Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals

Abstract

Abstract-The focus of this paper is to propose a new notion of neutrosophic crisp sets via neutrosophic crisp ideals and to study some basic operations and results in neutrosophic crisp topological spaces. Also, neutrosophic crisp L-openness and neutrosophic crisp Lcontinuity are considered as a generalizations for a crisp and fuzzy concepts. Relationships between the above new neutrosophic crisp notions and the other relevant classes are investigated. Finally, we define and study two different types of neutrosophic crisp functions.

Correlation of Neutrosophic Sets in Probability Spaces

“…We recollect some relevant basic preliminaries, and in particular, the work of Smarandache in [11,12,13,14,15] and Salama et al [1,2,3,4,5,6,7,16,17,18].…”

“…Smarandache [11,12,13,14,15] introduced another concept of imprecise sets called neutrosophic sets. Salama et al [1,2,3,4,5,6,7,16,17,18] introduced and studied the operations on neutrosophic sets. In statistical analysis, the correlation coefficient plays an important role in measuring the strength of the linear relationship between two variables.…”

The Information System by Uncertainty Theory

“…Established by Florentin smarandache in 1980 ,neurosophy was presented as the study of the origin , nature , and scope of neutralities, as well as their interactions with different ideational spectra The main Idea was to consider an entity ,"A" in relation to its opposite "Non-A , and to that which is neither "A" nor Non -A ", denoted by " Neut-A" .and from on, neutrosophy became the basis of neutrosophic set theory, neutrosophic logic , neutrosophic probability, and neutrosophic statistics . In 2012 neutrosophic crisp sets have been investigated by Salma et,al [8], [9], [10], [11], [12], [13].…”

Proposed Model for Evaluating Information Systems Quality Based on Single Valued Triangular Neutrosophic Numbers

“…The concept of neutrosophic set introduced a generalization of fuzzy set and intuitionistic fuzzy set [22,32] and it is characterized by its membership function and non-membership function between 0 and 1. In the neutrosophic set, the membership function independently indicates: Truthmembership-membership degree, false membership-membership degree, and indeterminacy-membership degree.…”