Novel decision-making approach based on hesitant fuzzy sets and graph theory

  • Sumera Naz
  • Muhammad AkramEmail author


Hesitant fuzzy set is a powerful and effective tool to express uncertain information in multi-attribute decision-making (MADM) process, as it permits the membership degree of an element to a set represented by several possible values in [0,1]. In this paper, we develop a new decision-making approach based on graph theory to deal with the MADM problems, in which the decision information is expressed by hesitant fuzzy elements. Meanwhile, we generalize this approach to make it suitable for processing interval-valued hesitant fuzzy and hesitant triangular fuzzy information. Moreover, we utilize the numerical examples concerning the energy project selection and software evaluation to show the detailed implementation procedure and reliability of our method in solving MADM problems under hesitant fuzzy, interval-valued hesitant fuzzy and hesitant triangular fuzzy environment.


Hesitant fuzzy set Interval-valued hesitant fuzzy set Hesitant triangular fuzzy set Graph theory Expected value 

Mathematics Subject Classification

68R10 03E72 



The authors are grateful to an Associate Editor and anonymous referees for their valuable comments.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest regarding the publication of the research article.


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© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan

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