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Estimado editor de la revista Serie Científica de la Universidad de las Ciencias Informáticas. Dirijo a usted esta carta resumen, de una conferencia sobre Neutrosofía y Plitogenia, impartida hace algún tiempo en Perú, por este autor. La Neutrosofía es una rama de la filosofía introducida por Florentin Smarandache en 1980. Estudia la neutralidad, es decir, la falta de pertenencia o no pertenencia a un conjunto. Plitogenia, también creada por Smarandache, es una generalización de la dialéctica y la neutrosofía. Se basa en la idea de que la realidad es más compleja que la simple dicotomía de verdadero o falso. Antecendentes: Los antecedentes de la Neutrosofía parten de la lógica de dos valores, ya sea aristotélica o clásica simbolista; y maneja un tipo dado de proposiciones que puede caracterizarse como idealista: El principio del tercero excluido establece que cualquier afirmación es verdadera o falsa, sin espacio para una tercera opción. El principio de no contradicción establece que una proposición no puede ser verdadera y falsa al mismo tiempo y en el mismo sentido. Los principios de no contradicción y del tercero excluido pueden considerarse falsos en algunas situaciones.

Abstract The study addressed the limitations of classical statistical methods when dealing with ambiguous data, emphasizing the importance of adopting neutrosophic statistics as a more effective alternative. Classical methods falter in managing uncertainty inherent in such data, necessitating a shift towards methodologies like neutrosophic statistics. To address this gap, the research introduced a novel sampling approach called “neutrosophic median ranked set sampling” and incorporated neutrosophic estimators tailored for estimating the population mean in the presence of ambiguity. This modification aims to address the inherent challenges associated with estimating the population mean when dealing with neutrosophic data. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Additionally, neutrosophic estimators were developed to leverage auxiliary information within the framework of median-ranked set sampling, enhancing the accuracy of population mean estimation under uncertain conditions. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Bias and mean squared error equations for the suggested estimators were provided, offering insights into their theoretical underpinnings. To illustrate the effectiveness and practical applications of the proposed methodology and estimators, a numerical demonstration and simulation study have been conducted using the R programming language. The key results highlighted the superior performance of the proposed estimators compared to existing alternatives, as demonstrated through comprehensive evaluations based on mean squared error and percentage relative efficiency criteria. The conclusions drawn underscored the effectiveness of the neutrosophic median ranked set sampling approach and suggested estimators in estimating the population mean under conditions of uncertainty, particularly when utilizing neutrosophic auxiliary information and validated real-life applicability. The methodology and estimators presented in the study were shown to yield interval-based results, providing a more realistic representation of uncertainty associated with population parameters. This interval estimation, coupled with minimum mean squared error considerations, enhanced the efficacy of the estimators in determining population mean values. The novelty of the work lies in its introduction of a tailored sampling approach and estimators designed specifically for neutrosophic data, filling a significant gap in the literature. By extending classical statistics to accommodate ambiguity, the study offers a substantial advancement in statistical methodology, particularly in domains where precise data is scarce and uncertainty is prevalent. Furthermore, the empirical validation through numerical demonstrations and simulation studies using the R programming language adds robustness to the proposed methodology and contributes to its practical applicability.

Due to data privacy concerns and a lack of broadly applicable modelling approaches, mental health prediction encounters substantial challenges. This research introduces a pioneering decentralized framework integrating federated learning with Neutrosophic Cognitive Maps (NCMs) to facilitate secure and accurate mental health predictions while preserving data privacy. This innovative approach allows collaborative NCMs training on sensitive patient data across diverse sites without centralizing or transferring the data. The NCMs incorporated into the framework effectively model relationships between various symptoms and mental health states, offering interpretable insights into the complex dynamics of mental health. To address the limitations of local data availability, a multi-task learning methodology is employed, leveraging commonalities between related mental health prediction tasks to enhance modelling. Experiments are done on a synthetic mental health dataset to validate the proposed approach, demonstrating significant improvements. The decentralized nature of the approach ensures robust privacy guarantees by preventing direct access to patient data. The proposed framework contributes to the responsible application of soft computing and AI in the sensitive mental health domain. Furthermore, the interpretability of NCM models facilitates a nuanced analysis of indeterminate interrelationships between various psychological concepts, offering valuable support for data-driven decision-making in mental health contexts.

