Hesitant fuzzy dual Muirhead mean operators and its application to multiple attribute decision making¹

Article type: Research Article

Authors: Hong, Zhiyong^a | Rong, Yuan^c | Qin, Ya^b | Liu, Yi^{b; c; *}

Affiliations: [a] School of Computer Science, Wuyi University, Jiangmen, Guangdong, P.R. China | [b] Data Recovery Key Lab of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan, P.R. China | [c] School of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan, P.R. China

Correspondence: [*] Corresponding author. Yi Liu. E-mail: liuyiyl@126.com.

Note: [1 ] This work is supported by National Natural Science Foundation of P.R.China (Grant no. 61673320); The Application Basic Research Plan Project of Sichuan Province (No.2015JY0120); The Scientific Research Project of Department of Education of Sichuan Province (18ZA0273,15TD0027); Natural Science Foundation of Guangdong Province (2016A030310003).

Abstract: The present work is focused on hesitant fuzzy multi-attribute decision making (HF-MADM) problem with the hesitant fuzzy information based on a new aggregation operator. To begin with, we present the new hesitant fuzzy dual Muirhead mean (HFDMM) to deal with MADM problems, including the HFDMM and the hesitant fuzzy dual weighted Muirhead mean (HFDWMM) operator, the main advantages of the two aggregation operators are that they can capture interrelationships of multiple attributes among any number of attributes by a parameter vector P and make information aggregation process more flexible by the parameter vector P. In addition, some properties of HFDMM and HFDWMM are obtained and some special cases are discussed where the parameter vector takes some different values. Moreover, we present a new method to solve the MADM problems with hesitant fuzzy information based on HFDWMM. Finally, an illustrative example is provided to show the feasibility and validity of the new method, the influences of parameter vector P on the decision making results are investigated and the advantages of proposed methods by comparing with the other existing methods are also analyzed by the example.

Keywords: Hesitant fuzzy set, Muirhead Mean Operators, Dual Muirhead Mean, aggregation operators, multiple attribute decision making

DOI: 10.3233/JIFS-172139

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 2, pp. 2161-2172, 2018