Neutrosophic Environment Research Articles

An extension of TOPSIS method using interval bipolar linguistic neutrosophic set and its application

TOPSIS, known as the “Technique for Order of Preference by Similarity to Ideal Solution” (TOPSIS), is one of the well-known methods for solving “multi-criteria decision-making” (MCDM) problems. Many TOPSIS methods have been developed to solve real-life problems using neutrosophic sets. However, no study has developed the TOPSIS method under interval bipolar linguistic neutrosophic environments. Therefore, this study aims to present a new concept of “interval bipolar linguistic neutrosophic set” (IBL_NS). IBL_NS is more flexible and adaptable to real-world applications than other sets. Some set-theoretic operations, such as “union”, “intersection”, and “complement”, and the “operational rules” of IBL_NS are defined. Then, a new TOPSIS procedure in IBL_NS is developed. In the proposed IBL_NS-TOPSIS method, ratings of alternatives and importance weights of criteria are expressed in IBL_NS. An application is presented demonstrating the advantages of the proposed IBL_NS-TOPSIS approach.

An Effective Analysis of Risk Assessment and Mitigation Strategies of Photovoltaic Power Plants Based on Real Data: Strategies, Challenges, Perspectives, and Sustainability

Due to the extensive usage of fossil fuels such as coal, oil, and gas, the energy crisis and environmental pollution issues have garnered global attention, making the creation of clean, renewable energy an unavoidable option. Solar photovoltaic energy production is regarded as one of the most promising technologies owing to its safety, dependability, and lack of environmental impact. However, the adoption of photovoltaic systems comes with some risks that may affect their deployment. This paper examines the risks of sustainable photovoltaic power plants through a realistic case study. A comprehensive approach is presented through which consultants can use linguistic variables to express their opinions about risks, priorities, and strategies for dealing with them. Evaluating and prioritizing risk assessment is a complex task that requires consideration of multiple criteria. Therefore, this paper proposes a hybrid multicriteria decision-making (MCDM) approach to deal with risks and their priorities. The risks of five aspects of sustainability were considered: the economic, technical, institutional, social, and environmental aspects. The developed approach consists of two decision-making methods: the criteria importance through intercriteria correlation (CRITIC) method, which is used to determine the weights of the criteria, and the evaluation based on distance from average solution (EDAS) method, which is used to arrange risks according to their priorities. The developed approach is performed in a neutrosophic environment and uses type-2 neutrosophic numbers (T2NN) to address uncertainty. Also, the paper adopts a developed model to determine the consultants’ reputation weights instead of assuming them. In addition, the model was applied to classify the risks of each aspect of sustainability into three levels, which are high, medium, and normal risks. The results indicate that 52% of the risks in all aspects are high risks, 36% are medium risks, and 12% are usual risks. Also, sensitivity analysis was performed to prove the correctness and stability of the developed approach with differences in weights.

Integrated Neutrosophic Best-Worst Method for Comprehensive Analysis and Ranking of Flood Risks: A Case Study Approach from Aswan, Egypt


 This paper presents a comprehensive framework for the analysis and ranking of flood risks with respect to regional variations and data uncertainties under a Neutrosophic environment. The research introduces a novel approach to flood risk mitigation and management, bringing together the scientifically robust Best-Worst Method (BWM) and single-valued Neutrosophic set for the first time. The unique application of a single-valued Neutrosophic set allows us to better illustrate and manage uncertainty, imprecision, and vagueness in data. Additionally, we employ BWM, a multi-factor decision-making method, for discerning and ranking the most influential flood risk factors. Together, the integrated methodologies provide a balanced, comprehensive guide for decision-makers and risk handlers, showcasing efficient and effective mitigation strategies. The paper emphasizes the importance of mitigating flood risks to save lives and properties and to manage and conserve environmental resources efficiently. A case study was conducted in Aswan, Egypt, to assess flood susceptibility. The results revealed that 12.60% of the study area exhibited very high susceptibility to flooding, 18.77% showed high susceptibility, 23.94% exhibited moderate susceptibility, 22.91% registered a low susceptibility, and the remaining 21.78% showed very low susceptibility to flooding.

