The 2-Tuple Fuzzy Linguistic Representation Model

Abstract

In this chapter, we introduce one of the most representative approaches in which in the membership function does not play an important role, both theoretically and in the empirical tests. This is the fuzzy linguistic approach (also called a symbolic approach) that is based on the idea that it is possible to avoid dealing with the problems due to the arbitrariness of membership functions by not using them in the first place. This is done by going back to the very first step of fuzzy sets theory, which is to preserve the fuzziness of the empirical world using variables the values of which are “words”. This chapater starts from a brief introduction to linguistic decision analysis and the notion of linguistic variables, followed with a discussion and review on how to aggregate information that is expressed in terms of ordinal linguistic terms. This is a crucial step of the process of decision making, as we need to aggregate the various bits of “linguistic” information (that is expressed in linguistic format) on the issue at hand under the condition of fulfilling certain criteria. The main focus is given on the 2-tuple fuzzy linguistic representation model (Herrera, et al. (2000b)), which provides a better representation and computation scheme to avoid the loss of information during the normal fuzzy ordinal linguistic approach. This chapter also explicates how to model the decision-making process using linguistic 2-tuple with applications to help readers understand the 2-tuple fuzzy linguistic representation model.