Soft Intersection Almost Bi-ideals of Semigroups
DOI:
https://doi.org/10.31181/sa21202415Keywords:
Soft set, semigroup, bi-ideal, soft intersection bi-ideal, soft intersection almost bi-idealAbstract
Soft intersection bi-ideal is a generalization of soft intersection quasi-ideals; and soft intersection quasi-ideal is a generalization of soft intersection left (right) ideal. In this study, as a generalization of nonnull soft intersection bi-ideals of semigroups, we introduced the concept of soft intersection almost bi-ideals and studied its basic properties in detail. By obtaining that if a nonempty set is almost bi-ideal, then its soft characteristic function is soft intersection almost bi-ideal and vice versa, we acquire many interesting relationships between almost bi-ideals and soft intersection almost bi-ideals concerning minimality, primeness, semiprimeness, and strongly primeness.
References
Good, R.A. & Hughes, D.R. (1952). Associated groups for a semigroup. Bulletin of the American Mathematical Society, 58, 624-625.
Steinfeld, O. (1956). Uher die quasi ideals, Von halbgruppend Publication Mathematical Debrecen, 4, 262-275.
Grosek, O. & Satko, L. (1980). A new notion in the theory of semigroup. Semigroup Forum, 20, 233–240.
Bogdanovic, S. (1981). Semigroups in which some bi-ideal is a group. Zbornik radova PMF Novi Sad, 11 (81) 261–266.
Wattanatripop, K., Chinram,, R. & Changphas T. (2018a). Quasi-A-ideals and fuzzy A-ideals in semigroups. Journal of Discrete Mathematical Sciences and Cryptograph, 21,1131–1138.
Kaopusek, N., Kaewnoi, T. & Chinram, R. (2020). On almost interior ideals and weakly almost interior ideals of semigroups. Journal of Discrete Mathematical Sciences and Cryptograph, 23, 773–778.
Iampan, A., Chinram, R. & Petchkaew, P. (2021). A note on almost subsemigroups of semigroups. International Journal of Mathematics and Computer Science, 16 (4), 1623–1629.
Chinram, R. & Nakkhasen, W. (2022).Almost bi-quasi-interior ideals and fuzzy almost bi-quasi-interior ideals of semigroups. Journal of Mathematics and ComputerScience, 26, 128–136.
Gaketem, T. (2022). Almost bi-interior ideal in semigroups and their fuzzifications. European Journal of Pure and Applied Mathematics, 15 (1), 281-289.
Gaketem, T. & Chinram, R. (2023). Almost bi-quasi ideals and their fuzzifcations in semigroups, Annals of the University of Craiova, Mathematics and Computer Science Series, 50 (2), 342-352.
Wattanatripop, K. & Chinram, R., Changphas T. (2018b). Fuzzy almost bi-ideals in semigroups, International Journal of Mathematics and Computer Science, 13, 51–58.
Krailoet, W., Simuen, A., Chinram, R. & Petchkaew, P. (2021). A note on fuzzy almost interior ideals in semigroups. International Journal of Mathematics and Computer Science, 16, 803–808.
Molodtsov, D. (1999.) Soft set theory-first results. Computers and Mathematics with Applications, 37 (4-5), 19–31.
Maji, P.K., Biswas, R. & Roy, A.R. (2003). Soft set theory. Computers and Mathematics with Applications, 45, 555–562.
Pei, D. & Miao, D. (2005). From soft sets to information systems. IEEE International Conference on Granular Computing, 2, 617-621.
Ali, M.I., Feng, F., Liu, X., Min, W.K. & Shabir, M. (2009). On some new operations in soft set theory. Computers Mathematics with Applications, 57 (9), 1547-1553.
Sezgin, A. & Atagün, A.O. (2011). On operations of soft sets. Computers and Mathematics with Applications, 61 (5), 1457-1467.
Feng, F., Jun, YB & Zhao X. (2008). Soft semirings, Computers and Mathematics with Applications, 56, (10), 2621-2628.
Ali, M.I., Shabir, M. & Naz M. (2011). Algebraic structures of soft sets associated with new operations. Computers and Mathematics with Applications, 61 (9), 2647–2654.
Sezgin, A., Ahmad S. & Mehmood A. (2019). A new operation on soft sets: Extended difference of soft sets. Journal of New Theory, 27, 33-42.
Stojanovic, N.S. (2021). A new operation on soft sets: Extended symmetric difference of soft sets. Military Technical Courier, 69 (4), 779-791.
Sezgin, A. & Atagün, A.O. (2023). New soft set operation: Complementary soft binary piecewise plus operation. Matrix Science Mathematic, 7 (2), 125-142.
Sezgin, A. & Aybek, F.N. (2023). New soft set operation: Complementary soft binary piecewise gamma operation. Matrix Science Mathematic (1), 27-45.
Sezgin, A. & Aybek, F.N. Atagün A.O. (2023). New soft set operation: Complementary soft binary piecewise intersection operation. Black Sea Journal of Engineering and Science, 6 (4), 330-346.
Sezgin, A., Aybek, F.N. & Güngör, N.B. (2023). New soft set operation: Complementary soft binary piecewise union operation. Acta Informatica Malaysia, (7)1, 38-53.
Sezgin, A. & Demirci, A.M. (2023). New soft set operation: complementary soft binary piecewise star operation. Ikonion Journal of Mathematics, 5 (2), 24-52.