Efficient Decision Making for Sustainable Energy Using Single-Valued Neutrosophic Prioritized Interactive Aggregation Operators

To reduce greenhouse gas emissions, conserve the environment, and reduce dependency on fossil fuels, the transition from fossil energy to renewable energy is deemed essential. Several companies around the globe, especially big conglomerates, were pioneers in the use of renewable energy. For sustainable growth, Pakistani businesses are growing increasingly interested in the use of green sources in manufacturing and economic activities. In recent years, there has been a growth in the number of companies that are eager to use renewable energies to produce products that correspond to green standards, therefore boosting their competitiveness. Yet, the selection of an appropriate energy source for any industrially complex project is not a simple task, as numerous qualitative and quantitative characteristics must be considered. To arrive at a feasible conclusion, this research provides a multi-criteria paradigm for sustainable energy selection in a single-valued neutrosophic environment. This work developed an innovative aggregation operators approach that interprets the input evaluation using single-valued neutrosophic numbers. For this, a “single-valued neutrosophic prioritized interactive weighted averaging operator and single-valued neutrosophic prioritized interactive weighted geometric operator” has been introduced. Several additional appealing features of these aggregation operators are also discussed. The application of the recommended operators for sustainable energy related to the industrial complex is discussed. A comparison analysis proves the empirical existence of the suggested methodology’s consistency and superiority.

Multi-item economic production quantity model under single valued bipolar neutrosophic environment based on possibilistic theory

It is challenging for a decision-maker to decide a proper decision in severe situations of multi-aspirated real-life problems.So there is always an ambiguity in the mind of decision maker. Keeping such vagueness in mind, this paper aims to incorporate some situation parameters imprecise in nature. The imprecise parameters are taken in single-valued bipolar neutrosophic environments. Different arithmetic operations on the single-valued bipolar neutrosophic number using the (α, β) cut method are proposed in this paper. Using this we have calculated the possibility mean of single valued bipolar neutrosophic numbers. A multi-item economic production quantity model with one time only discount is considered here with some parameters in single valued bipolar neutrosophic number as a case study of our proposed work. A possibilistic mean de-fuzzification technique is used here using possibility measures. Finally, numerical illustration and sensitivity analysis is done for different variables to emphasize the excellence of our proposed work.

A novel approach toward skin cancer classification through fused deep features and neutrosophic environment.

Variations in the size and texture of melanoma make the classification procedure more complex in a computer-aided diagnostic (CAD) system. The research proposes an innovative hybrid deep learning-based layer-fusion and neutrosophic-set technique for identifying skin lesions. The off-the-shelf networks are examined to categorize eight types of skin lesions using transfer learning on International Skin Imaging Collaboration (ISIC) 2019 skin lesion datasets. The top two networks, which are GoogleNet and DarkNet, achieved an accuracy of 77.41 and 82.42%, respectively. The proposed method works in two successive stages: first, boosting the classification accuracy of the trained networks individually. A suggested feature fusion methodology is applied to enrich the extracted features' descriptive power, which promotes the accuracy to 79.2 and 84.5%, respectively. The second stage explores how to combine these networks for further improvement. The error-correcting output codes (ECOC) paradigm is utilized for constructing a set of well-trained true and false support vector machine (SVM) classifiers via fused DarkNet and GoogleNet feature maps, respectively. The ECOC's coding matrices are designed to train each true classifier and its opponent in a one-versus-other fashion. Consequently, contradictions between true and false classifiers in terms of their classification scores create an ambiguity zone quantified by the indeterminacy set. Recent neutrosophic techniques resolve this ambiguity to tilt the balance toward the correct skin cancer class. As a result, the classification score is increased to 85.74%, outperforming the recent proposals by an obvious step. The trained models alongside the implementation of the proposed single-valued neutrosophic sets (SVNSs) will be publicly available for aiding relevant research fields.

MADM for Assessment the Nurses Knowledge and their Attitudes During Covid-19 Spread in Mosul City in the Perspective of Neutrosophic Environment

MADM for Assessment the Nurses Knowledge and their Attitudes During Covid-19 Spread in Mosul City in the Perspective of Neutrosophic Environment

Complex fermatean neutrosophic graph and application to decision making

A new growing area of neutrosophic set (NS) theory called complex neutrosophic sets (CNS) provides useful tools for dealing with uncertainty in complex valued physical variables that are observed in the actual world. A CNS take values for the truth, indeterminacy and falsity membership functions in the complex plane's unit circle. In this research, a novel concept of complex fermatean neutrosophic graph (CFNG) is established. We proposed the order, size, degree and total degree of a vertex of CFNG. Also, we presented the primary operations such as complement, union, join, ring-sum and cartesian product of CFNG. Moreover, the concept of regular graph under complex fermatean neutrosophic environment is discussed. Finally, an application of multi criteria decision making problem in educational system to evaluate lecturer’s research productivity using CFNG is discussed.

