New hesitation-based distance and similarity measures on intuitionistic fuzzy sets and their applications

ABSTRACT

In this paper, we present new definitions on distance and similarity measures between intuitionistic fuzzy sets (IFSs) by combining with hesitation degree. First, we discuss the limitations in traditional distance and similarity measures, which are caused by the neglect of hesitation degree's influence. Even though a vector-valued similarity measure was proposed, which has two components indicating similarity and hesitation aspects, it still cannot perform well in practical applications because hesitation works only when the values of similarity measures are equal. In order to overcome the limitations, we propose new definitions on hesitation, distance and similarity measures, and research some theorems which satisfy the requirements of the proposed definitions. Meanwhile, we investigate the relationships among hesitation, distance, similarity and entropy of IFSs to verify the consistency of our work and previous research. Finally, we analyse and discuss the advantages and disadvantages of the proposed similarity measure in detail, and then we apply the proposed measures (dH and SH) to deal with pattern recognition problems, and demonstrate that they outperform state-of-the-art distance and similarity measures.

KEYWORDS:

• Distance measure
• similarity measure
• intuitionistic fuzzy sets
• hesitation measure
• pattern recognition

Acknowledgments

The authors are highly grateful to the anonymous referees for their careful reading and insightful comments..

Disclosure statement

No potential conflict of interest was reported by the authors. .

Additional information

Funding

This work is supported by grants from the National Natural Science Foundation of China [number 61673327], [number 71271086]; Aviation Science Foundation [number 20140168001].

Notes on contributors

Yun Kang

Yun Kang is currently a Ph.D. student in Department of Automation, Xiamen University. Her research interests include data mining and knowledge discovery, decision analysis and granular computing.

Shunxiang Wu

Shunxiang Wu received the M.S. degree in Department of Computer Science and Engineering from Xi'an Jiaotong University in 1991 and the Ph.D. degree in School of Economics and Management, Nanjing University of Aeronautics & Astronautics in 2007. He is currently a professor in Department of Automation, Xiamen University. His research interests include intelligent computing, data mining and knowledge discovery, systems engineering theory and application.

Da Cao

Da Cao received the Ph.D. degree and master degree from Xiamen University of China in 2013 and 2017, respectively. During the PhD study period, he joined National University of Singapore for one year as a visiting student under the supervision of Prof. Chua Tat-Seng. He is currently an assistant professor in College of Computer Science and Electronic Engineering, Hunan University. His research interests include span recommender systems, multi-media retrieval, and natural language processing.

Wei Weng

Wei Weng currently is an associate professor with Xiamen University of Technology and a Ph.D. student in Department of Automation, Xiamen University. His research interests include data mining, community mining in complex networks, and recommendation techniques.