On ordering words using the centroid and Yager index of an Interval Type-2 Fuzzy Number

Comparing words where multiple people is involved on defining the meaning of every word is a common situation in different real scenarios such as decision making, natural reasoning, etc. When multiple people express their opinions about a word/lable/concept, then an Interval Type-2 Fuzzy Number can be used to represent uncertainty involved in their opinions, so an important task is how to establish an order of every word involved. To do so, we propose to use the centroid and Yager Index Rank of an Interval Type-2 fuzzy number to establish the order of different words defined by multiple people. We provide an application example and an analysis of the results including some recommendations for practical implementations of both type reduction methods.