Voir la notice de l'article provenant de la source Library of Science
@article{DMGAA_2022_42_2_a12, author = {Izhar, Muhammad and Khan, Asghar and Farooq, Muhammad and Hila, Kostaq}, title = {(M, {N)-Double-Framed} {Soft} {bi-Ideals} of {Abel} {Grassmann's} {Groupoids}}, journal = {Discussiones Mathematicae. General Algebra and Applications}, pages = {425--448}, publisher = {mathdoc}, volume = {42}, number = {2}, year = {2022}, language = {en}, url = {http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a12/} }
TY - JOUR AU - Izhar, Muhammad AU - Khan, Asghar AU - Farooq, Muhammad AU - Hila, Kostaq TI - (M, N)-Double-Framed Soft bi-Ideals of Abel Grassmann's Groupoids JO - Discussiones Mathematicae. General Algebra and Applications PY - 2022 SP - 425 EP - 448 VL - 42 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a12/ LA - en ID - DMGAA_2022_42_2_a12 ER -
%0 Journal Article %A Izhar, Muhammad %A Khan, Asghar %A Farooq, Muhammad %A Hila, Kostaq %T (M, N)-Double-Framed Soft bi-Ideals of Abel Grassmann's Groupoids %J Discussiones Mathematicae. General Algebra and Applications %D 2022 %P 425-448 %V 42 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a12/ %G en %F DMGAA_2022_42_2_a12
Izhar, Muhammad; Khan, Asghar; Farooq, Muhammad; Hila, Kostaq. (M, N)-Double-Framed Soft bi-Ideals of Abel Grassmann's Groupoids. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 425-448. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a12/
[1] U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl. 59 (2010) 3458–3463. https://doi.org/10.1016/j.camwa.2010.03.034
[2] A.O. Atagun and A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl. 61 (2011) 592–601. https://doi.org/10.1016/j.camwa.2010.12.005
[3] T. Asif, F. Yousafzai, A. Khan and K. Hila, Ideal theory in ordered AG-groupoids based on double framed soft sets, J. Mult.-Valued Logic Soft Comput. 33 (2019) 27–49.
[4] N. Cagman and S. Enginoglu, FP-soft set theory and its applications, Ann. Fuzzy Math. Inform. 2 (2011) 219–226.
[5] J.R. Cho, Pusan, J. Jezek and T. Kepka, Paramedial groupoids, Czechoslovak Math. J. 49 (124) (1996) 277–290. https://doi.org/10.1023/A:1022448218116
[6] B. Davvaz, M. Khan, S. Anis and S. Haq, Generalized fuzzy quasi-ideals of an intraregular Abel-Grassmann's groupoid, J. Appl. Math. 2012, Art. ID 627075, 16 pp. https://doi.org/10.1155/2012/627075
[7] W.A. Dudek, M. Khan and N. Khan, Characterizations of intra-regular Abel-Grassmann's groupoids, J. Intell. Fuzzy Systems 27 (2014) 2915–2925. https://doi.org/10.3233/IFS-141251
[8] F. Feng, Soft rough sets applied to multicriteria group decision making, Ann. Fuzzy Math. Inform. 2 (2011) 69–80.
[9] F. Feng, Y.B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl. 56 (2008) 2621–2628. https://doi.org/10.1016/j.camwa.2008.05.011
[10] P. Holgate, Groupoids satisfying a simple invertive law, Math. Students 61 (1992) 101–106. https://doi.org/10.1007/BF00163844
[11] M. Izhar and A. Khan, On (M, N) -DFS ideals of AG-groupoids, J. Intell. Fuzzy Sys. 35 (2018) 6313–6327. https://doi.org/10.3233/JIFS-181119
[12] M. Izhar, A. Khan and K. Hila, Double-framed soft generalized bi-ideals of intra-regular AG-groupoids, J. Intell. Fuzzy Sys. 35 (2018) 4701–4715. https://doi.org/10.3233/JIFS-181188
[13] Y.B. Jun, K.J. Lee and A. Khan, Soft ordered semigroups, Math. Logic Q. 56 (2010) 42–50. https://doi.org/10.1002/malq.200810030
[14] Y.B. Jun and S.S. Ahn, Double-framed soft sets with applications in BCK/BCI-algebras, J. Appl. Math. 2012, 15 pages. https://doi.org/10.1155/2012/178159
[15] Y.B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413. https://doi.org/10.1016/j.camwa.2008.02.035
[16] Y.B. Jun, K.J. Lee and C.H. Park, Soft set theory applied to ideals in d-algebras, Comput. Math. Appl. 57 (2009) 367–378. https://doi.org/10.1016/j.camwa.2008.11.002
[17] Y.B. Jun, K.J. Lee and J. Zhan, Soft p-ideals of soft BCI-algebras, Comput. Math. Appl. 58 (2009) 2060–2068. https://doi.org/10.1016/j.camwa.2009.07.072
[18] Y.B. Jun and C.H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178 (2008) 2466–2475. https://doi.org/10.1016/j.ins.2008.01.017
[19] M.A. Kazim and M. Naseeruddin, On almost semigroups, Aligarh Bull. Math. 2 (1972) 1–7.
