Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making
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College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China
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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
(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)
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.
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Keywords:
probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; multi-attribute decision making; aggregation operator
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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 StyleShao, 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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