The fuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making

Abstract

In this paper, the cross-entropy of intuitionistic hesitant fuzzy sets (IHFSs) is developed by integrating the cross-entropy of intuitionistic fuzzy sets (IFSs) and hesitant fuzzy sets (HFSs). First, several measurement formulae are discussed and their properties are studied. Then, two approaches, which are based on the developed intuitionistic hesitant fuzzy cross-entropy, are proposed for solving multi-criteria decision-making (MCDM) problems within an intuitionistic hesitant fuzzy environment. For both methods, an optimisation model is established in order to determine the weight vector for MCDM problems with incomplete information on criteria weights. Finally, an example is provided in order to illustrate the practicality and effectiveness of the proposed approaches.

Keywords:

• multi-criteria decision-making
• intuitionistic fuzzy sets
• hesitant fuzzy sets
• intuitionistic hesitant fuzzy sets
• intuitionistic hesitant fuzzy cross-entropy

Acknowledgements

The authors thank the editors and anonymous reviewers for their helpful comments and suggestions.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 71271218], [grant number 71431006], [grant number 71221061]; the Humanities and Social Sciences Foundation of Ministry of Education of China [grant number14YJA630079]; the Science Foundation for Doctors of Hubei University of Automotive Technology [grant number BK201405].

Notes on contributors

Juan-juan Peng

Juan-juan Peng received her M.Sc. degree in computational mathematics from Wuhan University of Technology, China, in 2007. She is currently a Ph.D. student in Business School, Central South University; she is also a lecturer in School of Economics and Management, Hubei University of Automotive Technology, China. Her current research focuses on decision-making theory and application, risk management and control, and information management.

Jian-qiang Wang

Jian-qiang Wang received the Ph.D. degree in management science and engineering from Central South University, Changsha, China, in 2005. He is currently a professor in Business School, Central South University. His current research interests include decision-making theory and application, risk management and control, and information management.

Xiao-hui Wu

Xiao-hui Wu received his M.Sc. degree in computing science from University of Portsmouth, UK, in 2006. He is currently a Ph.D. student in Business School, Central South University; he is also a lecturer in School of Econmics and Management, Hubei University of Automotive Technology, China. His current research focuses on decision-making theory and application, risk management and control, and big data mining.

Hong-yu Zhang

Hong-Yu Zhang received her Ph.D. degree in management science and engineering from Business School, Central South University, Changsha, China, in 2009. She is currently an associated professor in Business School, Central South University. Her research interests include the area of information management and its applications in production operations. Her current research focuses on remanufacturing production management and decision-making theory.

Xiao-hong Chen

Xiao-hong Chen received her Ph.D in Tokyo University of Technology, Japan, in 1999. She is currently a professor at the School of Business, Central South University, Changsha, China. Her current research interests lie in the field of decision theory & method, decision support system, resource-saving and environment-friendly society. He has published in several journals, including Decision Support system, Expert Systems with Applications, etc.