Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32727
Single Valued Neutrosophic Hesitant Fuzzy Rough Set and Its Application

Authors: K. M. Alsager, N. O. Alshehri


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.

Keywords: Single valued neutrosophic hesitant set, single valued neutrosophic hesitant relation, single valued neutrosophic hesitant fuzzy rough set, decision making method.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1195


[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.