Plant diseases are one of the factors that leadto yield and economic losses, which have a direct effect on national and international food production systems. One of the most essential ways to avoid agricultural product loss or reduction in amount is to diagnose plant diseases promptly and accurately. Hence, the diagnosis process for plants is crucial and should be conducted accurately. Moreover, this study focuses on this process by constructing an Artificiality Diagnostics Framework (ADF) to serve the study’s objectives which entailed conducting diagnosis for plants in a professional and precise mannerover uncertain environments. Thus, neutrosophic theory is considered the principal ingredient in our ADF. Due to the ability of neutrosophic to divide imagesinto Truth (T), Falsity (F), and Indeterminacy (I). Also, deep learning (DL) is considered another principal ingredientin treating vast samples of datasets. Our comparative analysis of the leavesof potatoesis conducted whether leveraging neutrosophic and without utilizing Neutrosophic. ResNet50, ResNet152, and MobileNetare the principal ingredients for the training dataset. The findings of implementing these networks indicated that ResNet50 achieved the highest accuracy of 0.915 in the T domain, ResNet152 achieved the highest accuracy of 0.905 in the True (T) domain, and MobileNet achieved the highest accuracy of 0.915 in Truth (T) domain. Accuracy of 0.863 in Indeterminate (I).

This research reports on the combined effects of heat and mass transfer (HMT) under the influences of the Soret and Dufour in natural convection steady 2D magnetohydrodynamic flow through the boundary layer in a porous vertical tube or duct. The current study is motivated by the significant applications of HMT in engineering processes such as casting and welding. The goal of this framework is to explore the assisting and opposing movements with HMT above a vertical porous channel under the influence of invariant suction and fluid dissipation which have not been reported in the earlier studies. The governing flow equations in terms of partial differential equations (PDEs) are altered to dimensionless ordinary differential equations (ODEs) by using dimensionless variables. Employing the BVP4C approach, the leading equations are solved numerically. The dual nature of solutions has been observed due to suction. Stability exploration has been provided to confirm a stable solution. A comparison between published and current studies shows outstanding agreement. Key parameter effects on flow characteristics are visually offered using graphs as well as tables. It is noteworthy that the influence of Soret effects becomes apparent in a suspended mixture of particles and fluids. These phenomena can be attributed to temperature differences, whereby the motion of fluid particles in the warmest region with the maximum energy level causes the particles to migrate towards the coldest region. Notably, the flow speed rate at the left plate is initially high and slowly diminishes near the right plate.

This article is a brief foray into the intricate realm of mythological and folkloric composite entities. Our analysis posits that these hybrid and superhybrid creatures serve as compelling evidence that the human psyche consistently transcends binary oppositions as in neutrosophy. Across diverse cultures and epochs, the human mind exhibits a propensity for nuanced and neutrosophic vantage points, defying simplistic categorizations. Additionally, we make some remarks pertaining to the subject matter, and open up a few less conventional questions.

One of the major challenges facing decision-makers at the present time is obtaining complete information about the issue under study, due to the unstable conditions of the work environment that are beyond the control of decision-makers, which requires them to reach an optimal decision in light of these circumstances and fluctuations and to benefit from the data that is collected. Collected by specialists to determine the appropriate probability distribution corresponding to random cases of nature, here we are faced with the issue of making a decision in the event of risk because the probability distribution is a distribution linked to the data controlled by the conditions of the work environment, which entails a great risk. Decision makers bear the responsibility of choosing the optimal decision that reduces This risk is achieved and the greatest possible profit and the least possible loss are achieved. The issue of decision-making becomes more complex as the number of events increases, and we are in dire need of an ideal study of the issue that takes into account all the circumstances of the work environment. The concept of missed opportunity is very useful in analyzing the decision making under risk, after making the decision and the occurrence of events, the decision makers may regret and wish they had chosen actions different from those they chose at the beginning. To reduce the regret of the decision makers and minimize the expected lost opportunity, researchers in the field of classical operations research presented the criterion of the expected lost opportunity through which the decision can be determined. The ideal with the least percentage of regret. In this research, we present a neutrosophic vision of the expected opportunity loss criterion by taking the data of the issue under study. neutrosophic values are ranges whose lowest limit expresses profit in the worst conditions, and only the highest represents profit in the best conditions.

Because of the advancements in technology, classification learning has become an essential activity in today's environment. Unfortunately, through the classification process, we noticed that the classifiers are unable to deal with the imbalanced data, which indicates there are many more instances (majority instances) in one class than in another. Identifying an appropriate classifier among the various candidates is a time-consuming and complex effort. Improper selection can hinder the classification model's ability to provide the right outcomes. Also, this operation requires preference among a set of alternatives by a set of criteria. Hence, multi-criteria decisionmaking (MCDM) methodology is the appropriate methodology can deploy in this problem. Accordingly, we applied MCDM and supported it through harnessing neurotrophic theory as motivators in uncertainty circumstances. Single value Neutrosophic sets (SVNSs) are applied as branch of Neutrosophic theory for evaluating and ranks classifiers and allows experts to select the best classifier So, to select the best classifier (alternative), we use MCDM method called MultiAttributive Ideal-Real Comparative Analysis (MAIRAC) and the criteria weight calculation method called Stepwise Weight Assessment Ratio Analysis (SWARA) where these methods consider singlevalue neutrosophic sets (SVNSs) to improve and boost these techniques in uncertain scenarios. All these methods are applied after modeling criteria and its sub-criteria through a novel technique is Tree Soft Sets (TrSS). Ultimately, the findings of leveraging these techniques indicated that the hybrid multi-criteria meta-learner (HML)-based classifier is the best classifier compared to the other compared models.

