A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals

Ülkü Develi; Filiz Çıtak

doi:10.53570/jnt.1145507

EN

A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals

Abstract

In recent years, soft sets have become popular in various fields. For this reason, many studies have been carried out in the field of algebra. In this study, soft intersection k-ideals are defined with the help of a semiring, and some algebraic structures are examined. Moreover, the quotient rings are defined by k-semiring. Isomorphism theorems are examined by quotient rings. Finally, some algebraic properties are investigated by defining soft intersection maximal k-ideals.

Keywords

Soft sets, soft k-ideals, soft k-semirings, soft maximal k-ideals, quotient k-semirings

References

L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338–353.
A. Rosenfeld, Fuzzy Groups, Journal of Mathematical Analysis and Application 35 (1971) 512–517.
Z. Pawlak, Rough Sets, International Journal of Computer and Information Science 11 (1982) 341–356.
B. Biswas, S. Nanda, Rough Groups and Rough Subgroups, Bulletin of the Polish Academy of Sciences Mathematics 42 (1994) 251–254.
D. Molodtsov, Soft Set Theory-First Results, Computers and Mathematics with Applications 37 (1999) 19–31.
P. K. Maji, A. R. Roy, An Application of Soft Sets in a Decision Making Problem, Computers and Mathematics with Applications 44 (2002) 1077–1083.
P. K. Maji, R. Biswas, A. R. Roy, Soft Set Theory, Computers and Mathematics with Applications 45 (2003) 555–562.
N. Cağman, S. Enginoğlu, Soft Set Theory and Uni-Int Decision Making, European Journal of Operational Research 207 (2010) 847–855.
A. Aygünoğlu, H. Aygün, Indroduction to Fuzzy Soft Groups, Computers and Mathematics with Applications 58 (2009) 1279–1286.
M. Shabir, M. I. Ali, T. Shaheen, Another Approach to Soft Rough Sets, Knowledge Based System 40 (2013) 72–80.

