Enhancing Critical Path Problem in Neutrosophic Environment Using Python

In the real world,one of the most common problems in project management is the unpredictability of resources and timelines.An efficient way to resolve uncertainty problems and overcome such obstacles is through an extended fuzzy approach,often known as neutrosophic logic.Our rigorous proposed model has led to the creation of an advanced technique for computing the triangular single-valued neutrosophic number.This innovative approach evaluates the inherent uncertainty in project durations of the planning phase,which enhances the potential significance of the decision-making process in the project.Our proposed method,for the first time in the neutrosophic set literature,not only solves existing problems but also introduces a new set of problems not yet explored in previous research.A comparative study using Python programming was conducted to examine the effectiveness of responsive and adaptive planning,as well as their differences from other existing models such as the classical critical path problem and the fuzzy critical path problem.The study highlights the use of neutrosophic logic in handling complex projects by illustrating an innovative dynamic programming framework that is robust and flexible,according to the derived results,and sets the stage for future discussions on its scalability and application across different industries.

An Adaptive Hate Speech Detection Approach Using Neutrosophic Neural Networks for Social Media Forensics

Detecting hate speech automatically in social media forensics has emerged as a highly challenging task due tothe complex nature of language used in such platforms. Currently, several methods exist for classifying hatespeech, but they still suffer from ambiguity when differentiating between hateful and offensive content and theyalso lack accuracy. The work suggested in this paper uses a combination of the Whale Optimization Algorithm(WOA) and Particle Swarm Optimization (PSO) to adjust the weights of two Multi-Layer Perceptron (MLPs)for neutrosophic sets classification. During the training process of the MLP, the WOA is employed to exploreand determine the optimal set of weights. The PSO algorithm adjusts the weights to optimize the performanceof the MLP as fine-tuning. Additionally, in this approach, two separate MLP models are employed. One MLPis dedicated to predicting degrees of truth membership, while the other MLP focuses on predicting degrees offalse membership. The difference between these memberships quantifies uncertainty, indicating the degree ofindeterminacy in predictions. The experimental results indicate the superior performance of our model comparedto previous work when evaluated on the Davidson dataset.

Applying an Ordinal Priority Approach Based Neutrosophic Fuzzy Axiomatic Design Approach to Develop Sustainable Geothermal Energy Source

Geothermal energy is considered a renewable,environmentally friendly,especially carbon-free,sustainable energy source that can solve the problem of climate change.In general,countries with geothermal energy resources are the ones going through the ring of fire.Therefore,not every country is lucky enough to own this resource.As a country with 117 active volcanoes and within the world’s ring of fire,it is a country whose geothermal resources are estimated to be about 40%of the world’s geothermal energy potential.However,the percentage used compared to the geothermal potential is too small.Therefore,this is the main energy source that Indonesia is aiming to exploit and use.However,the deployment and development of this energy source are still facing many obstacles due to many aspects from budget sources due to high capital costs,factory construction location,quality of resources,and conflicts of the local community.In this context,determining the optimal locations for geothermal energy sites(GES)is one of the most important and necessary issues.To strengthen the selection methods,this study applies a two-layer fuzzy multi-criteria decision-making method.Through the layers,the Ordinal Priority Approach(OPA)is proposed to weight the sub-criteria,the main criterion,and the sustainability factors.In layer 2,the Neutrosophic Fuzzy Axiomatic Design(NFAD)is applied to rank and evaluate potential locations for geothermal plant construction.Choosing the right geothermal energy site can bring low-cost efficiency,no greenhouse gas emissions,and quickly become the main energy source providing electricity for Indonesia.The final ranking shows Papua,Kawah Cibuni,and Moluccas as the three most suitable cities to build geothermal energy systems.Kawah Cibuni was identified as the most potential GES in Indonesia,with a score of 0.46.Papua is the second most promising GES with a score of 0.45.Next is the Moluccas,with a score of 0.39.However,the three least potential sites among the 15 studied sites are Lumut Balai,Moluccas and Patuha,with scores of 0.08,0.11 and 0.17,respectively.The conclusion of this study also classifies positions into groups to aid in decision-making.

