Abstract
Bu makalede, daha önceden çalışılmış olan bulanık kavramını kullanarak, sırasıyla bir bulanık halka, bulanık olmayan halkanın çekirdeği ve alt halka kavramını tanımlanmıştır. Ayrıca, bu çekirdeklerin sıradan cebirsel anlamda halkalar ile aynı özelliklere sahip olduğunu göstermenin yanı sıra, bulanık halkalar ve bulanık olmayan halkalar hakkında temel bilgiler verilmektedir. Çalışmanın giriş kısmında asıl konumuz olan Bulanık ve Bulanık Olmayan Halkaların Çekirdeği ile ilgili temel oluşturan; klasik grup ve halkalar ile ilgili tanımların yanı sıra bulanık mantığın tanımı verilmiştir. Ana kısımda ise konumuz gerekli tanımlamalar ve teoremler verilerek ispatlanmıştır. Ayrıca konu ile ilgili gerekli örnekler verilerek konu açıklanmıştır.
References
- Das P.S. Fuzzy groups and level subgroups. Journal of mathematical analysis and applications, 84:1 264-269, 1981.
- Palaniappan N., Naganathan S., Arjunan K. A study on intuitionistic L-fuzzy subgroups. Applied Mathematical Sciences, 3:53 2619-2624, 2009.
- Mukherjee N.P., Bhattacharya P. Fuzzy groups: some group-theoretic analogs. Information sciences, 39:3 247-267, 1986.
- Abobala M. On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings. Neutrosophic Sets and Systems, 2021.
- Abobala M. A Study of Nil Ideals and Kothe’s Conjecture in Neutrosophic Rings. International Journal of Mathematics and Mathematical Sciences, 2021.
- Gupta K.C., Sarma B.K. Nilpotent fuzzy groups. Fuzzy sets and systems, 101:1 167-176, 1999.
- Liu W.J. Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems, 8:2 133-139, 1982.
- Mukherjee N.P. Bhattacharya P. Fuzzy groups: some group-theoretic analogs. Information sciences, 39:3 247-267, 1986.
- Malik D.S., Mordeson J.N., Nair P.S. Fuzzy normal subgroups in fuzzy subgroups. Journal of the Korean Mathematical Society, 29:1 1-8, 1982.
- Šešelja B., Tepavcevic A. Fuzzy groups and collections of subgroups. Fuzzy Sets and Systems, 83:1 85-91, 1996.
- Yuan X., Lee E.S. Fuzzy Group Based on Fuzzy Binary Operation. Computers Math. Appl., 47 631-641, 2004.
- Mordeson J.N., Malik D.S. Fuzzy commutative algebra, World scientific, 1998.
- Ahmad K., Bal M., Aswad M. The Kernel of Fuzzy and Anti-Fuzzy Groups. Journal of Neutrosophic and Fuzzy Systems, 2022.
Abstract
In this article, using the previously studied fuzzy concept, the concept of a fuzzy ring, the kernel of the anti-fuzzy ring, and the subring are defined, respectively. We have shown that these kernels have the same properties as rings in the ordinary algebraic sense. Also, basic information about fuzzy rings and anti-fuzzy rings is given. In the introductory part of the study, our main topic, Fuzzy and anti-fuzzy ring kernel, which forms the basis; definitions of fuzzy logic are given as well as definitions of classical groups and rings. In the main part, our subject has been proved by giving necessary definitions and theorems. In addition, the subject is explained by giving necessary examples related to the subject.
References
- Das P.S. Fuzzy groups and level subgroups. Journal of mathematical analysis and applications, 84:1 264-269, 1981.
- Palaniappan N., Naganathan S., Arjunan K. A study on intuitionistic L-fuzzy subgroups. Applied Mathematical Sciences, 3:53 2619-2624, 2009.
- Mukherjee N.P., Bhattacharya P. Fuzzy groups: some group-theoretic analogs. Information sciences, 39:3 247-267, 1986.
- Abobala M. On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings. Neutrosophic Sets and Systems, 2021.
- Abobala M. A Study of Nil Ideals and Kothe’s Conjecture in Neutrosophic Rings. International Journal of Mathematics and Mathematical Sciences, 2021.
- Gupta K.C., Sarma B.K. Nilpotent fuzzy groups. Fuzzy sets and systems, 101:1 167-176, 1999.
- Liu W.J. Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems, 8:2 133-139, 1982.
- Mukherjee N.P. Bhattacharya P. Fuzzy groups: some group-theoretic analogs. Information sciences, 39:3 247-267, 1986.
- Malik D.S., Mordeson J.N., Nair P.S. Fuzzy normal subgroups in fuzzy subgroups. Journal of the Korean Mathematical Society, 29:1 1-8, 1982.
- Šešelja B., Tepavcevic A. Fuzzy groups and collections of subgroups. Fuzzy Sets and Systems, 83:1 85-91, 1996.
- Yuan X., Lee E.S. Fuzzy Group Based on Fuzzy Binary Operation. Computers Math. Appl., 47 631-641, 2004.
- Mordeson J.N., Malik D.S. Fuzzy commutative algebra, World scientific, 1998.
- Ahmad K., Bal M., Aswad M. The Kernel of Fuzzy and Anti-Fuzzy Groups. Journal of Neutrosophic and Fuzzy Systems, 2022.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Article |
| Authors | |
| Publication Date | June 1, 2022 |
| Published in Issue | Year 2022 |