Research Article
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Rough Hesitant Fuzzy Groups

Year 2020, Issue: 30, 35 - 44, 26.03.2020

Xueyou Chen

Abstract

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.

Keywords

Rough set hesitant fuzzy set group

References

  • 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.

Year 2020, Issue: 30, 35 - 44, 26.03.2020

Xueyou Chen

Abstract

References

  • 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.
There are 32 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Article
Authors

Xueyou Chen This is me

Publication Date March 26, 2020
Submission Date September 6, 2019
Published in Issue Year 2020 Issue: 30

Cite

APA Chen, X. (2020). Rough Hesitant Fuzzy Groups. Journal of New Theory(30), 35-44.
AMA Chen X. Rough Hesitant Fuzzy Groups. JNT. March 2020;(30):35-44.
Chicago Chen, Xueyou. “Rough Hesitant Fuzzy Groups”. Journal of New Theory, no. 30 (March 2020): 35-44.
EndNote Chen X (March 1, 2020) Rough Hesitant Fuzzy Groups. Journal of New Theory 30 35–44.
IEEE X. Chen, “Rough Hesitant Fuzzy Groups”, JNT, no. 30, pp. 35–44, March 2020.
ISNAD Chen, Xueyou. “Rough Hesitant Fuzzy Groups”. Journal of New Theory 30 (March 2020), 35-44.
JAMA Chen X. Rough Hesitant Fuzzy Groups. JNT. 2020;:35–44.
MLA Chen, Xueyou. “Rough Hesitant Fuzzy Groups”. Journal of New Theory, no. 30, 2020, pp. 35-44.
Vancouver Chen X. Rough Hesitant Fuzzy Groups. JNT. 2020(30):35-44.
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