A Pearson-like correlation-based TOPSIS method with interval-valued Pythagorean fuzzy uncertainty and its application to multiple criteria decision analysis of stroke rehabilitation treatments

  • Lun-Hui Ho
  • Yu-Li Lin
  • Ting-Yu ChenEmail author
Original Article


This paper extends one of the most extensively used multiple criteria decision analysis (MCDA) methods, the technique for order preference by similarity to ideal solutions (TOPSIS), to adapt to highly complicated uncertain environments based on interval-valued Pythagorean fuzzy (IVPF) sets. In contrast to classical TOPSIS methods, this paper develops a novel concept of Pearson-like IVPF correlation coefficients instead of distance measures to not only construct a useful and effective association measure between two IVPF characteristics but also depict the outranking relationship of IVPF information. Moreover, this paper proposes the (weighted) IVPF correlation-based closeness coefficients to establish a Pearson-like correlation-based TOPSIS model to manage MCDA problems within the IVPF environment. In particular, there is a definite improvement in determining the closeness coefficient required in the TOPSIS procedure. This paper considers anchored judgments with respect to the positive- and negative-ideal IVPF solutions and provides new approach- and avoidance-oriented definitions for the IVPF correlation-based closeness coefficient, which is entirely different from the traditional definition of relative closeness in TOPSIS. Furthermore, this paper proposes a comprehensive IVPF correlation-based closeness index to balance the consequences between ultra-approach orientation and ultra-avoidance orientation and acquire the ultimate compromise solution for decision support and aid. The feasibility and practicability of the developed methodology are illustrated by a practical MCDA problem of rehabilitation treatment for hospitalized patients with acute stroke. The application results, along with experimentations and comparative analyses, demonstrate that the developed methods are rational and effective.


Multiple criteria decision analysis TOPSIS Interval-valued Pythagorean fuzzy set Pearson-like IVPF correlation coefficient Correlation-based closeness coefficient Rehabilitation treatment 



The authors acknowledge the assistance of the respected editor and the anonymous referees for their insightful and constructive comments, which helped to improve the overall quality of the paper. The authors are grateful for grant funding support from the Taiwan Ministry of Science and Technology (MOST 105-2410-H-182-007-MY3) and Linkou Chang Gung Memorial Hospital (BMRP 574 and CMRPD2F0203) during the completion of this study.

Compliance with ethical standards

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of NursingLinkou Chang Gung Memorial HospitalTaoyuan CityTaiwan
  2. 2.Department of NursingChang Gung University of Science and TechnologyTaoyuan CityTaiwan
  3. 3.Graduate Institute of Business and Management, College of ManagementChang Gung UniversityTaoyuan CityTaiwan
  4. 4.Department of Industrial and Business Management, College of ManagementChang Gung UniversityTaoyuan CityTaiwan

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