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Distance Measure and Correlation Coefficient for Linguistic Hesitant Fuzzy Sets and Their Application
Volume 28, Issue 2 (2017), pp. 237–268
Pub. online: 1 January 2017      Type: Research Article      Open accessOpen Access
Received
1 January 2016
Accepted
1 March 2017
Published
1 January 2017

Abstract

Linguistic hesitant fuzzy sets (LHFSs) permit the decision maker to apply several linguistic terms with each having several membership degrees to denote his/her preference of one thing. This type of fuzzy sets can well address the qualitative and quantitative cognitions of the decision maker as well as reflect his/her hesitancy, uncertainty and inconsistency. This paper introduces a distance measure between any two LHFSs and then defines a correlation coefficient of LHFSs. Considering the application of LHFSs, the weighted distance measure and the weighted correlation coefficient of LHFSs are defined. To address the interactions between elements in a set, the Shapley weighted distance measure and the Shapley weighted correlation coefficient are presented. It is worth noting that when the elements are independent, they degenerate to the associated weighted distance measure and the weighted correlation coefficient, respectively. After that, their application to pattern recognition is studied. Furthermore, an approach to multi-attribute decision making under linguistic hesitant fuzzy environment is developed. Meanwhile, numerical examples are offered to show the concrete application of the developed procedure.

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Biographies

Guan Jian
guan_jian@csu.edu.cn

J. Guan received her PhD in management science and engineering from Business School of Central South University in 2006. Currently, she is a professor of management at Business School, Central South University, Changsha, China. She has contributed over 30 journal articles to professional journals. Her current research interests include decision analysis, strategic management and theory of firm in China.

Zhou Dao
zhoudao@csu.edu.cn

D. Zhou received his BS degree in computational mathematics from School of Mathematics and Computational Science in Xiantan University. He is a lecturer in Hunan University of Technology. Currently, he is a doctoral student in management science and engineering in Central South University. His current research interests includes fuzzy mathematics and decision making.

Meng Fanyong
mengfanyongtjie@163.com

F. Meng received his PhD degree in management science and engineering from Beijing Institute of Technology in 2011. Currently, he is an associate professor in Central South University. He has contributed over 80 journal articles to professional journals such as Omega, IEEE Transactions on Systems, Man and Cybernetics Systems, Information Sciences, Knowledge-Based Systems, Applied Mathematical Modelling, Applied Mathematics and Computation, Computers and Industrial Engineering. His current research interests include fuzzy mathematics, decision making, and game theory.


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Keywords
decision making linguistic hesitant fuzzy set correlation coefficient TOPSIS method the Shapley function

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