[20] A. Khan, T. Asif and Y.B. Jun, Double-framed soft ordered semigroups, submitted.
[21] A. Khan, M. Izhar and M.M. Khalaf, Double framed soft LA-semigroups, J. Intell. Fuzzy Sys. 33 (2017) 3339–3353. https://doi.org/10.1016/j.ins.2008.01.017
[22] A. Khan, M. Izhar and A.S. Sezer, Characterizations of intra-regular Abel-Grassmann's groupoids using Double Framed Soft Ideals, Int. J. Anal. Appl. 15 (2017) 62–74.
[23] A. Khan and M. Sarwar, Uni-soft Bi-ideals and Uni-soft interior ideals of AG-groupoids, Math. Sci. Letters 5 (2016) 271–277. https://doi.org/10.18576/msl/050308
[24] A. Khan, M. Izhar and K. Hila, On algebraic properties of DFS sets and its application in decision making problems, J. Intell. Fuzzy Sys. 36 (2019) 6265–6281. https://doi.org/10.3233/JIFS-182572
[25] M. Khan, F. Smarandache and S. Anis, Theory of Abel Grassmann's Groupoids, ISBN 978-1-59973-347-0 (Educational Publisher Columbus, 2015).
[26] M. Khan, F. Smarandache and T. Aziz, Fuzzy Abel Grassmann's Groupoids, ISBN 978-1-59973-340-1 (Educational Publisher Columbus, 2015).
[27] M. Khan and T. Asif, Characterizations of intra-regular left almost semigroups by their fuzzy ideals, J. Math. Research 2 (2010) 87–96. https://doi.org/10.5539/jmr.v2n3p87
[28] D.V. Kovkov, V.M. Kolbanov and D.A. Molodtsov, Soft sets theory based optimization, J. Comput. Syst. Sci. Int. 46 (6) (2007) 872–880. https://doi.org/10.1134/S1064230707060032
[29] P.K. Maji, R. Biswas and A.R. Roy, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077–1083. https://doi.org/10.1016/S0898-1221(02 )00216-X
[30] P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555–562. https://doi.org/10.1016/S0898-1221(03 )00016-6
[31] D. Molodtsov, Soft set theory – first results, Comput. Math. Appl. 37 (1999) 19–31. https://doi.org/10.1016/S0898-1221(99 )00056-5
[32] Q. Mushtaq and S.M. Yusuf, On LA-semigroups, Aligarh Bull. Math. 8 (1978) 65–70.
[33] Q. Mushtaq and M. Khan, Ideals in left almost semigroups, arXiv:0904.1635v1 [math.GR] (2009) 6 pages.
[34] M. Naseeruddin, Some Studies on Almost Semigroups and Flocks, PhD Thesis (The Aligarh Muslim University India, 1970).
[35] P.V. Protic and N. Stevanovic, On Abel-Grassmann's groupoids (review), in: Proceeding of Mathematics Conference in Pristina (1999) 31–38.
[36] A.R. Roy and P.K. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math. 203 (2007) 412–418. https://doi.org/10.1016/j.cam.2006.04.008
[37] A.S. Sezer, A new approach to LA-semigroup theory via the soft sets, J. Intell. Fuzzy Syst. 26 (2014) 2483–2495. https://doi.org/10.3233/IFS-130918
[38] A.S. Sezer, Certain characterizations of LA semigroups by soft sets, J. Intell. Fuzzy Syst. 27 (2014) 1035–1046. https://doi.org/10.3233/IFS-131064
[39] F. Yousafzai, A. Khan, V. Amjad and A. Zeb, On fuzzy fully regular AG-groupoids, J. Intell. Fuzzy Syst. 26 (2014) 2973–2982. https://doi.org/10.3233/IFS-130963
[40] J. Zhan, W.A. Dudek and J. Neggers, A new soft union set: characterizations of hemirings, Int. J. Mach. Learn. & Cyber. https://doi.org/10.1007/s13042-015-0343-8
[41] X. Ma and J. Zhan, Applications of a new soft set to h-hemiregular hemirings via (M, N)-SI-h-ideals, J. Intell. Fuzzy Syst. 26 (2014) 2515–2525. https://doi.org/10.3233/IFS-130922