Multi-attribute decision making with Pythagorean fuzzy sets via conversions to intuitionistic fuzzy sets and ORESTE method

Abstract

The aim of this paper is to study the conversions between Pythagorean fuzzy sets and Atanassov's intuitionistic fuzzy sets. Besides, an ORESTE method based on multi-attribute decision making with Pythagorean fuzzy sets is developed by utilising the developed conversions. In this paper, according to the geometric representations of Pythagorean fuzzy sets and Atanassov's intuitionistic fuzzy sets, two types of conversions between the two fuzzy sets are constructed, which are further used to derive information measures include entropy and cross-entropy measures of Pythagorean fuzzy sets. Then, by combining with the ORESTE method, a direct decision procedure for multi-attribute decision making with Pythagorean fuzzy information is developed. Finally, a numerical example of the evaluation of regional energy efficiency is shown to illustrate the feasibility and validity of the developed decision procedure.

Keywords:

• Pythagorean fuzzy sets
• multi-attribute decision making
• Atanassov's intuitionistic fuzzy sets
• ORESTE
• entropies

Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions which have helped immensely in improving the quality of this paper.

Disclosure statement

This manuscript has not been published in whole or in part elsewhere, which has also not currently been considered for publication in another journal. All authors have been personally and actively involved in substantive work leading to the manuscript and will hold themselves jointly and individually responsible for its content. The authors declare that there are no conflicts of interest.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [grant numbers 71701001, 71771001, 71871001, 71501002, 71901001], the Social Science Innovation and Development Research Project in Anhui Province [grant number 2019CX094], the Natural Science Foundation for Distinguished Young Scholars of Anhui Province [grant number 1908085J03], the Natural Science Foundation of Anhui Province [grant number 2008085QG334], the Humanities and Social Sciences Research Project of Universities in Anhui [grant number SK2019A0013] and the Humanities and Social Sciences Planning Project of the Ministry of Education [grant number 20YJAZH066].

Notes on contributors

Zhifu Tao

Zhifu Tao is an Associate Professor of School of Economics, Anhui University, China. He received his PhD degree in Statistics from Anhui University in 2015. He has contributed over 20 journal articles to professional journals including IEEE Transactions on System, Man and Cybernetics: Systems, Applied Soft Computing, Engineering Applications of Artificial Intelligence and Computers & Industrial Engineering, etc. His current research interests include fuzzy set theory, data-driven decision making, forecasting, recommender systems.

Jiaming Zhu

Jiaming Zhu is a Lecturer of School of Internet, Anhui University, China. He received his PhD degree in Statistics from Anhui University in 2018. He has contributed over 10 journal articles to professional journals including Physica A: Statistical Mechanics and its Applications, International Journal of Environmental Research and Public Health and International Journal of Machine Learning and Cybernetics, etc. His current research interests include Combination forecasting, data decomposition and decision making.

Ligang Zhou

Ligang Zhou is a Professor of School of Mathematical Sciences, Anhui University. He received his PhD degree in Statistics from Anhui University in 2013. He has contributed over 50 journal articles to professional journals, such as Fuzzy Sets and Systems, Applied Mathematical Modelling, Applied Soft Computing, Group Decision and Negotiation, Expert Systems with Applications, etc. His current research interests include group decision making, aggregation operators and combined forecasting.

Jinpei Liu

Jinpei Liu is a Professor of School of Business, Anhui University. He received his PhD degree in operations research from Tianjin University in 2012. He has contributed over 40 journal articles to professional journals, such as Fuzzy Sets and Systems, Applied Mathematical Modelling, Applied Soft Computing, Information Sciences, Expert Systems with Applications, etc. His current research interests include group decision making, information fusion and combined forecasting.

Huayou Chen

Huayou Chen is a Professor of School of Mathematical Sciences, Anhui University, China. He received his PhD degree in Operational Research from University of Science Technology of China in 2002. He graduated from Nanjing University for postdoctoral research work in 2005. He has published a book: The Efficient Theory of Combined Forecasting and Applications (Science Press, Beijing, 2008) and has contributed over 120 journal articles to professional journals, such as Fuzzy Sets and Systems, Information Sciences, Group Decision and Negotiation, etc. His current research interests include information fusion, multi-criteria decision making, aggregation operators and combined forecasting.