Title: Hesitant fuzzy sets with non-uniform linguistic terms: an application in multi-attribute decision making

Authors: Eshika Aggarwal; B.K. Mohanty

Addresses: Indian Institute of Management Lucknow, Lucknow – 226 013, India ' Indian Institute of Management Lucknow, Lucknow – 226 013, India

Abstract: The paper introduces a novel methodology for solving multi-attribute decision-making problems under hesitant fuzzy linguistic environment. It includes non-uniform, non-regular, or arbitrarily defined linguistic terms in hesitant fuzzy linguistic term set. The proposed methodology takes both normal and non-normal fuzzy numbers to represent linguistic terms in HFLTS. The combined approach of the concept of existence in ranking of fuzzy sets, α-cuts of fuzzy numbers, and ordering relations for hesitant fuzzy sets is used to value each alternative numerically. Binary integer programming is used to verify the consistency level of pairwise comparison matrix conforming to specified linguistic preferences as per the decision maker's expressions. The pairwise comparison matrices are aggregated over attributes to obtain the aggregated pairwise comparison matrix. The derived aggregated matrix calculates dominance/non-dominance levels of alternatives and selects best alternative. The proposed method is demonstrated with a numerical example, compared with similar methods and the advantages are highlighted.

Keywords: non-uniform linguistic term set; hesitant fuzzy linguistic term set; fuzzy number comparison; binary integer programming; aggregated pairwise comparison matrix; dominance degree.

DOI: 10.1504/IJMOR.2023.128629

International Journal of Mathematics in Operational Research, 2023 Vol.24 No.1, pp.1 - 28

Received: 27 Sep 2021
Accepted: 18 Nov 2021
Published online: 31 Jan 2023 *