d8cdbf11-0c50-4254-86ee-140cc8d34a0020220221022059051wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40511520221520222110.37394/23206.2022.21https://wseas.com/journals/mathematics/2022.phpAbdallahAl-HusbanDepartment of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, JORDANIn this paper, a new theory of fuzzy soft groups (FSG) based on fuzzy spaces (FS) from Dib’s point of view is found. The concept of FSG and fuzzy soft subgroup (FSSG) based on FS was elaborated. The relationship between FSG and FSG is also investigated.2182022218202253578https://wseas.com/journals/mathematics/2022/a165106-1338.pdf10.37394/23206.2022.21.8https://wseas.com/journals/mathematics/2022/a165106-1338.pdfZadeh, L.A, Fuzzy Sets, Inform. Control Vol.8, 1965, pp. 338-353. Rosenfeld, A, Fuzzy Groups. Journal of Mathematical Analysis and Applications Vol. 35, 1971, pp. 512-517. 10.1016/0020-0255(94)90079-5Dib, K. A. On Fuzzy Spaces and Fuzzy Group Theory. Information Sciences, Vol. 80, 1994, pp. 253-282. 10.1016/s0898-1221(99)00056-5Molodtsov, D, Soft Set Theory First Result. An International Journal of Computers and Mathematics with Applications, Vol. 37, 1999, pp. 19-31. Maji, P. K., Biswas, R, & Roy, A.R. Fuzzy Soft Set Theory. The Journal of Fuzzy Mathematics Vol. 9(3), 2001, pp. 589-602. 10.1016/s0165-0114(96)00338-7Dib, K.A. & Hassan, A.A.M. The fuzzy Normal Subgroup. Fuzzy Sets and Systems. Vol. 98, 1998, pp.393-402. Akta. H. Gagman N. Soft Sets and Soft group, Information Science Vol. 177, 2007, pp.2726- 2735. 10.12988/ijma.2014.410315Selvachandran, G. Fuzzy Soft Rings Based on Fuzzy Spaces. International Journal of Mathematical Analysis, 8(56), 2014, pp. 2781- 2787. Jaradat, A., & Al-Husban, A The Multi-Fuzzy Group Spaces on Multi-Fuzzy Space. J. Math. Comput. Sci, Vol. 11(6), 2021, pp.7535-7552. Rosenfeld A, Fuzzy Groups, Math .Anal .Appl. Vol. 35, 1971, pp. 512-517. 10.1016/0165-0114(82)90057-4Anthony, J. M. & Sherwood, H. A Characterization of Fuzzy Subgroups. Fuzzy Sets and Systems Vol. 7, 1982, pp. 297-305. Pazar. B.V & Aygunoglu. A & Ygun. H. On Fuzzy Soft Rings. Journal of Hyper structures Vol. 1(2), 2012, pp.1-15. 10.1016/0022-247x(81)90164-5Das, P. S. Fuzzy Groups and Level Subgroups. Journal of Mathematical Analysis and Applications. Vol. 84, 1981, pp.264-269. 10.1016/0165-0114(91)90134-cDib, K. A. & Youssef, N. L. Fuzzy Cartesian Product, Fuzzy Relations and Fuzzy Functions. Fuzzy Sets and Systems. Vol. 41, 1991, pp. 299-315. 10.1063/1.4937059Abdallah Al-Husban & Abdul Razak Salleh. Complex Fuzzy Group based on Complex fuzzy space. Global Journal of Pure and Applied Mathematics. Vol. 12(2), 2016, pp. 1433-1450. 10.1063/1.5111229Abdallah Al-Husban, Abdul Razak Salleh, & Nasruddin Hassan, Complex Fuzzy Normal Subgroup." THE ukm fst postgraduate colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2015 Postgraduate Colloquium. Vol. 1678. , 2015, pp. 060008-060015.10.1109/icrem.2015.7357062Abdallah Al-Husban & Abdul Razak Salleh, Complex Fuzzy Ring. Proceedings of 2nd International Conference on Computing, Mathematics and Statistics. PP. 241-245. Publisher: IEEE 2015. 10.1063/1.4937059Abdallah Al-Husban & Abdul Razak Salleh 2015. Complex Fuzzy Hyperring Based on Complex Fuzzy Spaces. Proceedings of 2nd Innovation and Analytics Conference & Exhibition (IACE). Vol. 1691, 2015, pp. 040009-040017. 10.1063/1.4937059Abdallah Al-Husban & Abdul Razak Salleh. Complex Fuzzy Hypergroup based on Complex Fuzzy Space. International Journal of Pure and Applied Mathematics. Vol. 107(4), 2016, pp. 949- 958. Al-Husban, A., Amourah, A., & Jaber, J. J. Bipolar complex fuzzy sets and their properties. Italian Journal of Pure and Applied Mathematics, N (43) 2020, pp. 754–761. Alsarahead, MIKHLED O., and A. G. Ahmad. "Complex Fuzzy Soft Group." Journal of Quality Management and Analysis vol.13.2, 2017, pp. 17-28. Riaz, M., Saeed, M., Saqlain, M., & Jafar, N. Impact of water hardness in instinctive laundry system based on fuzzy logic controller. Punjab University Journal of Mathematics, 2020, 51(4). 10.3390/sym11111381Luqman, A., Akram, M., Al-Kenani, A. N., & Alcantud, J. C. R. (2019). A study on hypergraph representations of complex fuzzy information. Symmetry, Vol. 11(11), 2019, pp.1381. 10.28924/2291-8639-16-2018-628Al Tahan, M., & Davvaz, B. (2018). Generalized Complex Fuzzy and Anti-Fuzzy H_v-Subgroups. International Journal of Analysis and Applications, 16(5), 2018, pp.628-642