International Journal of Neutrosophic Science

In this paper, the definition of neutrosophic thick function and its integral are introduced. The main objective is defining a differential linear equation based on the thick function and finding solutions for this equation.

  In this paper, we generalize the classical Erlang service queueing model, which has determined and crisp parameters to neutrosophic Erlang service queueing model which is more accurate because it opens the ability to deal with imprecise and incomplete knowledge of parameters. We have used the neutrosophic statistical interval method introduced by F. Smarandache to describe the parameters of the Erlang service queueing model and to find the neutrosophic performance measures. 

In a recent paper, we describe a model of quantum communication based on combining consciousness experiment and entanglement, which can serve as impetus to stop 5G-network-caused diseases. Therefore, in this paper we consider superluminal physics and superluminal communication as a bridge or intermediate way between subluminal physics and action-at-a-distance (AAAD) physics, especially from neutrosophic logic perspective. Although several ways have been proposed to bring such a superluminal communication into reality, such as Telluric wave or Telepathy analog of Horejev and Baburin, here we also review two possibilities: quaternion communication and also quantum communication based on quantum noise. Further research is recommended in the direction outlined herein. Aim of this paper: We discuss possibilities to go beyond 4G and 5G network, and avoid the unnecessary numerous health/diseases problems caused by massive 5G network. Contribution: We consider quaternionic communication and quantum communication based on quantum noise, which are largely unnoticed in literature. Limitation: We don’t provide scheme for operationalization, except what we have provided in other paper.

In this paper, we introduce the concept of AH-subspace of a neutrosophic vector space and AHS-linear transformations. We study elementary properties of these concepts such as Kernel, AH-Quotient, and dimension.

In this paper, we initially introduce a novel type of matrix representation of Plithogenic Crisp/Fuzzy/Intuitionistic/Neutrosophic Hypersoft Set named as Plithogenic Crisp/Fuzzy/Intuitionistic/Neutrosophic Hypersoft Matrix, which is generated by multiple parallel sheets of matrices. Furthermore, these parallel sheets are representing parallel universes or parallel realities (a combination of attributes and sub-attributes w.r.t. subjects). We represent cross-sectional cuts of these hyper-soft matrices as parallel sheets (images of the expanded universe). Later, we utilize these Hypersoft matrices to formulate Plithogenic Subjective Crisp/Fuzzy/Intuitionistic/Neutrosophic Hyper-Super-Soft Matrix. These matrices are framed by the generalization of Whole Hyper-Soft Set to Subjective Whole Hyper-Soft Set and then their representation in such hyper-super-soft-matrix (parallel sheets of matrices) whose elements are matrices. The Hypersoft matrices and hyper-super-soft matrices are tensors of rank three and four, respectively, having three and four indices of variations. Later we provide an application of these Plithogenic Hyper super soft matrices in the form of Local, Global, Universal Subjective Ranking Model. The specialty of this model is that it offers precise classification of the universe from micro-universe to macro-universe levels by observing them through several angles of visions in many environments having several ambiguities and hesitation levels. This model provides optimal and neutral values of universes and can compact the expanded universe to a single point in such a way that the compacted universe reflects the cumulative effect of the whole universe. It further offers a transparent ranking by giving a percentage authenticity measure of the ranking. Finally, we provide an application of the model as a numerical example.