Sezgin, A. & Yavuz, E. (2023). New soft set operation: Complementary Soft Binary Piecewise Lambda Operation. Sinop University Journal of Natural Sciences, 8 (2), 101-133.
Sezgin, A. & Yavuz, E. (2023). A new soft set operation: Soft binary piecewise symmetric difference operation. Necmettin Erbakan University Journal of Science and Engineering, 5 (2), 189-208.
Sezgin, A. & Çağman, N. (2024). New soft set operation: Complementary soft binary piecewise difference operation. Osmaniye Korkut Ata University Journal of the Institute of Science and Technology, 7 (1), 58-94.
Çağman, N. & Enginoğlu, S. (2010). Soft set theory and uni-int decision making. European Journal of Operational Research, 20, 7 (2), 848-855.
Çağman, N., Çıtak, F., & Aktaş, H. (2012). Soft int-group and its applications to group theory. Neural Computing and Applicatons, 2, 151–158.
Sezer, A.S., Çağman, N., Atagün, A.O., Ali, M.I. & Türkmen E. (2015). Softintersection semigroups, ideals and bi-ideals; a new application on semigroup theory I. Filomat, 29 (5), 917-946.
Sezer, A.S., Çağman, N. & Atagün, A. O. (2014). Soft intersection interior ideals, quasi-ideals and generalized bi-ideals; a new approach to semigroup theory II. Journal of Multiple-valued Logic and Soft Computing, 23 (1-2), 161-207.
Sezgin, A. & Orbay, M. (2022). Analysis of semigroups with soft intersection ideals. Acta Universitatis Sapientiae Mathematica, 14 (1), 166-210.
Mahmood, T., Rehman, Z.U., & Sezgin, A. (2018). Lattice ordered soft near rings. Korean Journal of Mathemtics, 26 (3), 503-517.
Jana, C., Pal, M., Karaaslan, F. & Sezgin, A. (2019). (α, β)-soft intersectional rings and ideals with their applications. New Mathematics and Natural Computation, 15 (2), 333–350.
Muştuoğlu, E., Sezgin, A. & Türk, Z.K. (2016). Some characterizations on soft uni-groups and normal soft uni-groups. International Journal of Computer Applications, 155 (10), 1-8.
Sezer, A.S. Certain Characterizations of LA-semigroups by soft sets. (2014). Journal of Intelligent and Fuzzy Systems, 27 (2), 1035-1046.
Sezer, A.S., Çağman, N. & Atagün, A.O. (2015b). Uni-soft substructures of groups. Annals of Fuzzy Mathematics and Informatics, 9 (2), 235–246.
Özlü, Ş. & Sezgin, A. (2020). Soft covered ideals in semigroups. Acta Universitatis Sapientiae Mathematica, 12 (2), 317-346.
Atagün, A.O. & Sezgin, A. (2018) Soft subnear-rings, soft ıdeals and soft n-subgroups of near-rings. Mathematical Science Letters, 7 (1), 37-42.
Sezgin, A. (2018). A new view on AG-groupoid theory via soft sets for uncertainty modeling. Filomat, 32(8), 2995–3030.
Sezgin, A., Çağman, N. & Atagün, A.O. (2017). A completely new view to soft intersection rings via soft uni-int product. Applied Soft Computing, 54, 366-392.
Sezgin, A., Atagün, A.O., Çağman, N. & Demir H. (2022). On near-rings with soft union ideals and applications. New Mathematics and Natural Computation, 18(2), 495-511.
Rao, M.M.K. (2018). Bi-interior ideals of semigroups. Discussiones Mathematicae General Algebra and Applications 38, 69–78.
Rao, M.M.K. (2018). A study of a generalization of bi-ideal, quasi ideal and interior ideal of semigroup. Mathematica Moravica, 22, 103–115.
Rao, M.M.K. (2020). Left bi-quasi ideals of semigroups. Southeast Asian Bulletin of Mathematics, 44, 369–376.
Rao, M.M.K. (2020). Quasi-interior ideals and weak-interoir ideals. Asia Pacific Journal of Mathematics, 7(21), 1-20.
Baupradist, S., Chemat, B., Palanivel, K. & Chinram R. (2021). Essential ideals and essential fuzzy ideals in semigroups. Journal of Discrete Mathematical Sciences and Cryptography, 24 (1), 223-233.
Sezgin A. & İlgin A. (2024). Soft intersection almost subsemigroups of semigroups. International Journal of Mathematics and Physics, 14 (1): in press.
Sezgin A. & İlgin A. (2024). Soft intersection almost ideals of semigroups, Journal of Innovative Engineering and Natural Science, 4(2): in press.
Pant S., Dagtoros K., Kholil M.I. & Vivas A. (2024). Matrices: Peculiar determinant property. Optimum Scince Journal, 1: 1–7.
Sezgin A. & Çalışıcı H. (2024). A comprehensive study on soft binary piecewise difference operation. Eskişehir Technical University Journal of Science and Technology B - Theoretical Sciences, 12(1), 32-54.
Sezgin A. & Dagtoros K. (2023). Complementary soft binary piecewise symmetric difference operation: A novel soft set operation. Scientific Journal of Mehmet Akif Ersoy University, 6(2), 31-45.
Sezgin A. & Sarıalioğlu M. (2023). New soft set operation: Complementary soft binary piecewise theta operation. Journal of Kadirli Faculty of Applied Sciences, 4(2), 1-33.
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