B. Sun, W. Ma, Soft Fuzzy Rough Sets and its Applications in Decision Making, Artificial Intelligence Review 41 (2014) 67–80.
X. Ma, J. Zhan, M. I. Ali, Application of a Kind of Novel Z-Soft Fuzzy Rough Ideals to Hemirings, Journal of Intelligent and Fuzzy Systems 32 (3) (2017) 1–12.
J. Zhan, M. I. Ali, N. Mehmood, On a Novel Uncertain of Set Model: Z-Soft Fuzzy Rough Set Model and Corresponding Decision Making Methods, Applied Soft Computing 56 (2017) 446–457.
H. Aktaş, N. Çağman, Soft Sets and Soft Groups, Informations Sciences 177 (2007) 2726–2735.
Q. M. Sun, Z. L. Zhang, J. Liu, Soft Sets and Soft Modules, Lecture Notes in Computer Science 5009 (2008) 403–409.
F. Feng, Y. B. Jun, X. Zhao, Soft Semiring, Computers and Mathematics with Applications 10 (2008) 10–16.
Y. B. Jun, K. J. Lee, J. Zhan, Soft p-ideals of Soft BCI-Algebras, Computers and Mathematics with Applications 58 (2009) 2060–2068.
Y. B. Jun, Soft BCK/BCI-Algebras, Computer and Mathematics with Applications 56 (2008) 1408–1413.
K. V. Babitha, J. J. Sunil, Soft Set Relations and Functions, Computers and Mathematics with Applications 60 (7) (2010) 1840–1849.
P. Majumdar, S. K. Samanta, On Soft Mapping, Computers and Mathematics with Applications 60 (9) (2010) 2666–2672.
J. Zhan, Y. B. Jun, Soft BL-Algebras Based on Fuzzy Sets, Computers and Mathematics with Applications 59 (6) (2010) 2037–2046.
O. Kazancı, Ş. Yılmaz, S. Yamak, Soft Sets and Soft BCH-Algebras, Hacettepe Journal of Mathematics and Statistics 39 (2010) 205–217.
U. Acar, F. Koyuncu, B. Tanay, Soft Sets and Soft Rings, Computers and Mathematics with Applications 59 (2010) 3458–3463.
M. I. Ali, M. Shabir, M. Naz, Algebraic Structures of Soft Sets Associated with New Operations, Computers and Mathematics with Applications 61 (9) (2011) 2647–2654.
M. Shabir, M. Naz, On Soft Topological Spaces, Computers and Mathematics with Applications 61 (7) (2011) 1786–1799.
N. Çağman, F. Çıtak, H. Aktaş, Soft int-group and its Applications to Group Theory, Neural Computing and Applications 21 (1) (2012) 151–158.
F. Çıtak, N. Çağman, Soft int-rings and its Algebraic Applications, Journal of Intelligent and Fuzzy Systems 28 (2015) 1225–1233.
T. Mahmood, U. Tariq, Generalized k-ideals in Semirings Using Soft Intersectional Sets, International Journal of Algebra and Statistics 4 (1) (2015), 20–38.
T. Mahmood, A. Waqas, M. A. Rana, Soft Intersectional Ideals in Ternary Semirings, Science International 27 (5) 3929–3934.
C. Jana, M. Pal, Application of New Soft Intersection Set on Groups, Annals of Fuzzy Mathematics and Informatics 11 (6) (2016) 923–944.
F. Çıtak, N. Çağman, Soft k-int-ideals of Semiring and its Algebraic Structures, Annals of Fuzzy Mathematics and Informatics 13 (4) (2017) 531–538.
F. Çıtak, Soft k-uni Ideals of Semirings and its Algebraic Applications, Journal of the Institute of Science and Technology 8 (4) (2018) 281–294.
A. Sezgin, Characterizations of Certain Classes of Semigroups via Soft Intersection Ideals, Italian Journal of Pure and Applied Mathematics 38 (1) (2017) 1–38.
A. Sezgin, N. Çağman, F. Çıtak, α-inclusions Applied to Group Theory via Soft and Logic, Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 68 (1) (2018) 334–352.
M. Tuncay, A. Sezgin, Soft Union Ring and its Applications to Ring Theory, International Journal of Computer Application 151 (9) (2016) 7–13.
T. Mahmood, A Novel Approach towards Bipolar Soft Sets and Their Applications, Journal of Mathematics Article ID 4690808 (2020) 11 pages.
T. Aydın, S. Enginoğlu, Interval-Valued Intuitionistic Fuzzy Parameterized Interval-Valued Intuitionistic Fuzzy Soft Matrices and Their Application to Performance-Based Value Assignment to Noise-Removal Filters, Computational and Applied Mathematics 41 (2022) Article Number 192.
S. Memiş, S. Enginoğlu, U. Erkan, Fuzzy Parameterized Fuzzy Soft k-nearest Neighbor Classifier, Neurocomputing 500 (2022) 351–378.
Z. P. Parmaksız, B. Arslan, S. Memiş, S. Enginoğlu, Diagnosing COVID-19, Prioritizing Treatment, and Planning Vaccination Priority via Fuzzy Parameterized Fuzzy Soft Matrices, Journal of New Theory (39) (2022) 54–83.
F. Karaaslan, N. Çağman, Bipolar Soft Rough Sets and Their Applications in Decision Making, Afrika Matematika 29 (2018) 823-–839.
J. S. Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science, Addison and Wesley Longman, Edinburgh Gate Harlow, 1992.
Y. B. Chun, H. S. Kim, A Study on the Structure of Semiring, Journal of the Natural Science Research Institute 11 (1983) 69–74.
D. R. La Torre, On h-ideals and k-ideals in Hemirings, Publicationes Mathematicae Debrecen 12 (1965) 219–226.
Y. B. Chun, H. S. Kim, Isomorphism Theorem in k-semiring, Yonsei Nonchong 21 (1985) 1–9.
O. Atagün, A. Sezgin, Int-Soft Substructures of Groups and Semirings, Applied Mathematics and Information Science 11 (1) (2017) 105–113.
Ö. Gölbaşı, E. Koç, Generalized Derivations on Lie ideals in Prime Rings, Turkish Journal of Mathematics 35 (1) (2011) 23–28.
Albayrak, D. Yeşil, Closed Lie Ideals of Prime Rings with Generalized α-Derivations, International Journal of Mathematics Trends and Technology 65 (7) (2019) 101–109.
Ö. Gölbaşı, Multiplicative Generalized Derivations on Ideals in Semiprime Rings, Mathematica Slovaca 66 (6) (2016) 1285–1296.
H. Karahan, N. Aydın, D. Yeşil, Multiplicative (Generalised) (α,α)-Derivations of Semiprime Rings, Journal of New Theory (39) (2022) 42–53.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Ülkü Develi This is me
0000-0002-7320-8537
Türkiye

Filiz Çıtak ^*
0000-0003-1784-1845
Türkiye

Publication Date

December 31, 2022

Submission Date

July 19, 2022

Acceptance Date

November 3, 2022

Published in Issue

Year 2022 Number: 41

DOI

https://doi.org/10.53570/jnt.1145507

IZ

https://izlik.org/JA87FF69NS

APA

Develi, Ü., & Çıtak, F. (2022). A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals. Journal of New Theory, 41, 18-34. https://doi.org/10.53570/jnt.1145507

AMA

1.Develi Ü, Çıtak F. A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals. JNT. 2022;(41):18-34. doi:10.53570/jnt.1145507

Chicago

Develi, Ülkü, and Filiz Çıtak. 2022. “A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals”. Journal of New Theory, nos. 41: 18-34. https://doi.org/10.53570/jnt.1145507.

EndNote

Develi Ü, Çıtak F (December 1, 2022) A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals. Journal of New Theory 41 18–34.

IEEE

[1]Ü. Develi and F. Çıtak, “A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals”, JNT, no. 41, pp. 18–34, Dec. 2022, doi: 10.53570/jnt.1145507.

ISNAD

Develi, Ülkü - Çıtak, Filiz. “A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals”. Journal of New Theory. 41 (December 1, 2022): 18-34. https://doi.org/10.53570/jnt.1145507.

JAMA

1.Develi Ü, Çıtak F. A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals. JNT. 2022;:18–34.

MLA

Develi, Ülkü, and Filiz Çıtak. “A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals”. Journal of New Theory, no. 41, Dec. 2022, pp. 18-34, doi:10.53570/jnt.1145507.

Vancouver

1.Ülkü Develi, Filiz Çıtak. A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals. JNT. 2022 Dec. 1;(41):18-34. doi:10.53570/jnt.1145507