthermore, by comparative study, a connection is shown between the interval consistency index and the normalization method, demonstrating that the normalization method should be con- sidered as an approximate average consistency index of a HFLPR.