New Correlation Coefficients Between Probabilistic Hesitant Fuzzy Sets and Their Applications in Cluster Analysis
- 65 Downloads
The hesitant fuzzy set (HFS) is very significant in dealing with the multi-criteria decision-making problems when the decision makers have hesitancy in providing their assessments. However, with the deepening of the research, it may lose information in its applications. Hence, the probabilistic hesitant fuzzy set (P-HFS) has been proposed to improve the HFS, associating the probability with the HFS and remaining more information than the HFS. Considering the correlation coefficient is one of the most important tools in data analysis, we propose two new correlation coefficient formulas to measure the relationship between the P-HFSs, based on which, a new probabilistic hesitant fuzzy clustering algorithm is also developed. To do so, we define the mean of the probabilistic hesitant fuzzy element and the P-HFS, respectively. Furthermore, a practical case study is conducted to demonstrate practicability and validity of the proposed clustering algorithm.
KeywordsProbabilistic hesitant fuzzy set Correlation coefficient Human–environment risk Cluster analysis
- 8.Zhu, B.: Decision Method for Research and Application Based On Preference Relation. Southeast University, Nanjing (2014)Google Scholar
- 11.Jiang, F., Ma, Q.: Multi-attribute group decision making under probabilistic hesitant fuzzy environment with application to evaluate the transformation efficiency. Appl. Intell. 1, 1–13 (2017)Google Scholar
- 32.Wang, P.Z.: Fuzzy Set Theory and Applications. Shanghai Scientific and Technical Publishers, Shanghai (1983)Google Scholar
- 34.Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: IEEE International Conference on Fuzzy Systems, pp. 1378–1382 (2009)Google Scholar