Pythagorean Neutrosophic Planar Graphs with an Application in Decision-Making

Graph theory has a significant impact and is crucial in the structure of many real-life situations.To simulate uncertainty and ambiguity,many extensions of graph theoretical notions were created.Planar graphs play a vital role in modelling which has the property of non-crossing edges.Although crossing edges benefit,they have some drawbacks,which paved the way for the introduction of planar graphs.The overall purpose of the study is to contribute to the conceptual development of the Pythagorean Neutrosophic graph.The basic methodology of our research is the incorporation of the analogous concepts of planar graphs in the Pythagorean Neutrosophic graphs.The significant finding of our research is the introduction of Pythagorean Neutrosophic Planar graphs,a conceptual blending of Pythagorean Neutro-sophic and Planar graphs.The idea of Pythagorean Neutrosophic multigraphs and dual graphs are also introduced to deal with the ambiguous situations.This paper investigates the Pythagorean Neutrosophic planar values,which form the edges of the Pythagorean neutrosophic graphs.The concept of Pythagorean Neutrosophic dual graphs,isomorphism,co-weak and weak isomorphism have also been explored for Pythagorean Neutrosophic planar graphs.A decision-making algorithm was proposed with a numerical illustra-tion by using the Pythagorean Neutrosophic fuzzy graph.

Neutrosophic Adaptive Clustering Optimization in Genetic Algorithm and Its Application in Cubic Assignment Problem

In optimization theory,the adaptive control of the optimization process is an important goal that people pursue.To solve this problem,this study introduces the idea of neutrosophic decision-making into classical heuristic algorithm,and proposes a novel neutrosophic adaptive clustering optimization thought,which is applied in a novel neutrosophic genetic algorithm(NGA),for example.The main feature of NGA is that the NGA treats the crossover effect as a neutrosophic fuzzy set,the variation ratio as a structural parameter,the crossover effect as a benefit parameter and the variation effect as a cost parameter,and then a neutrosophic fitness function value is created.Finally,a high order assignment problem in warehousemanagement is taken to illustrate the effectiveness of NGA.

A new hybrid approach to assessing soil quality using neutrosophic fuzzy-AHP and support vector machine algorithm in sub-humid ecosystem

Soil quality determination and estimation is an important issue not only for terrestrial ecosystems but also for sustainable management of soils.In this study,soil quality was determined by linear and nonlinear standard scoring function methods integrated with a neutrosophic fuzzy analytic hierarchy process in the micro catchment.In addition,soil quality values were estimated using a support vector machine(SVM)in machine learning algorithms.In order to generate spatial distribution maps of soil quality indice values,different interpolation methods were evaluated to detect the most suitable semivariogram model.While the soil quality index values obtained by the linear method were determined between 0.458-0.717,the soil quality index with the nonlinear method showed variability at the levels of 0.433-0.651.There was no statistical difference between the two methods,and they were determined to be similar.In the estimation of soil quality with SVM,the normalized root means square error(NRMSE)values obtained in the linear and nonlinear method estimation were determined as 0.057 and 0.047,respectively.The spherical model of simple kriging was determined as the interpolation method with the lowest RMSE value in the actual and predicted values of the linear method while,in the nonlinear method,the lowest error in the distribution maps was determined with exponential of the simple kriging.

Multi-Criteria Group Decision-Making Method Based on an Improved Single-Valued Neutrosophic Hamacher Weighted Average Operator and Grey Relational Analysis

This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.

