Neutrosophic Environment Research Articles

Towards a Computational Theory of Perceptions under Neutrosophic Environment

Computing and reasoning with perceptions in AI are shifting from traditional methods to those that mimic human cognitive processes. Humans intuitively measure and evaluate without explicit computations, using sensory input and past experiences for quick judgments. The theory of perceptions can enhance AI's ability to replicate human-like assessment by providing a framework for handling the nuances of human reasoning. Traditionally, information granularity is either crisp (c-granular) or fuzzy (f-granular), focusing on measurement-based and perception-based information. This paper outlines a neutrosophic-based computational theory of perceptions (n-CTP), introducing neutrosophic granular (n-granular) information and neutrosophic constraint-centered semantics of natural languages (n-CSNL). Based on the neutrosophy theory, which deals with truth, falsity, and indeterminacy, managing uncertainties and vagueness in real-world data can be done more effectively than with traditional methods. The n-CTP has the potential to enhance AI's ability to process and reason with complex, uncertain, and ambiguous information.

Novel supply chain decision making model under m-polar quadripartitioned neutrosophic environment

Novel supply chain decision making model under m-polar quadripartitioned neutrosophic environment

An Attempt on Investment Selection Problem under Neutrosophic Environment based on Weighted Value Method

The main aim of this study is to develop a ranking algorithm in neutrosophic environment and applying this algorithm to choose the best option for investment selection problems. Firstly, the concept of single valued triangular neutrosophic numbers (SVTrN-numbers) and it’s characteristics are presented briefly. Here we define the λ-weighted value of SVTrN-numbers and applied it to the best selection of investment selection problem (ISP). Finally, to determine the feasibility and validity of this algorithm, we compared the resultant ranking by the proposed method with other existing approaches.

Multi-Objective Optimization based decision-making process using Dombi Logarithmic aggregation operator in CNN environment and its application to optimally select suitable greenhouse site for tomato crops

In this research article, we have defined Dombi Logarithmic aggregation operational laws in the framework of Cylindrical Neutrosophic Numbers (CNN) and utilized these laws to establish a new aggregation operator namely Cylindrical Neutrosophic Dombi Weighted Logarithmic Aggregation Operator(C N DW L A ). The said aggregation operational laws & aggregation operator have been used to present a new and novel decision making process where Full Consistency Method (FUCOM) and Multi-Objective Optimization(MOO) have been inte- grated and embedded fruitfully. Here the objective functions were formulated using the concept of a single-layer neural network and the FUCOM method to assess criterion weights. We have resolved the most favorable Pareto optimal solution derived from Multi-Objective Optimization by employing simulation and the Technique for Or- der of Preference by Similarity to Ideal Solution (TOPSIS) approach. Finally, we have applied our proposed decision making method along with MARCOS and MOORA techniques to determine the best greenhouse site for cultivating tomato crops. An exhaustive sensitivity and comparative analysis has been conducted to assess the robustness and stability of our Multi Criteria Group Decision Making (MCGDM) techniques. It is observed that our proposed method has some advantages in cylindrical neutrosophic environment and it produces stable robust results with the variation of underlying model parameters.

Extended Certainty Factors utilizing Neutrosophic Logic

Addressing uncertainty is a significant challenge in the field of artificial intelligence (AI). AI systems often encounter uncertainty due to incomplete data, ambiguous information, or inherent unpredictability in specific situations. To tackle this uncertainty, various solutions have been developed. These solutions range from probabilistic approaches like Bayesian networks and Monte Carlo methods to fuzzy logic and neural networks. These strategies enable AI systems to model and make judgments amid ambiguity by assigning probabilities, dealing with imprecise data, or utilizing learning processes that adapt to changing and uncertain contexts. However, probabilistic methods have limitations when it comes to handling uncertainty. These limitations include assumptions of independence, computational complexity, difficulty in capturing subjectivity, and interpretability. To address these limitations, other methods have been proposed, such as the model of certainty factors. This model offers a framework for reasoning under uncertainty by assigning a numerical value to statements or propositions. Additionally, neutrosophic logic extends classical logic by incorporating the concept of indeterminacy through truth/indeterminacy/falsity-membership functions. In this paper, we propose a method for investigating how certainty factors adapt to a neutrosophic environment. This method contributes to the development of more robust and adaptable decision support systems capable of dealing with diverse uncertainty. Our method, introduced for the first time in related literature, addresses issues such as the limited handling of indeterminacy, the inability to address contradictions, and the limited binary representation of uncertainty that characterize the model of certainty factors. We will provide a clear illustration of these implications through an example that demonstrates the superiority of our suggested method over the traditional technique of certainty factors.

