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## Rough Hesitant Fuzzy Groups

#### Xueyou CHEN [1]

In 2010, Torra introduced the notion of a hesitant fuzzy set, which is a generalization of Zadeh's fuzzy set. In the paper, we define two rough operators on hesitant fuzzy group by means of a normal hesitant fuzzy subgroup and investigate some of their properties.
Rough set, hesitant fuzzy set, group
• L. A. Zadeh, Fuzzy Sets, Information and Control 8(3) (1965) 338-353.
• A. Rosenfeld, Fuzzy Groups, Journal of Mathematical Analysis and Applications 35 (1971) 512- 517.
• Z. Pawlak, Rough Sets, International Journal of Computer and Information Sciences 11 (1982) 341-356.
• D. Dubois, H. Prade, Rough Fuzzy Sets and Fuzzy Rough Sets, International Journal of General Systems 17 (1990) 191-209.
• R. Biswas, S. Nanda, Rough Groups and Rough Subgroups, Bulletin of the Polish Academy of Sciences Mathematics 42 (1994) 251-254.
• X. Chen, Rough Approximations on L-Groups, Annals of Fuzzy Mathematics and Informatics 18(1) (2019) 45-55.
• B. Davvaz, Roughness Based on Fuzzy Ideals, Information Science 164 (2006) 2417-2437.
• N. Kuroki, P. P. Wang, The Lower and Upper Approximations in a Fuzzy Group, Information Science 90 (1996) 203-220.
• J. Mordeson, K. R. Bhutani, A. Rosenfeld, Fuzzy Subsets and Fuzzy Subgroups, Studies in Fuzzi- ness and Soft Computing 182 (2005) 1-39.
• N. Yaqoob, M. Aslam, R. Chinram, Rough Prime bi-Ideals and Rough Fuzzy Prime bi-Ideals in Semigroups, Annals of Fuzzy Mathematics and Informatics 3(2) (2012) 203-211.
• N. Yaqoob, Approximations in Left Almost Polygroups, Journal of Intelligent and Fuzzy Systems 36 (2019) 517-526.
• V. Torra, Hesitant Fuzzy Sets, International Journal of Intelligent Systems 25 (2010) 529-539.
• Z. Pei, L. Yi, A Note on Operators of Hesitant Fuzzy Sets, International Journal of Computational Intelligence Systems 8(2) (2015) 226-239.
• G. S. Thakur, R. Thakur, R. Singh, New Hesitant Fuzzy Operators, Fuzzy Information and Engineering 6 (2014) 379-392.
• D. Divakaran, S. J. John, Hesitant Fuzzy Rough Sets through Hesitant Fuzzy Relations, Annals of Fuzzy Mathematics and Informatics 8(1) (2014) 33-46.
• D. Divakaran, S. J. John, Homomorphism of Hesitant Fuzzy Subgroups, International Journal of Scienti c and Engineering Research 5(9) (2014) 9-14.
• D. Divakaran, S. J. John, Hesitant Fuzzy Subgroups, Journal of New Theory 11 (2016) 54-68.
• V. Deepa , S. J. John, Dual Hesitant Fuzzy Rough Subrings and Ideals, Annals of Fuzzy Mathe- matics and Informatics 13(3) (2017) 437-448.
• Y. B. Jun, S. S. Ahn, Hesitant Fuzzy Sets Theory Applied to BCK/BCI-Algebras, Journal of Computational Analysis and Applications 20(4) (2016) 635-646.
• H. Alshehri, N. Alshehri, Hesitant Anti-Fuzzy Soft Set in BCK-Algebras, Mathematical Problems in Engineering (2017), Article ID 3634258, 13 pages.
• B. Davvaz, Rough Algebraic Structures Corresponding to Ring Theory, DOI: 10.1007/978-3-030- 01162-8-9, In book: Algebraic Methods in General Rough Sets (2018) 657-695.
• D. Deepak, S. J. John, Information Systems on Hesitant Fuzzy Sets, International Journal of Rough Sets and Data Analysis 3(1) (2016) 71-97.
• D. Deepak, S. J. John, Rough Approximations on Hesitant Fuzzy sets, Book Chapter: Generalized and Hybrid Set Structures and Applications for Soft Computing, IGI Global USA, (2016) 269-279.
• A. H. Dehmiry, M. Mashinchi, Hesitant L-Fuzzy Relations, 6th Iranian Joint Congress on Fuzzy and Intelligent Systems (2018) 102-104.
• Y. B. Jun, K. J. Lee, S. Z. Song, Hesitant Fuzzy bi-Ideals in Semigroups, Communications of the Korean Mathematical Society 30(3) (2015) 143-154.
• A. Solariaju, S.Mahalakshmi, Hesitant Intuitionistic Fuzzy soft Groups, International Journal of Pure and Applied Mathematics 118(10) (2018) 223-232.
• M. S. Sindhu, T. Rashid, M. Khan, Group Decision Making Based on Hesitant Fuzzy Ranking of Hesitant Preference Relations, Journal of Intelligent and Fuzzy Systems 37(2) (2019) 2563-2573.
• C. Wang, D.Chen, A Short Note on Some Properties of Rough Groups, Computers and Mathematics with Applications 59(2010) 431-436.
• X. Chen, Q. Li, Construction of Rough Approximations in Fuzzy Setting, Fuzzy Sets and Systems 158 (2007) 2641-2653.
• Y. Y. Yao, Constructive and Algebraic Methods of The Theory of Rough Sets, Information Science 109 (1998) 21{47.
• J. G. Lee, K. Hur, Hesitant Fuzzy Topological Spaces, Mathematics 8(2) 188 (2020) pp 1-21.
• X. Chen, Rough Approximations Induced by a Soft Relation, Annals of Fuzzy Mathematics and Informatics, 11(1) (2016) 135-144.
Primary Language en Mathematics, Applied Mart Research Article Author: Xueyou CHEN (Primary Author)Institution: Shandong University of TechnologyCountry: China Publication Date : March 26, 2020
 Bibtex @research article { jnt707501, journal = {Journal of New Theory}, issn = {2149-1402}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2020}, volume = {}, pages = {35 - 44}, doi = {}, title = {Rough Hesitant Fuzzy Groups}, key = {cite}, author = {CHEN, Xueyou} } APA CHEN, X . (2020). Rough Hesitant Fuzzy Groups. Journal of New Theory , (30) , 35-44 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/53260/707501 MLA CHEN, X . "Rough Hesitant Fuzzy Groups". Journal of New Theory (2020 ): 35-44 Chicago CHEN, X . "Rough Hesitant Fuzzy Groups". Journal of New Theory (2020 ): 35-44 RIS TY - JOUR T1 - Rough Hesitant Fuzzy Groups AU - Xueyou CHEN Y1 - 2020 PY - 2020 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 35 EP - 44 VL - IS - 30 SN - 2149-1402-2149-1402 M3 - UR - Y2 - 2020 ER - EndNote %0 Journal of New Theory Rough Hesitant Fuzzy Groups %A Xueyou CHEN %T Rough Hesitant Fuzzy Groups %D 2020 %J Journal of New Theory %P 2149-1402-2149-1402 %V %N 30 %R %U ISNAD CHEN, Xueyou . "Rough Hesitant Fuzzy Groups". Journal of New Theory / 30 (March 2020): 35-44 . AMA CHEN X . Rough Hesitant Fuzzy Groups. JNT. 2020; (30): 35-44. Vancouver CHEN X . Rough Hesitant Fuzzy Groups. Journal of New Theory. 2020; (30): 44-35.

Authors of the Article
[1]