Neutrosophic Log-Logistic Distribution Model in Complex Alloy Metal Melting Point Applications

The log-logistic distribution is more comprehensively applied in the area of survival and reliability engineering analysis for modeling the lifetime data practices of both human and electronic designs. The goal of this paper is to develop a generalization of the classical pattern log-logistic distribution, known as the neutrosophic log-logistic distribution (NLLD), to model various survival and reliability engineering data with indeterminacies. The developed distribution is especially useful for modeling indeterminate data that is roughly positively skewed. This paper discusses the developed NLLD’s main statistical properties such as neutrosophic survival function, neutrosophic hazard rate, neutrosophic moments, and neutrosophic mean time failure. Furthermore, the neutrosophic parameters are estimated using the well-known maximum likelihood (ML) estimation method in a neutrosophic environment. A simulation study is carried out to establish the achievement of the estimated neutrosophic parameters. As a final point, the proposed NLLD applications in the real world have been discussed with the help of real data. The real data illustrated that the efficiency of the proposed model as compared with the existing models.

An interval-valued neutrosophic based MAIRCA method for sustainable material selection

A plethora of Multi-Criteria Decision-Making (MCDM) methods is available for selecting an optimal material for a design problem with quantitative measurements. However, little research has been conducted on material selection methods in an interval neutrosophic environment to address uncertainty. In this research paper, a unique framework is presented that combines Interval-Valued Neutrosophic Sets (IVNSs) with the entropy–MultiAtributive Ideal-Real Comparative Analysis (MAIRCA) framework with the aim of simultaneously handling the objective criteria with crisp inputs and subjective criteria with ambiguous or uncertain information. To demonstrate the applicability of the proposed approach, a wing-spar of a Human-Powered Aircraft (HPA) is considered. At first, a panel of three subject experts makes judgments on the alternatives or criteria linguistically through IVNSs. Next, the skill level of each expert involved in the decision-making process is assessed using a novel weighting approach with linguistic information. After obtaining the objective criteria weights using the entropy weighting method, the performance of candidate materials for the HPA spar is evaluated using the MAIRCA method. The results indicate that S-glass70%-Epoxy Continuous Fibers, Ti-2Fe-3Al-10V and Al-7075 T6 are the top-ranked alternatives for spar application. The strong correlation of the proposed approach with other extant MCDM techniques demonstrates the reliability of the results obtained. In addition, the efficacy and practicality of the material selection tool is also validated with an outranking method in a simplified neutrosophic environment.

An n-valued neutrosophic set method for the assessment of an offshore oil spill risk.

With the development of maritime transportation, oil spill accidents occur frequently. In this paper, a scientific and reasonable assessment of ship oil spills, offshore oil platform oil spills, and subsea pipeline oil spills is carried out, and a risk assessment method of an offshore oil spill based on an n-value neutrosophic set is proposed. First, the oil spill risk evaluation index systems of these three risk sources are constructed, respectively, and the entropy weight method is used to calculate the weight. Second, we establish a risk assessment model under the n-value neutrosophic environment. Furthermore, we use the n-value neutrosophic-weighted arithmetic average (NVNWAA) to calculate the risk levels of the following three risk sources: ship oil spills, offshore oil platform spills, and submarine pipeline spills. Finally, according to the results of the risk assessment, the countermeasures to strengthen the preventive measures of oil spill accidents are put forward.

An Intelligent Decision Support Model for Optimal Selection of Machine Tool under Uncertainty: Recent Trends