Forgotten Topological Index and its Properties on Neutrosophic Graphs

Topological indices play a significant role in crisp, fuzzy graphs and their real-life application. But to avoid the vagueness in the final result, these indices should be dealt with in the neutrosophic environment since it consolidates the uncertain quantity or values of an event in the name of "indeterminacy membership". Except for the wiener index, no other indices are introduced under the neutrosophic graphical setting. In this article, we consider the forgotten topological index (ToI) and the Edge forgotten index in the 3-valued logic neutrosophic graph and came up with some important theorem results and applications.

The Application of Integrated Neutrosophic CRITIC and Preference Selection Index Methods for Multi Criteria Decision Making Over the Implementation of An Integrated Fish Farming System

This paper presents the application of integrated Neutrosophic CRITIC (The Criteria Importance Through Inter-criteria Correlation) and PSI (Preference Selection Index) methods using by the linguistic variables are converted to Neutrosophic set, which is an effective decision making model in a real life environment. This integrated methods is used to rank the 5 alternatives (Labeo rohita , Cirrhina mrigala , Catfishes, Catla catla, Murrels or Snakeheads) and 6 main criteria( Azolla with Duck Cum-Fish Culture, Paddy -Cum -Fish Culture, Duck- Cum -Fish farming, Fish - Cum -Poultry farming, Fish- cum Pig Culture, Cattle -Fish integrated farming system) for the growth of different varieties of fish by using Neutrosophic Environment.

An Integrated Pythagorean Neutrosophic DEMATEL- Grey Relational Analysis Framework for Assessing Recent Technological Advancements in Maternal Healthcare

This study proposes a novel methodology that integrates the Decision making trial and evolution laboratory (DEMATEL) technique and Grey relational analysis (GRA) in a Pythagorean neutrosophic environment. This multi-criteria decision-making approach uses the DEMATEL technique to analyze the weights of the criteria and Grey relational analysis to prioritize the alternatives. The proposed approach is utilized to evaluate the most recent technological advancements in maternity healthcare, along with a pertinent numerical example.

Stability Analysis of Diabetes Mellitus Model in Neutrosophic Fuzzy Environment

Neutrosophic differential equation (NDE) plays a vital role in mathematical modeling on uncertainty during last few years.It is established that NDE comprises a neutrosophic number whose membership function contains three parts like as truth function, indeterministic and falsity functions.In this paper, a diabetes mellitus model has been formulated in neutrosophic fuzzy environment to get more realistic mathematical model. The initial conditions of diabetes system are considered as trapezoidal neutrosophic fuzzy number. The concept of NDE via nuetrosophic generalised derivative of type-1 and type-2 has used in this article. This is the first article in which the stability analysis of diabetes model in neutrosophic environment is introduced. The existence of strong solution and weak neutrosophic solution of the proposed system are employed in the manuscript. Also, we have exposed the comparison of the suggested model between fuzzy environment and neutrosophic environment.The all results, formulas are confirmed graphically and numerically by MATLAB software.

Multivariate Exponentially Weighted Moving Average Control Chart under Neutrosophic Environment: A Bootstrap Approach

Multivariate Exponentially Weighted Moving Average Control Chart under Neutrosophic Environment: A Bootstrap Approach

Neutrosophic Pre Generalized Pre Regular Star Weakly Closed Sets

The objective of this paper is to emphasis the generalization of pre generalized pre regular weakly closed sets in Neutrosophic environment namely Neutrosophic Pre generalized Pre Regular Star Weakly Closed Sets. Its properties and characterizations are defined and its relationships with other Neutrosophic Sets are studied with suitable examples.

