Geometric Lattice Structure of Covering-Based Rough Sets through Matroids
المؤلفون المشاركون
المصدر
Journal of Applied Mathematics
العدد
المجلد 2012، العدد 2012 (31 ديسمبر/كانون الأول 2012)، ص ص. 1-25، 25ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2012-12-18
دولة النشر
مصر
عدد الصفحات
25
التخصصات الرئيسية
الملخص EN
Covering-based rough set theory is a useful tool to deal with inexact, uncertain, or vague knowledge in information systems.
Geometric lattice has been widely used in diverse fields, especially search algorithm design, which plays an important role in covering reductions.
In this paper, we construct three geometric lattice structures of covering-based rough sets through matroids and study the relationship among them.
First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by a covering.
Then its characteristics, such as atoms, modular elements, and modular pairs, are studied.
We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets.
Second, we present three sufficient and necessary conditions for two types of covering upper approximation operators to be closure operators of matroids.
We also represent two types of matroids through closure axioms and then obtain two geometric lattice structures of covering-based rough sets.
Third, we study the relationship among these three geometric lattice structures.
Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices.
In a word, this work points out an interesting view, namely, geometric lattice, to study covering-based rough sets.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Huang, Aiping& Zhu, William. 2012. Geometric Lattice Structure of Covering-Based Rough Sets through Matroids. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-993053
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Huang, Aiping& Zhu, William. Geometric Lattice Structure of Covering-Based Rough Sets through Matroids. Journal of Applied Mathematics No. 2012 (2012), pp.1-25.
https://search.emarefa.net/detail/BIM-993053
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Huang, Aiping& Zhu, William. Geometric Lattice Structure of Covering-Based Rough Sets through Matroids. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-993053
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-993053
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
تقوم هذه الخدمة بالتحقق من التشابه أو الانتحال في الأبحاث والمقالات العلمية والأطروحات الجامعية والكتب والأبحاث باللغة العربية، وتحديد درجة التشابه أو أصالة الأعمال البحثية وحماية ملكيتها الفكرية. تعرف اكثر