Many scholars have been interested in the subject of machine tool selection as a result of the growing number of different machines and the continuous advancement of technology associated with these machines. The selection of an unsuitable machine tool may lead to a variety of issues, including limitations on production capacities and productivity indicators when taking into account both time and money from an industrial and practical perspective. The present strategy of selecting machine tools, known as multi-criteria decision-making (MCDM), relies on the subjective viewpoint the vast majority of the time. When selecting an appropriate machining tool, however, it is necessary to take both the subjective and objective points of view into consideration. This is due to the fact that the objective assessment accurately reflects the performance of the machine tools. As a result, the purpose of this work is to provide a strategy for selecting machine tools that are based on an innovative hybrid MCDM framework. The study was conducted under a neutrosophic environment and using triangular neutrosophic numbers (TNNs). In the beginning, the CRiteria Importance through Intercriteria Correlation (CRITIC) method is used to assess and prioritize the criteria set for the study. Then, the Additive Ratio Assessment (ARAS) method is applied to evaluate and rank four machine tools that were selected and used as alternatives in the study. The results indicate that the criteria of maximum spindle speed and linkage accuracy are the most important in determining the best machine tool. Also, the results indicate that the best alternative among the four tools used is FIDLA GTF-28. As a result, the requirements and priorities for research in the future are highlighted.

A Solution Technique of Transportation Problem in Neutrosophic Environment


 In this article, we presented a ranking system based on the sign distance in a new direction, such that to compare different single-valued neutrosophic numbers (SVN-numbers), a decision maker has the chance of flexibility. We also developed some important definitions, like level-(α,β,γ) neutrosophic point, and some properties related to the sign distance ranking function. Finally, the sign distance ranking function is applied to solving the neutrosophic transportation problem (NTP) with SVN-number converted into a transportation problem (TP) with crisp data, and to illustrate the appropriateness of this function, we gave two numerical illustrations.

A multi-criteria decision-making with regret theory-based MULTIMOORA method under interval neutrosophic environment

The MULTIMOORA (multiple multi-objective optimization by ratio analysis) method is useful for multiple criteria decision-making method. It is based on expected utility theory and assumes that decision makers are completely rational. However, some studies show that human beings are usually bounded rational, and their regret aversion behaviors play an important role in the decision-making process. Interval neutrosophic sets can more flexibly depict uncertain, incomplete and inconsistent information than single-valued neutrosophic sets. Therefore, this paper improves the traditional MULTIMOORA method by combining the regret theory under interval neutrosophic sets. Firstly, the regret theory is used to calculate the utility value and regret-rejoice value of each alternatives. Secondly, the criteria weights optimization model based on the maximizing deviation is constructed to obtain the weight vector. Then, the MULTIMOORA method is used to determine the order of the alternatives. Finally, an illustrative example about school selection is provided to demonstrate the feasibility of the proposed method. Sensitivity analysis shows the validity of the regret theory in the proposed method, and the ranking order change with different regret avoidance parameter. Comparisons are made with existing approaches to illustrate the advantage of the proposed method in reflecting decision makers’ psychological preference.

Rank and Analysis Several Solutions of Healthcare Waste to Achieve Cost Effectiveness and Sustainability Using Neutrosophic MCDM Model

Managing healthcare waste (HCWTT) from healthcare facilities is difficult. It's high up on the list of health concerns. This growth in HCWTT has been especially visible in recent years, as the quantity of medical services available has increased. Because of the potential danger, this garbage poses to people and the planet, it must be properly disposed of. Because of ineffective waste management practices, inadequate financial resources, and a lack of adequate facilities, HCWT administration is especially crucial in developing nations. Reducing HCWT via appropriate treatment is important for the area's financial and environmental health. In order to solve single-valued neutrosophic (SVN) group decision-making issues with missing weight details, this research creates a unique multi-criterion decision-making (MCDM) approach. First, it's important to remember that various decision-makers (DMs) have varying levels of expertise. To get over the problem that the standards cannot compensate for each other, an improved version of ELECTRE is studied. The ELECTRE method is used under neutrosophic environment to rank solutions of HCWT.

An ANP-TOPSIS model for tourist destination choice problems under Temporal Neutrosophic environment

Decision-making is a systematic process of solving real-world problems that provide an optimal solution after checking the achievable set of alternatives. As decision-making theory plays an increasingly important role in real life, there is more and more research on decision-making. All possible options are sorted through a multi-criteria decision-making system, allowing users to choose the suitable solution. In the face of many alternatives, the lack of appropriate skills and limited time has led to eventful human judgments. In this framework, the paper introduces the definition of a Temporal Complex neutrosophic set (TCNS) and the operations and properties of TCNS. Then, the TCNS-ANP-TOPSIS model based on TCNS is presented, which extends the ANP model to determine the weights for group multi-criteria and TOPSIS to rank alternatives collected from different time intervals. Further, to prove the feasibility and potentiality of the proposed model, a case study of choosing a tourist destination in Vietnam is described under the TCNS context. A comparative analysis with existing algorithms demonstrates the proposed model’s effectiveness, consistency, and availability.