Developments and Applications of Neutrosophic Theory in Civil Engineering Fields:A Review

Neutrosophic theory can effectively and reasonably express indeterminate,inconsistent,and incomplete information.Since Smarandache proposed the neutrosophic theory in 1998,neutrosophic theory and related research have been developed and applied to many important fields.Indeterminacy and fuzziness are one of the main research issues in the field of civil engineering.Therefore,the neutrosophic theory is very suitable for modeling and applications of civil engineering fields.This review paper mainly describes the recent developments and applications of neutrosophic theory in four important research areas of civil engineering:the neutrosophic decision-making theory and applied methods,the neutrosophic evaluation methods and applications of slope stability,the neutrosophic expressions and analyses of rock joint roughness coefficient,and the neutrosophic structural optimization methods and applications.In terms of these research achievements in the four areas of civil engineering,the neutrosophic theory demonstrates its advantages in dealing with the indeterminate and inconsistent issues in civil engineering and the effectiveness and practicability of existing applied methods.In the future work,the existing research results will be further improved and extended in civil engineering problems.In addition,the neutrosophic theory will also have better application prospects in other fields of civil engineering.

Marketing Model Analysis of Fashion Communication Based on the Visual Analysis of Neutrosophic Systems

In order to Improvement the Neutrosophic sets as effective tools to deal with uncertain and inconsistent information.The research takes method-ology of combined single-valued neutrosophic rough set and multi-scale deci-sion systems.This paper proposes the optimal scale selection and reduction algorithms based on multi-scale single-valued neutrosophic dominance rough set model.User requirements were analyzed using KJ method to construct a hierarchical model.According to the statistics of representative studies from China and the West,we found that,on the one hand,classical theory has been expanded and supplemented in fashion culture communication and market-ing.The topics are more micro-diverse,and the research methods are inspired by other disciplines;on the other hand,Chinese practice and Chinese cultural perspective need to fill the gap.The fashion content in the new fashion,however,needs to broaden its boundaries,and in addition to integrating with cultural theory and sociology,it needs to be integrated with fashion products,including product design,visual communication,image design and so on.Aesthetic communication needs to be taken into account as an important connotation,with visual communication and the communication of images as important research elements.On the whole,this research abroad inspires the development of domestic fashion culture communication and marketing research.

Type-2 Neutrosophic Set and Their Applications in Medical Databases Deadlock Resolution

Electronic patient data gives many advantages,but also new difficulties.Deadlocks may delay procedures like acquiring patient information.Distributed deadlock resolution solutions introduce uncertainty due to inaccurate transaction properties.Soft computing-based solutions have been developed to solve this challenge.In a single framework,ambiguous,vague,incomplete,and inconsistent transaction attribute information has received minimal attention.The work presented in this paper employed type-2 neutrosophic logic,an extension of type-1 neutrosophic logic,to handle uncertainty in real-time deadlock-resolving systems.The proposed method is structured to reflect multiple types of knowledge and relations among transactions’features that include validation factor degree,slackness degree,degree of deadline-missed transaction based on the degree of membership of truthiness,degree ofmembership of indeterminacy,and degree ofmembership of falsity.Here,the footprint of uncertainty(FOU)for truth,indeterminacy,and falsity represents the level of uncertainty that exists in the value of a grade of membership.We employed a distributed real-time transaction processing simulator(DRTTPS)to conduct the simulations and conducted experiments using the benchmark Pima Indians diabetes dataset(PIDD).As the results showed,there is an increase in detection rate and a large drop in rollback rate when this new strategy is used.The performance of Type-2 neutrosophicbased resolution is better than the Type-1 neutrosophic-based approach on the execution ratio scale.The improvement rate has reached 10%to 20%,depending on the number of arrived transactions.

Emerging Trends in Social Networking Systems and Generation Gap with Neutrosophic Crisp Soft Mapping

This paper aims to introduce the novel concept of neutrosophic crisp soft set(NCSS),including various types of neutrosophic crisp soft sets(NCSSs)and their fundamental operations.We define NCS-mapping and its inverse NCS-mapping between two NCS-classes.We develop a robust mathematical modeling with the help of NCS-mapping to analyze the emerging trends in social networking systems(SNSs)for our various generations.We investigate the advantages,disadvantages,and natural aspects of SNSs for five generations.With the changing of the generations,it is analyzed that emerging trends and the benefits of SNSs are increasing day by day.The suggested modeling with NCS-mapping is applicable in solving various decision-making problems.

Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering for Noisy Data

Clustering is a crucial method for deciphering data structure and producing new information.Due to its significance in revealing fundamental connections between the human brain and events,it is essential to utilize clustering for cognitive research.Dealing with noisy data caused by inaccurate synthesis from several sources or misleading data production processes is one of the most intriguing clustering difficulties.Noisy data can lead to incorrect object recognition and inference.This research aims to innovate a novel clustering approach,named Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering(PNTS3FCM),to solve the clustering problem with noisy data using neutral and refusal degrees in the definition of Picture Fuzzy Set(PFS)and Neutrosophic Set(NS).Our contribution is to propose a new optimization model with four essential components:clustering,outlier removal,safe semi-supervised fuzzy clustering and partitioning with labeled and unlabeled data.The effectiveness and flexibility of the proposed technique are estimated and compared with the state-of-art methods,standard Picture fuzzy clustering(FC-PFS)and Confidence-weighted safe semi-supervised clustering(CS3FCM)on benchmark UCI datasets.The experimental results show that our method is better at least 10/15 datasets than the compared methods in terms of clustering quality and computational time.

单值三角Neutrosophic交叉熵的TOPSIS方法

多准则决策(Multi-Criteria Decision Making,MCDM)问题涉及到大量不精确、不完整和不一致的信息,而单值三角Neutrosophic数(Single Valued Triangular Neutrosophic Numbers,SVTrN-numbers)作为Neutrosophic数(Neutrosophic Numbers,NN)的一个分支可以有效地处理这类问题。同时交叉熵很适合度量决策信息的差异程度,但是现有的交叉熵测度存在不足。考虑到SVTrN-numbers具有的优势,结合TOPSIS理论,提出一种新的交叉熵测度,并对其性质进行证明,据此提出了一个SVTrN-numbers环境下解决MCDM问题的新方法。通过一个案例表明交叉熵公式的合理性。

On Single Valued Neutrosophic Regularity Spaces

This article aims to present new terms of single-valued neutrosophic notions in theˇSostak sense,known as singlevalued neutrosophic regularity spaces.Concepts such as r-single-valued neutrosophic semi￡-open,r-single-valued neutrosophic pre-￡-open,r-single valued neutrosophic regular-￡-open and r-single valued neutrosophicα￡-open are defined and their properties are studied as well as the relationship between them.Moreover,we introduce the concept of r-single valued neutrosophicθ￡-cluster point and r-single-valued neutrosophicγ￡-cluster point,r-θ￡-closed,andθ￡-closure operators and study some of their properties.Also,we present and investigate the notions of r-single-valued neutrosophicθ￡-connectedness and r-single valued neutrosophicδ￡-connectedness and investigate relationship with single-valued neutrosophic almost￡-regular.We compare all these forms of connectedness and investigate their properties in single-valued neutrosophic semiregular and single-valued neutrosophic almost regular in neutrosophic ideal topological spaces inˇSostak sense.The usefulness of these concepts are incorporated to multiple attribute groups of comparison within the connectedness and separateness ofθ￡andδ￡.

Novel applications of bipolar single-valued neutrosophic competition graphs

Bipolar single-valued neutrosophic models are the generalization of bipolar fuzzy models. We first introduce the concept of bipolar single-valued neutrosophic competition graphs. We then, discuss some important propositions related to bipolar single-valued neutrosophic competition graphs. We define bipolar single-valued neutrosophic economic competition graphs and m-step bipolar single-valued neutrosophic economic competition graphs. Further, we describe applications of bipolar single-valued neutrosophic competition graphs in organizational designations and brands competition. Finally, we present our improved methods by algorithms.

Decision Making Algorithmic Approaches Based on Parameterization of Neutrosophic Set under Hypersoft Set Environment with Fuzzy, Intuitionistic Fuzzy and Neutrosophic Settings

Hypersoft set is an extension of soft set as it further partitions each attribute into its corresponding attribute-valued set.This structure is more flexible and useful as it addresses the limitation of soft set for dealing with the scenarios having disjoint attribute-valued sets corresponding to distinct attributes.The main purpose of this study is to make the existing literature regarding neutrosophic parameterized soft set in line with the need of multi-attribute approximate function.Firstly,we conceptualize the neutrosophic parameterized hypersoft sets under the settings of fuzzy set,intuitionistic fuzzy set and neutrosophic set along with some of their elementary properties and set theoretic operations.Secondly,we propose decision-making-based algorithms with the help of these theories.Moreover,illustrative examples are presented which depict the structural validity for successful application to the problems involving vagueness and uncertainties.Lastly,the generalization of the proposed structure is discussed.

