COVID-19 outbreak is a reminder of the fact that the pandemics have happened in the past and will also occur in the future. The COVID-19 not only has affected the economy; but also it has affected the livelihood, which leads to the changes in businesses. This study aims to identify the most significant indicator (or parameter) that impacts the sustainability of industries. The study should also develop a real-time monitoring system for the sustainability of industries affected by COVID 19. In this work, the Polynomial Neural Network (PNN) and cosine similarity measure under SVPNS (Single-Valued Pentapartitioned Neutrosophic Set) environment have found their use in analyzing the sustainability of the industry.
Read MoreDoi: https://doi.org/10.54216/IJNS.190302
Vol. 19 Issue. 3 PP. 16-28, (2022)
We introduce logarithmic summability in Neutrosophic Normed Spaces [NNS] and give some Taubarian conditions for which logarithmic summability yields convergence in NNS. Besides we define the concept of slow oscillation with respect to logarithmic summability in NNS, Investigate its relation with the concept of q-boundedness and give Taubarian theorems by means of q-boundedness and slow oscillation with respect to logarithmic summability. A comparison theorem between CesaroSummability method and logarithmic summability method in NNS is also proved in the paper.
Read MoreDoi: https://doi.org/10.54216/IJNS.190303
Vol. 19 Issue. 3 PP. 29-39, (2022)
In this paper, we study neutrosophic of one important types of algebra namely BCK-algebra. Some new results of a generalization of BCK-algebra (Ω-BCK-algebra) have been introduced. Several facts about neutrosophic Ω-BCK-algebra are presented such as neutrosophic of homomorphic image and neutrosophic of kernel homomorphism. Finally, some definitions, examples, and other properties of neutrosophic BCK-algebra and neutrosophic Ω-BCK-algebra are given.
Read MoreDoi: https://doi.org/10.54216/IJNS.190301
Vol. 19 Issue. 3 PP. 08-15, (2022)
The traveling salesman problem (TSP) is an important and well known classical combinatorial network optimization problem in operation research, where the TSP finds a shortest possible route through a set of n nodes such that each and every node are visited exactly one time except for the starting node. In this problem, the arc lengths are generally considered to represent the traveling time or travelling cost rather than geographical distance. It is not possible to predict the exact arc length because the traveling time or traveling cost fluctuated with payload, weather, traffic conditions and so on. neutrosophic set theory provides a new tool to handle the uncertainties in TSP. In this paper, we concentrate on TSP on a network in which neutrosophic set, Instead of real number is assigned to edge as edge weight. We propose a mathematical model for a TSP with neutrosophic arc lengths. We present the utility of neutrosophic sets as arc length for TSP. An algorithmic method based on Genetic Algorithm (GA) is proposed for solving this problem. We have designed a new heuristic crossover and heuristic mutation our proposed GA. We have used a numerical example to illustrate the effectiveness of our proposed algorithm.
Read MoreDoi: https://doi.org/10.54216/IJNS.190304
Vol. 19 Issue. 3 PP. 40-46, (2022)
Neutrosophic topological space is an extension of fuzzy topology. Neutrosophic topological space addresses each element’s membership, indeterminacy and non-membership grades. Dropping an axiom in the neutrosophic topological space produces a new topological space called neutrosophic supra topological space. Elements in this neutrosophic supra topology are neutrosophic sets. We established the neutrosophic αψ-supra open set in neutrosophic supra topological spaces in this paper. Also, we investigate the properties of the newly defined set. Neutrosophic αψ -supra continuity is introduced and studied subsequently.
Read MoreDoi: https://doi.org/10.54216/IJNS.190305
Vol. 19 Issue. 3 PP. 47-52, (2022)