Pythagorean fuzzy set (PFS), originally proposed by Yager, is more capable than intuitionistic fuzzy set (IFS) to handle vagueness in the real world. The main purpose of this paper is to investigate the relationship between the distance measure, the similarity measure, the entropy, and the inclusion measure for PFSs. The primary goal of the study is to suggest the systematic transformation of information measures (distance measure, similarity measure, entropy, inclusion measure) for PFSs. For achieving this goal, some new formulae for information measures of PFSs are introduced. To show the efficiency of the proposed similarity measure, we apply it to pattern recognition, clustering analysis, and medical diagnosis. Some illustrative examples are given to support the findings and also demonstrate their practicality and effectiveness of similarity measure between PFSs.

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BackgroundMany large-scaled public hospitals have established branched hospitals in China. This study is to provide evidence for strategy making on the management and development of multi-branched hospitals by evaluating and comparing the operational efficiencies of different hospitals before and after their establishment of branched hospitals.MethodsDEA (Data Envelopment Analysis) window analysis was performed on a 7-year data pool from five public hospitals provided by health authorities and institutional surveys.ResultsThe operational efficiencies of sample hospitals measured in this study (including technical efficiency, pure technical efficiency and scale efficiency) had overall trends towards increase during this 7-year period of time, however, a temporary downturn occurred shortly after the establishment of branched hospitals; pure technical efficiency contributed more to the improvement of technical efficiency compared to scale efficiency.ConclusionsThe establishment of branched-hospitals did not lead to a long-term negative effect on hospital operational efficiencies. Our data indicated the importance of improving scale efficiency via the optimization of organizational management, as well as the advantage of a different form of branch-establishment, merging and reorganization. This study brought an insight into the practical application of DEA window analysis on the assessment of hospital operational efficiencies.