Journal
APPLIED MATHEMATICAL MODELLING
Volume 37, Issue 4, Pages 2197-2211Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2012.04.031
Keywords
Correlation coefficient; Hesitant fuzzy set (HFS); Interval-valued HFS
Funding
- National Natural Science Foundation of China [71071161]
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Hesitant fuzzy sets (HFSs), which allow the membership degree of an element to a set represented by several possible values, can be considered as a powerful tool to express uncertain information in the process of group decision making. We derive some correlation coefficient formulas for HFSs and apply them to clustering analysis under hesitant fuzzy environments. Two real world examples, i.e. software evaluation and classification as well as the assessment of business failure risk, are employed to illustrate the actual need of the clustering algorithm based on HFSs, which can incorporate the difference of evaluation information provided by different experts in clustering processes. In order to extend the application domain of the clustering algorithm in the framework of HFSs, we develop the interval-valued HFSs and the corresponding correlation coefficient formulas, and then demonstrate their application in clustering with interval-valued hesitant fuzzy information through a specific numerical example. (C) 2012 Elsevier Inc. All rights reserved.
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