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Note on the aggregation operators and ranking of hesitant interval-valued fuzzy elements

  • Wenyi Zeng
  • Deqing Li
  • Yundong Gu
Methodologies and Application
  • 21 Downloads

Abstract

Hesitant interval-valued fuzzy set, which allows decision makers to use several interval numbers to assess a variable, is a useful tool to deal with situations in which people are hesitant in providing their interval-valued assessments. In this paper, we investigate the properties of hesitant interval-valued fuzzy aggregation operators and the approach for ranking a set of hesitant interval-valued fuzzy elements. Some flaws about the properties presented by Wei et al. (Knowl Based Syst 46:43–53, 2013) are pointed out and analyzed by counterexamples, and some modifications on the properties are given. Simultaneously, two flaws about the approach for ranking hesitant interval-valued fuzzy elements provided by Wei et al. (2013) are analyzed by counterexamples. A new algorithm for ranking a set of hesitant interval-valued fuzzy elements is provided. The rationality of the modified ranking approach is investigated.

Keywords

Hesitant fuzzy sets Hesitant interval-valued fuzzy elements Prioritized aggregation operators Power aggregation operators Ranking function 

Notes

Acknowledgements

The authors wish to express their gratitude to the anonymous referee and the Editor-in-Chief, Professor Antonio Di Nola, for their kind suggestions and helpful comments in revising the paper. This work is supported by grants from the National Natural Science Foundation of China (No. 10971243).

Compliance with ethical standards

Conflict of interest

We declare that we have no conflict of interest.

Ethical approach

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

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing Normal UniversityBeijingPeople’s Republic of China
  2. 2.Department of MathematicsShijiazhuang Mechanical Engineering CollegeShijiazhuangPeople’s Republic of China
  3. 3.School of Mathematics and PhysicsNorth China Electric Power UniversityBeijingPeople’s Republic of China

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