Single Valued Neutrosophic Hesitant Fuzzy Rough Set and Its Application

In this paper, we proposed the notion of single valued
neutrosophic hesitant fuzzy rough set, by combining single valued
neutrosophic hesitant fuzzy set and rough set. The combination
of single valued neutrosophic hesitant fuzzy set and rough set
is a powerful tool for dealing with uncertainty, granularity and
incompleteness of knowledge in information systems. We presented
both definition and some basic properties of the proposed model.
Finally, we gave a general approach which is applied to a
decision making problem in disease diagnoses, and demonstrated the
effectiveness of the approach by a numerical example.

Authors:

• K. M. Alsager
• N. O. Alshehri

Keywords:

• Single valued neutrosophic hesitant set
• single valued neutrosophic hesitant relation
• single valued neutrosophic hesitant fuzzy rough set
• decision making method.

References:

[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and systems
20(1968)87-96.
[2] S. Broumi, F. Smarandache, M. Dhar, Rough neutrosophic sets, Ital. J.
Pure. Appl. Math. 32(2014).
[3] C. F. Liu, Y. S. Luo, New aggregation operators of single-valued
neutrosophic hesitant fuzzy set and their application in multi-attribute
decision making, Pattern Anal. Appls. (2017)1-11.
[4] J. Pang, J. Wang, X. Wu, Multi-valued neutrosophic sets and power
aggregation operators with their applications in multi-criteria group
decision-making problems, Int. J. Comput. Int. Sys. 8(2015)345-363.[5] Z. Pawlak, Rough sets, International journal of computer and Information
Sciences 11(1982), 341-356.
[6] F. Smarandache, A unifying field in logics, Neutrosophic logic, Multi.
Valued Logic 8(1999)489-503.
[7] V. Torra, Hesitan fuzzy sets, Int J. Intell. Syst. 25(2010)529-539.
[8] H. Wang, P. Madiraju, Interval-neutrosophic sets, J.
Mech.1(2004)274-277.
[9] H. Wang, F. Smarandache, Y. Zhng, R. Sunderraman, Single-valued
neutrosophic sets, Multispace and Multistructure 4(2010)410-413.
[10] M. M. Xia and Z. S. Xu, Hesitant fuzzy information aggregation in
decision making, Int. J. Approx. Reason. 52 (2011), 395?407.
[11] XB. Yang, XN, Song, YS. Qi, JY. Yang, Constructive and
axiomatic approaches to hesitant fuzzy rough set. Soft Computing
18(2014)1067-1077.
[12] J. Ye, Multi-attribute decision making method under a single
valued neutrosophic hesitant fuzzy environment, J. Intell. Syst.
24(1)(2015)23-34.
[13] L. A. Zadeh, Fuzzy sets, Information and control 8(1965), 338-353.