Decision Making in Neutrosophic Environment

Frequently in real life situations decision making takes place under fuzzy conditions, because the corresponding goals and/or the existing constraints are not clearly defined. Maji et al. introduced a method of parametric decision making using soft sets as tools. In reality, however, cases appear in which the decision maker has doubts about the correctness of the parameters assigned to some or all of the elements of the set of the discourse. In order to study more effectively the decision making process in such cases, we introduce neutrosophic sets here and we replace the binary elements in the tabular matrix of the method of Maji et al. by neutrosophic triplets. Our method is illustrated by suitable examples.

Comparative study between GRA and MEREC technique on an agricultural-based MCGDM problem in pentagonal neutrosophic environment.

In this research article, an improved Multi-criteria group decision-making (MCGDM) strategy has been developed in pentagonal neutrosophic environment incorporating grey relational analysis and method on the removal effects of criteria (MEREC) techniques to address the relative advantages and disadvantages of these aspects in MCGDM. The aim of the study is to improve MCGDM technique which can capture the underlying uncertainties in robust way and can produce consistent results in a more rigorous way. Here, the conception of Hamming distance between two pentagonal neutrosophic number (PNN)s is introduced and the weighted arithmetic and geometric averaging operators in PNN arena are deployed to craft our computational technique more progressive and robust. An agriculture-based numerical problem is illustrated to demonstrate the ranking results of the alternatives by both of the techniques. After evaluating the problem by two aggregation operators, it is found that "plantation crop" is the best alternative under certain circumstances. Lastly, the sensitivity investigation is performed which reveals that withthe appliance of arithmetic and geometric aggregation operators the best ranked alternative preserves its position by both of the ranking methods, which definitely exhibit the consistency and robustness of our executed methodology.

On neutrosophic multi-level multi-objective linear programming problem with application in transportation problem

In this research, we use the harmonic mean technique to present an interactive strategy for addressing neutrosophic multi-level multi-objective linear programming (NMMLP) problems. The coefficients of the objective functions of level decision makers and constraints are represented by neutrosophic numbers. By using the interval programming technique, the NMMLP problem is transformed into two crisp MMLP problems, one of these problems is an MMLP problem with all of its coefficients being upper approximations of neutrosophic numbers, while the other is an MMLP problem with all of its coefficients being lower approximations of neutrosophic numbers. The harmonic mean method is then used to combine the many objectives of each crisp problem into a single objective. Then, a preferred solution for NMMLP problems is obtained by solving the single-objective linear programming problem. An application of our research problem is how to determine the optimality the cost of multi-objective transportation problem with neutrosophic environment. To demonstrate the proposed strategies, numerical examples are solved.

Some Results on Submodules Using (μ,ν,ω)-Single-Valued Neutrosophic Environment

The use of a single-valued neutrosophic set (svns) makes it much easier to manage situations in which one must deal with incorrect, unexpected, susceptible, faulty, vulnerable, and complicated information. This is a result of the fact that the specific forms of material being discussed here are more likely to include errors. This new theory has directly contributed to the expansion of both the concept of fuzzy sets and intuitionistic fuzzy sets, both of which have experienced additional development as a direct consequence of the creation of this new theory. In svns, indeterminacy is correctly assessed in a way that is both subtle and unambiguous. Furthermore, membership in the truth, indeterminacy, and falsity are all completely independent of one another. In the context of algebraic analysis, certain binary operations may be regarded as interacting with algebraic modules. These modules have pervasive and complicated designs. Modules may be put to use in a wide variety of different applications. Modules have applications in a diverse range of industries and market subsets due to their adaptability and versatility. Under the umbrella of the triplet (μ,ν,ω) structure, we investigate the concept of svns and establish a relationship between it and the single-valued neutrosophic module and the single-valued neutrosophic submodule, respectively. The purpose of this study is to gain an understanding of the algebraic structures of single-valued neutrosophic submodules under the triplet structure of a classical module and to improve the validity of this method by analyzing a variety of important facets. In this article, numerous symmetrical features of modules are also investigated, which demonstrates the usefulness and practicality of these qualities. The results of this research will allow for the successful completion of both of these objectives. The tactics that we have devised for use in this article are more applicable to a wide variety of situations than those that have been used in the past. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are some of the tactics that fall under this category.