Author

# H. M. Abu-Donia

Other affiliations: Shaqra University

Bio: H. M. Abu-Donia is an academic researcher from Zagazig University. The author has contributed to research in topics: Metric space & Rough set. The author has an hindex of 7, co-authored 28 publications receiving 208 citations. Previous affiliations of H. M. Abu-Donia include Shaqra University.

Topics: Metric space, Rough set, Fixed-point theorem, Mathematics, Fixed point

##### Papers

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TL;DR: This paper presents new types of rough set approximations using multi knowledge base, that is, family of finite number of (reflexive, tolerance, dominance, equivalence) relations by two ways.

Abstract: Rough set theory is an important technique in knowledge discovery in databases. In covering based rough sets, many types of rough set models are established in recent years. This paper presents new types of rough set approximations using multi knowledge base, that is, family of finite number of (reflexive, tolerance, dominance, equivalence) relations by two ways. Properties and applications of these approximation operators are studied and many examples are given.

67 citations

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TL;DR: This paper generalizes three types of lower and upper approximations of any set with respect to any relation based on right neighborhood into two ways by using a finite number of any binary relations.

Abstract: In this paper, we discuss three types of lower and upper approximations of any set with respect to any relation based on right neighborhood. We generalize these three types of approximations into two ways by using a finite number of any binary relations. The first way based on the intersection of the right neighborhoods for a family of binary relations, the second based on the union and intersection of lower and upper approximations of a set according to a family of binary relations {R"i:i=1,2,...,n}. Also, we make a comparison between these types in tables.

43 citations

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TL;DR: In this article, the authors discussed some common fixed point theorems for fuzzy mappings in metric space under ϕ -contraction condition, which are related to the fuzzy form of Hausdorff metric.

Abstract: Some common fixed point theorems for multi-valued mappings under ϕ -contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for ϕ -contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194–204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191–207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566–9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under ϕ -contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding e ∞ -space [El-Naschie MS. On the unification of the fundamental forces and complex time in the e ∞ -space. Chaos, Solitons & Fractals 2000;11:1149–62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons & Fractals 2002;13:1935–45].

29 citations

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TL;DR: Parlak's rough set theory is extended to a topological model where the set approximations are defined using the topological notion @d@b-open sets and it is proved that some of the properties of Pawlak'srough set model are special instances of those of topological generalizations.

24 citations

01 Jan 2005

TL;DR: In this paper, the authors introduce some classes of sets in a bitopological space (X, τ 1, τ 2 ) and show that some of these classes are infra topologies and some are supra topologies.

Abstract: In this paper we introduce some classes of sets in a bitopological space (X, τ 1 , τ 2 ). We show that some of these classes are infra topologies and some are supra topologies. Also, we use these classes to introduce new bitopological properties and new types of continuous functions between bitopological spaces. We prove that some of the introduced bitopological separation properties are preserved under some types of continuous functions.

18 citations

##### Cited by

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TL;DR: A framework for the study of covering based rough set approximations is proposed and three equivalent formulations of the classical rough sets are examined by using equivalence relations, partitions, and @s-algebras.

440 citations

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TL;DR: An extended rough set model, called as composite rough sets, is presented, and a novel matrix-based method for fast updating approximations is proposed in dynamic composite information systems.

160 citations

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TL;DR: A new approach to multiple criteria group decision making problems, based on variable precision multigranulation fuzzy decision-theoretic rough set over two universes, and a cost-based method for sorting among all alternatives of group decision-making problems are established.

155 citations

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TL;DR: The proposed models not only enrich the theory of multigranulation rough set but also make a tentative to provide a new perspective for multiple criteria group decision making with uncertainty.

Abstract: The original Pawlaks rough set approach based on indiscernibility relation (single granularity) has been extended to multigranulation rough set structure in the recent years. Multigranulation rough set approach has become a flouring research direction in rough set theory. This paper considers rough approximation of a fuzzy concept under the framework of multigranulation over two different universes of discourse, i.e., multigranulation fuzzy rough set models over two universes. We present three types of multigranulation fuzzy rough set over two universes by the constructive approach, respectively. Some interesting properties of the proposed models are discussed and also the interrelationships between the proposed models and the existing rough set models are given. We then propose a new approach to a kind of multiple criteria group decision making problem based on multigranulation fuzzy rough set model over two universes. The decision rules and algorithm of the proposed method are given and an example of handling multiple criteria group decision making problem of clothes ranking illustrates this approach. The main contribution of this paper is twofold. One is to establish the multigranulation fuzzy rough set theory over two universes. Another is to try presenting a new approach to multiple criteria group decision making based on multigranulation fuzzy rough set over two universes. The proposed models not only enrich the theory of multigranulation rough set but also make a tentative to provide a new perspective for multiple criteria group decision making with uncertainty.

149 citations