Üst Yaklaşım Sayılarının Öncül Komşuluklarla Elde Edilmesi

Year 2018, Volume: 9 Issue: 2, 151 - 156, 12.06.2018

Sadık Bayhan , Nazlı Tuğçe Baytaroğlu

https://doi.org/10.29048/makufebed.416745

Abstract

Kaba küme teorisi belirsizliğe matematiksel bir
yaklaşım olarak düşünülmüş; yararlı ve etkili bir araç olarak çeşitli bilim
alanlarında kullanılmaktadır. Lineer cebirde yer alan lineer bağımlılık, lineer
bağımsızlık, taban, rank gibi temel kavramlarının genelleştirilmesi Matroid
teorisiyle olanaklı olmuştur. Bu çalışmada 
bir bağıntıdan oluşturulan matroid için öncül komşuluklara dayalı üst
yaklaşım sayısal fonksiyonu tanımlanarak genelleştirilmiş kaba kümelerle ilişkileri
incelenmiştir.

Keywords

Kaba küme, Matroid, Alt yaklaşım, Üst yaklaşım

Obtaining Upper Approximation Numbers with Predecessor Neighborhoods

Abstract

Rough set theory is considered as a mathematical approach to uncertainty
as a useful and effective tool in various fields of science. The generalization
of the basic concepts such as linear dependence, linear independence, base and
rank in linear algebra is possible by matroid theory. In this study, the upper
approximation number function based on predecessor neighborhoods will be
defined for the matroid generated from a relation and generalized rough sets
associations will be examined.

Keywords

Rough set, Matroid, Lower approximation, Upper approximation

References

• Oxley, J. (1992). Matroid Theory, Oxford University Press, New York.
• Pawlak, Z. (1982). Rough sets, International Journal of Computer & Information Sciences 11 (5): 341–356.
• Whitney, H. (1935). On the abstract properties of linear dependence,, Amer. J. Math. 57: 509-533.
• Yao, Y. Y. (1996). Two views of the theory of rough sets in finite universes, International Journal of Approximate Reasoning. 15 (4): 291–317.
• Yao, Y. Y. (1998). Constructive and algebraic methods of the theory of rough sets, Information Sciences 109: 21–47.
• Yao , Y. Y. (1998). Relational interpretational of neighborhood operators and rough set approximation operators, Information Sciences 111: 239–259.
• Zhu, W. (2007). Generalized rough sets based on relations, Information Sciences. 177: 4997-5011.
• Zhu, W. (2009). Relationship between generalized rough sets based on binary relation and covering, Information Sciences 179: 210–225.
• Zhu, W., Wang, S. (2011). Matroidal approaches to generalized rough sets based on relations, International Journal of Machine Learning and Cybernetics 2: 273– 279.