Journal
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
Volume 30, Issue 2, Pages 691-703Publisher
IOS PRESS
DOI: 10.3233/IFS-151790
Keywords
Hesitant fuzzy entropy; fuzzy factor; hesitant factor; cross-entropy; parameterized uncertainty measures
Categories
Funding
- National Nature Science Foundation of China [71273048, 71473036]
- Founding of Jiangsu Innovation Program for Graduate Education [KYZZ15_0070]
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The main purpose of the paper is to develop a general analytical framework of uncertainty measures, which provides a fresh new look into the uncertain information of hesitant fuzzy sets (HFSs). We first refine the axiomatic principles of hesitant fuzzy entropy based on the fuzzy factor and hesitant factor, and propose some distance-based entropy formulas of HFSs. Then, a novel hesitant fuzzy cross-entropy is defined to measure the discrimination of uncertain information of different HFSs. Meanwhile, the relationship between cross-entropy and entropy of HFSs is also discussed, and the hesitant fuzzy entropy may be divided into arithmetic average of fuzzy entropy and hesitant entropy. Moreover, some parameterized uncertainty measures are investigated, and two comparative examples are presented to demonstrate their reasonability. Finally, we apply these proposed measures in multiple attribute decision-making problem to illustrate their efficiency and applicability.
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