Power Aggregation Operators of Simplified Neutrosophic Sets and Their Use in Multi-attribute Group Decision Making

The simplified neutrosophic set(SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power weighted averaging(SNNPWA) operator, simplified neutrosophic number power weighted geometric(SNNPWG) operator, simplified neutrosophic number power ordered weighted averaging(SNNPOWA) operator and simplified neutrosophic number power ordered weighted geometric(SNNPOWG) operator. We present some useful properties of the operators and discuss the relationships among them. Moreover, an approach to multiattribute group decision making(MAGDM) within the framework of SNSs is developed by the above aggregation operators.Finally, a practical application of the developed approach to deal with the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with uncertain decision making problems.

An Improved Method Based on TODIM and TOPSIS for Multi-Attribute Decision-Making with Multi-Valued Neutrosophic Sets

Due to the complexity of decision-making problems and the subjectivity of decision-makers in practical application,it is necessary to adopt different forms of information expression according to the actual situation of specific decision-making problems and choose the best method to solve them.Multi-valued neutrosophic set,as an extension of neutrosophic set,can more effectively and accurately describe incomplete,uncertain or inconsistent information.TODIM and TOPSIS methods are two commonly used multi-attribute decision-making methods,each of which has its advantages and disadvantages.This paper proposes a new method based on TODIM and TOPSIS to solve multi-attribute decision-making problems under multi-valued neutrosophic environment.After introducing the related theory of multi-valued neutrosophic set and the traditional TODIM and TOPSIS methods,the new method based on a combination of TODIM and TOPSIS methods is described.And then,two illustrative examples proved the feasibility and validity of the proposed method.Finally,the result has been compared with some existing methods under the same examples and the proposed method’s superiority has been proved.This paper studies this kind of decision-making problem from algorithm idea,algorithm steps and decision-making influencing factors.

Linguistic Single-Valued Neutrosophic Power Aggregation Operators and Their Applications to Group Decision-Making Problems

Linguistic single-valued neutrosophic set(LSVNS)is a more reliable tool,which is designed to handle the uncertainties of the situations involving the qualitative data.In the present manuscript,we introduce some power aggregation operators(AOs)for the LSVNSs,whose purpose is to diminish the influence of inevitable arguments about the decision-making process.For it,first we develop some averaging power operators,namely,linguistic single-valued neutrosophic(LSVN)power averaging,weighted average,ordered weighted average,and hybrid averaging AOs along with their desirable properties.Further,we extend it to the geometric power AOs for LSVNSs.Based on the proposed work;an approach to solve the group decision-making problems is given along with the numerical example.Finally,a comparative study and the validity tests are present to discuss the reliability of the proposed operators.

Neutrosophic Mathematical Programming for Optimization of Multi-Objective Sustainable Biomass Supply Chain Network Design

In this paper,a multi-objective sustainable biomass supply chain network under uncertainty is designed by neutrosophic programming method.In this method,for each objective function of the problem,three functions of truth membership,non-determination and falsehood are considered.Neutrosophic programming method in this paper simultaneously seeks to optimize the total costs of the supply chain network,the amount of greenhouse gas emissions,the number of potential people hired and the time of product transfer along the supply chain network.To achieve the stated objective functions,strategic decisions such as locating potential facilities and tactical decisions such as optimal product flow allocation and vehicle routing must be made.The results of the implementation of neutrosophic programming method show the high efficiency of this method in achieving the optimal values of each objective function.Also,by examining the rate of uncertainty,it was observed that with increasing this rate,the total costs of supply chain network design,greenhouse gas emissions and product transfer times have increased,and in contrast,the potential employment rate of individuals has decreased.