Affiliations: [a] College of Management Science and Engineering, Shanxi University of Finance and Economics, Taiyuan, Shanxi, China
| [b] Institute of management and decision, Shanxi University, Taiyuan, Shanxi, China
| [c] School of Economics and Management, Shanxi University, Taiyuan, Shanxi, China
| [d]
Guilin Tourism University, Guilin, China
Correspondence:
[*]
Corresponding authors. W. Qu, Institute of Management and Decision, School of Economics and Management, Shanxi University 030006, China. Tel.: +86 3517011130; E-mail: [email protected]. and F. Deng, Guilin Tourism University Guilin 541006, China. Tel.: +86 3517011130; E-mail: [email protected].
Abstract: The aim of this paper is to investigate dual hesitant fuzzy multiple attribute decision making problems where the attribute values provided by experts are expressed in dual hesitant fuzzy element, and the attribute weight is unknown. We present a new method to derive the weights of attributes and rank the preference order of alternatives based on bidirectional projection models. We introduce some notions, such as some dual hesitant fuzzy operational laws, dual hesitant fuzzy ideal point, the modules of dual hesitant fuzzy elements, and distance between two intuitionistic trapezoidal fuzzy numbers. We also introduce the cosine of the included angle between the attribute value vectors of each alternative and the dual hesitant fuzzy ideal point. Then we establish the bidirectional projection models to measure the similarity degrees between each alternative and the dual hesitant fuzzy ideal point, and the Jaynes maximum information entropy method is used to determine the attribute weight. Furthermore, we establish a nonlinear optimization model to obtain the weight vector of attributes. Finally, we illustrate the developed projection models with a numerical example.