Optimal multi-period source-sink matching in carbon capture, utilization, and storage (CCUS) systems under neutrosophic environment

Carbon capture, utilization, and storage (CCUS) is an important technology for mitigating the effect of climate change. It involves the capture of CO2 from a point source, transport it through pipelines and store it in geological reservoirs for permanent storage. CCUS enables the use of fossil fuel-based power plant sources that produce a steady amount of energy and the reduction of CO2 emissions from these sources simultaneously. While CO2 sources are easy to characterize, the storage parameters of geological reservoirs are more difficult to measure, thus, estimates are provided and used for planning large-scale CCUS systems. CO2 utilization can provide a means to delay CO2 emissions by converting it highly valuable products, however, its sequestration potential is highly uncertain. A systematic mathematical approach is needed to effectively plan CCUS systems considering the risks associated with the estimates in the characteristics of the geological reservoir and the sequestration benefits from CO2 utilization. In this study, an optimization model is developed for planning multi-period CCUS systems under neutrosophic environment. The model considers managing storage risk by maximizing satisfaction from minimizing risks, minimizing dissatisfaction from consequences brought by these risks, and minimizing indeterminacy from inaccuracy of storage characteristics estimates. For utilization, the model considers the satisfaction for CO2 utilization benefits, dissatisfaction for opportunity losses, and indeterminacy in sequestration potential. Two case studies are used to illustrate the model where a sensitivity analysis is performed to illustrate the effect of the different risk appetite on the optimal solution. These cases studies reveal important insights on scheduling operations between CO2 sources and sinks and the allocation of captured CO2 for storage and utilization. The model can be used to develop policies for considering the risks associated with these uncertainties and how it will be managed.

An Inventory Model for Deteriorating Items with Price Dependent Demand Under Fuzzy and Neutrosophic Fuzzy Environment

This paper represents an inventory model of deteriorating items under fuzzy and neutrosophic environment without allowing shortages in inventory. Demand is price dependent and is compared between crisp, fuzzy and neutrosophic fuzzy demand. Realistically it is observed that although the cycle time of any supply chain system is uncertain but uncertainty is mainly dependent on the selling price. So, here we have compared the model using crisp, fuzzy and neutrosophic fuzzy demand. The result is illustrated with the help of numerical example under fuzzy and neutrosophic fuzzy demand. KEYWORDS: Inventory, Fuzzy and Neutrosophic Fuzzy Price dependent Demand.

Assessment of Cybersecurity in Industry 4.0 using Delphi-Based Factor Relationships and Comprehensive Distance-Based Ranking Methods under Uncertainty

Industry 4.0 is a new revolution in which internet connection technologies are interfaced with various components of industrial systems to create the smart factories and manufacturing organizations of the future to achieve a sustainable manufacturing framework. A large number of networked devices presents a significant chance to gather important data for improving the technology of decision-making to enhance product life-cycle management. Industry 4.0 technologies will face significant challenges and obstacles due to the cybersecurity and data privacy problems suffered by current Internet technology. In actuality, cybersecurity poses an important challenge to the advancement of sustainable manufacturing. Cybersecurity architectures are widely employed to prevent intrusions and attacks on computers and networks. As a result, there is a major decrease in the adoption of Industry 4.0 technologies and the sustainable manufacturing framework within organizations. To achieve the implementation of this sustainable manufacturing in companies we suggested five cybersecurity measures and six criteria. The proposed decision-making method aims to rank the cybersecurity procedures. The ranking of these measures used a combination of Delphi-FARE (factor relationship) and COBRA (comprehensive distance-based ranking) methods based on a neutrosophic environment. The result showed that alternative one “Data Encryptions” is the best one, and alternative five “Cloud Servers” is the worst one. We conducted a sensitivity and comparison analysis to verify the stability of the model and its performance with other models and demonstrated impressive results.

