International Journal of Neutrosophic Science

In this study, we presented a new generalization of the Fermatean interval valued fuzzy soft set (FIVFSS) and the neutrosophic interval valued soft set called the neutrsophic Fermatean interval valued soft set (NSFIVSS). The NSFIVSS decision matrix aggregated operations are the topic of our current discussion. Strong points of view for the generalization of the interval valued fuzzy soft set (IVFSS) known as multi-criteria group decision making (MCGDM) are the TOPSIS and VIKOR techniques. We discuss a score function that combines TOPSIS, VIKOR, and NSFIVSS-positive ideal solution (PIS) and NSFIVSS-negative ideal solution (NIS) techniques. The TOPSIS and VIKOR methods also offer decision-making weights. The nearness condition is used to determine the best alternative. An educational trust intends to give some money to those underdeveloped schools since they lack amenities like restrooms, a campus environment that is favorable to learning, sports equipment, and classroom furnishings like desks and lights. In order to lower the factor, they declared a payment to be made in the amounts of 30, 25, 20, 15, and 10. Find the top five under performing schools in the state.

We discuss innovative square root Diophantine neutrosophic normal interval-valued set (SRDioNSNIVS)- based approaches to multiple attribute decision-making (MADM) problems. Square root neutrosophic sets, interval-valued Diophantine neutrosophic sets and neutrosophic normal interval-valued (NSNIV) sets are both extensions of square root Diophantine neutrosophic sets. In this section, we will look over several aggregating operations and how those interpretations have evolved over time. The article is focused on a novel idea known as square root NSNIV weighted averaging (SRDioNSNIVWA), square root NSNIV weighted geometric (SRDioNSNIVWG), generalized square root NSNIV weighted averaging (GSRDioNSNIVWA), and generalized square root NSNIV weighted geometric (GSRDioNSNIVWG). In order to solve MADM problems, we also begin an algorithm based on the aforementioned operators. The use of the euclidean and hamming distances is described, and examples from real-world situations are given. The main characteristics of these sets under various algebraic operations will be discussed in this communication. They are more practical and straightforward, and the ideal choice may be determined quickly. As a result, the defined models are more accurate and closely tied to Φ. In order to show the reliability and usefulness of the models under examination, we also compare a few of the proposed and current models. The study’s results are also fascinating and intriguing.

The use of "drones" stands out in precision agriculture for the analysis of vegetation and soil indices, the present work contemplates a redesign, construction and implementation of a "drone" using computer tools based on software engineering and technologies of info-communications, which allows optimizing one of the existing platforms in the drone market (SKYWALKER (X8)) for the evaluation of vegetation indices, as estimators of changes in different types of vegetation cover in Pitahaya crops in the province del Guayas, also carry out precise monitoring of large extensions of crops, minimizing human presence, controlling soil conditions through special systems, such as hydration, temperature or plant growth rate, chlorophyll level, among others, and the appearance of plagues that could affect the Pitahaya crops located prematurely, as well as the bases for a neutrosophic control system in designing platforms by using simulators. For the neutrosophic control, neutrosophic uninorms were used for the aggregation of the measurement results by regions.  

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.

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.

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.

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.

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.