Yazar "Ozcan, Abdullah Fatih" seçeneğine göre listele

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    Actions of R-module groupoids
    (Univ Nis, Fac Sci Math, 2023) Ozcan, Abdullah Fatih; Icen, Ilhan
    Let R be a ring, 1R be the identity of ring R and N be an R-module on R. In this work, we are going to give a new definition that it is called an action of R-module groupoids. First, we are going to give the definition of the action of the R-module groupoids on the R-module N. Then we obtained a new category RMGpdOp(Omega) of actions of Omega on R-modules. We also find that there is a groupoid Omega (sic) N on N. Omega (sic) N is called action R-module groupoid. Finally, we prove that the category RMGpdOp(Omega) of actions of R-module groupoids is equivalent to RMGpdCov(Omega) of coverings of R-module groupoids.
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    From rough categories to rough groupoids
    (Tubitak Scientific & Technological Research Council Turkey, 2025) Beydagi, Mehmet Mustafa; Ozcan, Abdullah Fatih; Icen, Ilhan
    In this study, we introduce the concepts of rough category and rough groupoid by combining the concepts of category theory and groupoid with rough set theory. We present some properties and examples of these concepts, which are discussed for the first time. Additionally, by defining a rough functor among the rough categories, the category of rough categories were created. Moreover, rough groupoid homomorphism, rough action groupoid, and category of the rough groupoids have been examined algebraically and introduced to the literature.
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    Soft Sets and Soft Topology on Nearness Approximation Spaces
    (Univ Nis, Fac Sci Math, 2017) Tasbozan, Hatice; Icen, Ilhan; Bagirmaz, Nurettin; Ozcan, Abdullah Fatih
    Near set theory presents a fundamental basis for observation, comparison and classification of perceptual granules. Soft set theory is proposed as a general framework to model vagueness. The purpose of this paper is to combine these two theories in what are known near soft sets in defining near soft topology based on a nearness approximation space.