Selection of Sustainable Material for the Construction of Drone Aerodynamic Wing using Neutrosophic RAWEC

In light of the expansion of the use of drones in many fields, the development of the drone industry has gained the attention of many researchers. The process of selecting the materials used in developing and constructing the wing of the drone has become a very important and complex matter due to its reliance on multiple and sometimes conflicting criteria. Therefore, it must have an informed approach to the selection and decision-making process thoughtfully. The goal of this research is to introduce a new approach in a neutrosophic environment for the first time, to select the most suitable material for constructing a drone wing. The material must meet several criteria, including low weight, high rigidity, resistance to deformation, durability, and excellent stability. Neutrosophic is one of the most effective tools for dealing with ambiguity since it addresses the problem of uncertainty in the decision-making process. We have presented the SVTNSs - LMAW (single value triangular neutrosophic sets-logarithm methodology of additive weights) approach for calculating the weights of criteria and the new SVTNSs - RAWEC (single value triangular neutrosophic sets-ranking alternatives with weights of criterion) approach for ranking available alternatives involves straightforward computation steps, eliminating the need for pairwise comparisons in contrast to other MCDM approaches and saving time. Also, we examined the impact of changing the normalization method on the rank of the alternatives. We have conducted a sensitivity analysis to ensure the strength and stability of our proposed approach, and the results have proven that the proposed approach for selecting the appropriate material in light of ambiguity and lack of certainty that occurs in real life is very effective. By using the SVTNSs-LMAW-RAWEC approach the companies and factories will choose the most effective and efficient materials to develop and create a drone wing.

A Novel Technique to Detect an Optimal Two Layer Supply Chain Model for Imperfect Items Under Various Neutrosophic Environment

A Novel Technique to Detect an Optimal Two Layer Supply Chain Model for Imperfect Items Under Various Neutrosophic Environment

Multi-attribute decision-making problem in career determination using single-valued neutrosophic distance measure

In this paper, we introduce a distance measure on single-valued neutrosophic sets by sine function which is a generalization of intuitionistic fuzzy sine distance measure. The axiom of metric on single-valued neutrosophic sets is verified and shows that the difference of distance measure from unity is a similarity measure. A new methodology for multi-attribute decision-making problems (MADM) is developed for the most common decision by the smallest measure value of the proposed single-valued neutrosophic distance measure. We further apply this distance measure to a multi-attribute decision-making problem (MADM) for student career determination in a neutrosophic environment to find the best career for suitable students. Finally, the comparison is made between the proposed distance measure and the other distance measures for the final decision chosen from the most common decisions of them.

Extended Dombi–Hamy mean operator and Gaussian likelihood-based ranking approach for solving MCDM problems in interval-valued neutrosophic environment

The contrivance of this paper is two-dimensional. The first is to formulate an extended Dombi-Hamy mean operator in an interval-valued neutrosophic environment for assembling inter-related multiple parameters. The second one is to develop a new ranking procedure named as GLF ranking by introducing the concept of Gaussian likelihood function for solving multi-criteria decision-making problems in an interval-valued neutrosophic circumstance. Also, we have proposed a novel algorithm named Gaussian likelihood function based algorithm or GLF algorithm in solving multi-criteria decision-making problem from the field of medical science to find out the vital cause responsible for the occurrence of cancer in India. Finally, we have verified the flexibility and etiquette of GLF method by comparing it with the existing multi-criteria decision-making methods such as Aiwu’s method and Jun Ye’s method.

Selection of Academic Staff Based on a Hybrid Multi-criteria Decision Method Under Neutrosophic Environment

Multi-criteria decision-making (MCDM) is a decision-making process that involves assessing and selecting the best alternative from a group of options based on various criteria or qualities. In this research work, we propose and elucidate the theory of neutrosophic logic, which is unique in its approach to evaluating candidates’ performance in a manner that takes into account significant elements and criteria that are essential for the overall process when dealing with unclear, inaccurate, or incomplete data. We propose a novel hybrid integrated MCDM methodology based upon neutrosophic Delphi (N-Delphi) and neutrosophic AHP (N-AHP) methods, which takes into consideration the importance of each decision-maker and their preferences per evaluation criterion. A new MAXMIN threshold value technique treats the criteria under consideration as the decision alternatives and their score functions as their payoff values, thus reducing unnecessary resources by eliminating unimportant criteria during the personnel selection process.

Q-Rung Neutrosophic Sets and Topological Spaces


 The concept of the q-rung orthopair neutrosophic set is introduced in this paper, and fundamental properties of it are studied. Also, the ordinary notion of topological space is extended to the q-rung orthopair neutrosophic environment, as well as the fundamental concepts of convergence, continuity, compactness, and Hausdorff topological space. All these generalizations are illustrated by suitable examples.