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This article explores the interconnections among the single-valued neutrosophic grill, single-valued neutrosophic primal and their stratification, uncovering their fundamental characteristics and correlated findings. By introducing the notion of a single-valued neutrosophic primal, a broader framework including the fuzzy primal and intuitionistic fuzzy primal is established. Additionally, the concept of a single-valued neutrosophic open local function for a single-valued neutrosophic topological space is presented. We introduce an operator based on a single-valued neutrosophic primal, illustrating that the single-valued neutrosophic primal topology is finer than the single-valued neutrosophic topology. Lastly, the concept of single-valued neutrosophic open compatibility between the single-valued neutrosophic primal and single-valued neutrosophic topologies is introduced, along with the establishment of several equivalent conditions related to this notion. [ABSTRACT FROM AUTHOR]

This paper aims to mark out new terms of single-valued neutrosophic notions in a Šostak sense called single-valued neutrosophic semi-closure spaces. To achieve this, notions such as β £ -closure operators and β £ -interior operators are first defined. More precisely, these proposed contributions involve different terms of single-valued neutrosophic continuous mappings called single-valued neutrosophic (almost β £ , faintly β £ , weakly β £ ) and β £ -continuous. Finally, for the purpose of symmetry, we define the single-valued neutrosophic upper, single-valued neutrosophic lower and single-valued neutrosophic boundary sets of a rough single-valued neutrosophic set α n in a single-valued neutrosophic approximation space (F ˜ , δ) . Based on α n and δ , we also introduce the single-valued neutrosophic approximation interior operator int α n δ and the single-valued neutrosophic approximation closure operator Cl α n δ . [ABSTRACT FROM AUTHOR]

This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal- R i (r- S V N I R i , for short), where i = { 0 , 1 , 2 , 3 } , and r-single valued neutrosophic ideal- T j (r- S V N I T j , for short), where j = { 1 , 2 , 2 1 2 , 3 , 4 } , are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied. [ABSTRACT FROM AUTHOR]

This paper aims to introduce the notion of r-single-valued neutrosophic connected sets in single-valued neutrosophic topological spaces, which is considered as a generalization of r-connected sets in Šostak's sense and r-connected sets in intuitionistic fuzzy topological spaces. In addition, it introduces the concept of r-single-valued neutrosophic separated and obtains some of its basic properties. It also tries to show that every r-single-valued neutrosophic component in single-valued neutrosophic topological spaces is an r-single-valued neutrosophic component in the stratification of it. Finally, for the purpose of symmetry, it defines the so-called single-valued neutrosophic relations. [ABSTRACT FROM AUTHOR]

Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion of single-valued neutrosophic ideals sets in Šostak's sense, which is considered as a generalization of fuzzy ideals in Šostak's sense and intuitionistic fuzzy ideals. The concept of single-valued neutrosophic ideal open local function is also introduced for a single-valued neutrosophic topological space. The basic structure, especially a basis for such generated single-valued neutrosophic topologies and several relations between different single-valued neutrosophic ideals and single-valued neutrosophic topologies, are also studied here. Finally, for the purpose of symmetry, we also define the so-called single-valued neutrosophic relations. [ABSTRACT FROM AUTHOR]