A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making

  • Yuanna Liu
  • Wen JiangEmail author
Methodologies and Application


Interval-valued intuitionistic fuzzy sets are widely used in multi-attribute decision-making problems to select the optimal alternative, but how to measure uncertainty is an open and significant problem. In this paper, a new distance measure of interval-valued intuitionistic fuzzy sets is proposed based on the distance of interval numbers. With the advantages of taking account of the whole number in the interval and having definite physical meaning, the proposed distance measure of interval-valued intuitionistic fuzzy sets shows superiority in measuring uncertainty and imprecision. In addition, the proposed distance measure is compared with some recent research works and classical distances through numerical examples. Graphs are drawn to visually display the variation characteristics and analyze the properties of the distance measures. The results prove that the proposed distance measure of interval-valued intuitionistic fuzzy sets outperforms other metrics in measuring uncertainty and avoiding counterintuitive cases. Some illustrative examples of multi-attribute decision making under real life are conducted, which demonstrates the strong discrimination capability and effectiveness of the proposed distance measure.


Interval-valued intuitionistic fuzzy set Distance measure Decision making Uncertainty 



The authors greatly appreciate the reviews’ suggestions and the editor’s encouragement.


This study is partially supported by National Natural Science Foundation of China (Program No. 61671384, 61703338).

Compliance with ethical standards

Conflict of interest

Author Yuanna Liu declares that she has no conflict of interest. Author Wen Jiang declares that she has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electronics and InformationNorthwestern Polytechnical UniversityXi’anChina

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