Abstract
Bu çalışmada, bir R halkası
için T-intuitionistic fuzzy -althalka kavramı yeniden tanımlandı ve bazı yeni
özellikleri elde edildi. Bu yapıların bazı temel özellikleri çalışıldı.
Özellikle, idempotent özelliği altında, nin bir alt kümesi ile tanımlı bir intuitionistic fuzzy
kümenin T-intuitionistic -althalka olması için gerek yeter koşulun H alt kümesinin
bir -althalka olması gerektiği gösterilmiştir. Bu özellik
yardımı ile bir halkanın, sürekli t-norm ile tanımlanmış T-intuitionistic
fuzzy -alt halkası için, bir hiperhalkanın faktör halkasının yine
bir T-intuitionistic fuzzy -halka olduğu çalışmanın ana teoremi olarak verilmiştir.
References
- [1] Atanassov K.T., Intuitionistic Fuzzy Sets, VII ITKR's Session, Sofia, June (1983) [2] Atanassov K.T., Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20, (1986) p.87-96. [3] Davvaz B., Fuzzy groups, Fuzzy Sets and System (1999),101, 191-195. [4] Davvaz B., Fuzzy -submodules, Fuzzy Sets and System (2001),117, 477-484. [5] Davvaz B., T-fuzzy -subrings of an -ring, The Journal of Fuzzy Mathematics, (2003), 11, 215-224. 127-132 [6] Klement E.P., Mesiar R., and Pap E., Triangular Norms, Kluwer Academic Publishers, Dordrecht, (2000). [7] Marty F., Sur une generalization de la notion de groupe, congres Math. Skandinaves, Stockholm, (1934), 45-49. [8] Vougiouklis T., On -ring and -representations, Discrete Math, (1999),10, 615-620. [9] Vougiouklis T.,The Fundamental relation in hyperrings.The general hyperfield,in Algebraic Hyperstructures and Applications, WorldSci. Pulb.,Teaneck, NJ (1990), 203-211. [10] Zadeh L.A., Fuzzy Sets, Information and Control, 8, (1965), p. 338-353.
Abstract
This research redefined
T-intuitionistic fuzzy -subring of a ring R and obtained some new related
properties. Some of their fundamental relation properties were studied.
Especially, under idempotent property, it is given that any IFS defined by a subset of is T-IF -subring of a ring
if and only if H is a -subring of the
ring. Using this property, the main theorem was given as for a
T-intuitionistic fuzzy -subring of any
ring with continuous t-norm, a factor subring formed using the hyperring is a
T-intuitionistic -subring.
References
- [1] Atanassov K.T., Intuitionistic Fuzzy Sets, VII ITKR's Session, Sofia, June (1983) [2] Atanassov K.T., Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20, (1986) p.87-96. [3] Davvaz B., Fuzzy groups, Fuzzy Sets and System (1999),101, 191-195. [4] Davvaz B., Fuzzy -submodules, Fuzzy Sets and System (2001),117, 477-484. [5] Davvaz B., T-fuzzy -subrings of an -ring, The Journal of Fuzzy Mathematics, (2003), 11, 215-224. 127-132 [6] Klement E.P., Mesiar R., and Pap E., Triangular Norms, Kluwer Academic Publishers, Dordrecht, (2000). [7] Marty F., Sur une generalization de la notion de groupe, congres Math. Skandinaves, Stockholm, (1934), 45-49. [8] Vougiouklis T., On -ring and -representations, Discrete Math, (1999),10, 615-620. [9] Vougiouklis T.,The Fundamental relation in hyperrings.The general hyperfield,in Algebraic Hyperstructures and Applications, WorldSci. Pulb.,Teaneck, NJ (1990), 203-211. [10] Zadeh L.A., Fuzzy Sets, Information and Control, 8, (1965), p. 338-353.
Details
| Subjects | Mathematical Sciences |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 1, 2017 |
| Submission Date | April 19, 2017 |
| Acceptance Date | April 25, 2017 |
| Published in Issue | Year 2017 |
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