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Open AccessArticle

Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making

1
College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China
2
Department of Mathematics, School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, China
3
Department of Mathematics, College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China
4
College of Science, Nanjing University of Science and Technology, Nanjing 210000, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(9), 419; https://doi.org/10.3390/sym10090419
Received: 21 August 2018 / Revised: 11 September 2018 / Accepted: 14 September 2018 / Published: 19 September 2018
The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced. By definition, we know that the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) is a special case of the probabilistic interval neutrosophic hesitant fuzzy set (PINHFS). PSVNHFSs can satisfy all the properties of PINHFSs. An example is given to illustrate that PINHFS compared to PSVNHFS is more general. Then, PINHFS is the main research object. The basic operational relations of PINHFS are studied, and the comparison method of probabilistic interval neutrosophic hesitant fuzzy numbers (PINHFNs) is proposed. Then, the probabilistic interval neutrosophic hesitant fuzzy weighted averaging (PINHFWA) and the probability interval neutrosophic hesitant fuzzy weighted geometric (PINHFWG) operators are presented. Some basic properties are investigated. Next, based on the PINHFWA and PINHFWG operators, a decision-making method under a probabilistic interval neutrosophic hesitant fuzzy circumstance is established. Finally, we apply this method to the issue of investment options. The validity and application of the new approach is demonstrated. View Full-Text
Keywords: probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; multi-attribute decision making; aggregation operator probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; multi-attribute decision making; aggregation operator
MDPI and ACS Style

Shao, S.; Zhang, X.; Li, Y.; Bo, C. Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making. Symmetry 2018, 10, 419. https://doi.org/10.3390/sym10090419

AMA Style

Shao S, Zhang X, Li Y, Bo C. Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making. Symmetry. 2018; 10(9):419. https://doi.org/10.3390/sym10090419

Chicago/Turabian Style

Shao, Songtao; Zhang, Xiaohong; Li, Yu; Bo, Chunxin. 2018. "Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making" Symmetry 10, no. 9: 419. https://doi.org/10.3390/sym10090419

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