Measuring consistency of linguistic preference relations: a 2-tuple linguistic approach

A 2-tuple fuzzy linguistic representation model is used and an algorithm to improving consistency degree in linguistic preference relations is proposed, and the proof of the convergence of this algorithm is given.

Abstract

By using the 2-tuple fuzzy linguistic representation model and by proposing the concept of the individual consistency evaluations, this paper develops a 2-tuple linguistic index to measure the consistency degree of linguistic preference relations. Comparing with the existing numerical consistency indexes, the proposed linguistic index not only measures the consistency degree of linguistic preference relations via a linguistic way, but also can reflect the individual difference on consistency degree of linguistic preference relations. Further, this paper proposes an algorithm to improving consistency degree in linguistic preference relations, and the proof of the convergence of this algorithm is also given. The results in this paper provide a theoretic basis for the application of consistent linguistic preference relations in decision making problems.