Galoitica: Journal of Mathematical Structures and Applications

A neutrosophic set assigns to each element three (generally independent) degrees: truth, indeterminacy, and falsity. A q-fractional fuzzy set assigns membership and nonmembership degrees in [0,1] to each element, constrained by (μ +ν)/q ≤ 1 for q ≥ 2. A q-fractional fuzzy graph is a graph whose vertices and edges carry q-fractional fuzzy degrees, with edge membership bounded by endpoints and edge nonmembership dominating them. In this paper, we introduce q-fractional neutrosophic sets and graphs as an extension of q-fractional fuzzy sets and q-fractional fuzzy graphs, and we investigate their fundamental properties.

This paper studies graph-based higher-order structures related to metagraphs and edge-labeled hierarchical networks. After reviewing MetaGraphs and Iterated MetaGraphs, we introduce the notion of an Edge-MetaGraph, in which each edge is labeled by a two-ported internal graph, allowing edge-substitution expansion through port gluing. We then define Iterated Edge-MetaGraphs recursively, so that edges may carry nested Edge-MetaGraph structures. Concrete examples from biomedical systems, software pipelines, and logistics are presented to illustrate the expressive power of the proposed framework

In this paper, we give a brief overview of the advances in mathematical modelling applied to epidemiology and the achievements that have been made in epidemiological research using mathematical models. Since the early 1900s when the well-known susceptible–infected–recovered model was proposed, mathematical treatments have played an important role in epidemiology. We introduce the deterministic SIR model and explain the value of computational tools, mathematical modelling and statistical analysis for the understanding of the development of disease and the size of emerging outbreaks. These are issues that are of major concern in everyday life and public health. With the emergence of the novel coronavirus in recent times, it has become evident that mathematical modeling along with computational and statistical tools are extremely relevant. Hence, this study explains the mathematical modelling in Epidemiology and demonstrates the advancement of the discipline over the years.

In recent times, investigating data with Turiyam attributes and its analysis has been considered one of the crucial tasks. It provides a way to characterize fuzziness in attributes in four independent ways: the true region (t), false region ( f ), indeterminate region (i), and liberal region (l). Numerous algorithms have been suggested for applications of the Turiyam set as a graph, a Turiyam matrix and algebraic properties of a Turiyam matrix. It tries to use words to calculate whenever there’s a human consciousness. One suitable example is the voting system in a democratic country like India where people vote according to their conduit metaphor or they select NOTA. There are, however, several older four valued methods, such as those of Nagarjuna (Catuskoti) and Aristotle’s logic and Belnap’s logic. The author gives an example to compare the Turiyam logic with each of these approaches in this paper.