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Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model

journal contribution
posted on 2009-12-01, 00:00 authored by Y Dong, Y Xu, Shui Yu
When using linguistic approaches to solve decision problems, we need the techniques for computing with words (CW). Together with the 2-tuple fuzzy linguistic representation models (i.e., the Herrera and Mart´ınez model and the Wang and Hao model), some computational techniques for CW are also developed. In this paper, we define the concept of numerical scale and extend the 2-tuple fuzzy linguistic representation models under the numerical scale.We find that the key of computational techniques
based on linguistic 2-tuples is to set suitable numerical scale with
the purpose of making transformations between linguistic 2-tuples
and numerical values. By defining the concept of the transitive
calibration matrix and its consistent index, this paper develops an optimization model to compute the numerical scale of the linguistic term set. The desired properties of the optimization model are also presented. Furthermore, we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations. The results in this paper are pretty helpful to complete the fuzzy 2-tuple representation models for CW.

History

Journal

I E E E transactions on fuzzy systems

Volume

17

Issue

6

Pagination

1366 - 1378

Publisher

I E E E

Location

Piscataway, NJ

ISSN

1063-6706

eISSN

1941-0034

Language

eng

Publication classification

C1 Refereed article in a scholarly journal

Copyright notice

2009, IEEE