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

  • Authors:

  • Yucheng Dong;Yinfeng Xu;Shui Yu

  • Affiliations:

  • Department of Organization and Management, Management School, Xi'an Jiaotong University, Xi'an, China;Department of Management Science, School of Management, The State Key Laboratory forManufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an, China;School of Engineering and Information Technology, Deakin University, Burwood, Vic., Australia

  • Venue:
  • IEEE Transactions on Fuzzy Systems
  • Year:
  • 2009

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Abstract

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 Martínez 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.