Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft covering approximation space and soft covering rough approximation operators and present their basic properties. We show that a new type of the soft covering upper approximation operator is smaller than soft upper approximation operator. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our data are 78 patients from Selçuk University Meram Medicine Faculty.
Many researchers defined some basic notions on soft topology and studied many properties. In this paper, we define soft regular generalized closed and open sets in soft topological spaces and studied their some properties. We introduce these concepts which are defined over an initial universe with a fixed set of parameters. We investigate behavior relative to union, intersection and soft subspaces of soft regular generalized closed sets. We show that every soft generalized closed set is soft regular generalized closed. Also, we investigate many basic properties of these concepts.
In this work we define soft covering based rough set and present its related properties. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our datas are 56 patients from Selcuk University Meram Medicine Faculty.
In this paper, we introduce soft A-sets and soft B-sets in soft topological spaces which are defined over an initial universe with a fixed set of parameters and discuss their relationships with each other and other soft open sets like soft semiopen sets, soft preopen sets and soft α-open sets with the help of counterexamples. We also introduce the concepts of soft A-continuous functions and soft B-continuous functions. Finally, we obtain decompositions of soft continuity: f pu is a soft continuous function if and only if it is both soft α-continuous and soft A-continuous and also f pu is a soft continuous function if and only if it is both soft precontinuous and soft B-continuous.
In this paper, we define soft generalized preregular closed and open sets in soft topological spaces which are defined over an initial universe with a fixed set of parameters and we investigate some basic properties of these concepts. Also we discuss their relationships with different types of subsets of soft topological spaces with the help of counterexamples.
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