On Single-Valued Neutrosophic Ideals in Šostak Sense

Abstract

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.

Single-Valued Neutro Hyper BCK-Subalgebras

“…is concept handles problems involving imprecise, indeterminacy, and inconsistent data and describes an important role in the modelling of unsure hypernetworks in all sciences. Recently, due to the importance of these subjects, by combining the neutrosophic sets and (hyper) BCK-algebras, some researchers worked in more branches of neutrosophic (hyper) BCK-algebras such as MBJ-neutrosophic hyper BCK-ideals in hyper BCK-algebras, an approach to BMBJ-neutrosophic hyper BCK-ideals of hyper BCK-algebras, structures on doubt neutrosophic ideals of (BCK/BCI)-algebras under (S, T)-norms, BMBJ-neutrosophic subalgebras in (BCI/BCK)-algebras, MBJ-neutrosophic ideals of (BCK/BCI)-algebras, implicative neutrosophic quadruple BCK-algebras and ideals, neutrosophic hyper BCK-ideals, implicative neutrosophic quadruple BCK-algebras and ideals, bipolar-valued fuzzy soft hyper BCK ideals in hyper BCKalgebras, single-valued neutrosophic ideals in Sostak's sense, and multipolar intuitionistic fuzzy hyper BCK-ideals in hyper BCK-algebras [6][7][8][9][10][11][12][13][14][15][16]. Recently, a novel concept of neutrosophy theory titled neutro (hyper) algebra as development of classical (hyper) algebra and partial (hyper) algebra is introduced by Smarandache [17].…”

A New Multi-Sensor Fusion Target Recognition Method Based on Complementarity Analysis and Neutrosophic Set

“…Therefore, Ye [38] introduced a simplified neutrosophic set (SNS), which limits the true value, uncertainty, and false membership function to the actual standard interval [0, 1]. In addition, SNS also includes single value neutrosophic set (SVNS) [39][40][41] and interval neutrosophic set (INS) [42].…”

Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis

“…In this way, people's hands are comparatively free, and machines are more intelligent and comprehensive; however, this kind of full automation greatly increases the probability of mechanical equipment failure as well [6][7][8][9][10][11]. If the mechanical equipment has faults, the quality of the manufactured products will not pass the standard, which will affect the economic benefits of the enterprise [12][13][14][15]; additionally, it will bring potential danger to personal safety [16][17][18][19]. In order to solve this problem, it is necessary to carry out fault diagnosis on mechanical equipment on a regular basis to detect and repair mechanical equipment and ensure its normal operation.…”