Physics thrives on precision, but paradoxes in set theory reveal limitations in our understanding of well-defined boundaries. Neutrosophic logic, challenging the excluded middle principle, introduces the concept of "betweenness" and partial belonging. This article explores among other things several possible avenues to resolve set theory paradoxism, including potential applications of neutrosophic logic in cosmology and particles, from set boundary, to the hypothetical "cosmosphere" boundary, to mixed fermion-boson condensate hypothesis. Embracing indeterminacy and fuzzy boundaries paves the way for a more holistic understanding of the universe's complexity.

Simulation is a numerical technique used to perform tests on a numerical computer, and involves logical and mathematical relationships interacting with each other to describe the behavior and structure of a complex system in the real world over a period of time. Analysis using simulation is a "natural" and logical extension of the mathematical analytical models inherent in operations research, because most operations research methods depend on building mathematical models that closely approximate the real-world environment and we obtain the optimal solution for them using algorithms appropriate to the type of these models. The importance of the simulation process comes In all branches of science, there are many systems that cannot be studied directly, due to the great difficulty that we may encounter when studying, and the high cost, in addition to the fact that some systems cannot be studied directly. The simulation process depends on generating a series of numbers. Randomness subject to a uniform probability distribution over the domain [0,1], then converting these numbers into random variables subject to the law of probability distribution by which the system to be simulated works, using known transformation methods. In previous research, we presented a neutrosophical vision of the reverse transformation method and the method of rejection and acceptance. Which are used to transform random numbers into random variables that follow probability distributions such as: uniform distribution, exponential distribution, beta distribution..., In this research, we present a neutrosophical vision of the Composition method )the mixed method of inverse transformation method and rejection method), used to generate random variables that follow... To some Poisson distribution, the aim is to obtain neutrosophic random variables that we use when simulating systems that operate according to this distribution in order to obtain more accurate simulation results.

The dynamic landscape of cloud computing design presents significant challenges regarding power consumption and quality of service (QoS). Virtual machine (VM) consolidation is essential for reducing power usage and enhancing QoS by relocating VMs between hosts. OpenStack Neat, a leading framework for VM consolidation, employs the Modified Best-Fit Decreasing (MBFD) VM placement technique, which faces issues related to energy consumption and QoS. To address these issues, we propose an Energy Efficient VM Consolidation (EEVMC) approach. Our method introduces a novel host selection criterion based on the incurred loss during VM placement to identify the most efficient host. For validation, we conducted simulations using real-time workload traces from Planet-Lab and Materna over ten days, leveraging the latest CloudSim toolkit to compare our approach with state-of-the-art techniques. For Planet-Lab’s workload, our EEVMC approach shows a reduction in energy consumption by 80.35%, 59.76%, 21.59%, and 7.40%, and fewer system-level agreement (SLA) violations by 94.51%, 94.85%, 47.17%, and 17.78% when compared to Modified Best-Fit Decreasing (MBFD), Power-Aware Best Fit Decreasing (PABFD), Medium Fit Power Efficient Decreasing (MFPED), and Power-Efficient Best-Fit Decreasing (PEBFD), respectively. Similarly, for Materna, EEVMC achieves a reduction in energy consumption by 16.10%, 61.0%, 4.94%, and 4.82%, and fewer SLA violations by 76.99%, 88.88%, 12.50%, and 48.65% against the same benchmarks. Additionally, Loss-Aware Performance Efficient Decreasing (LAPED) significantly reduces the total number of VM migrations and SLA time per active host, indicating a substantial improvement in cloud computing efficiency.

In this paper we extend the SuperHyperAlgebra, SuperHyperGraph, SuperHyperTopology, SuperHyperSoft Set, endowed with SuperHyperOperations, SuperHyperAxioms, and SuperHyperFunctions, to the most general form of structure, from our real world, called SuperHyperStructure in any field of knowledge. A practical application of the SuperHyperStructure is presented at the end. The prefix “Hyper” [Marty, 1934] stand for the codomain of the functions and operations to be P(H), or the powerset of the set H. While the prefix “Super” [Smarandache, 2016] stands for using the Pn (H), n ≥ 2, or the n-th PowerSet of the Set H {because the set (or system) 𝐻 (that may be a set of items, a company, institution, country, region, etc.) is organized in sub-systems, which in their turn are organized in sub-sub-systems, and so on} in the domain and/or codomain of the functions and operations.

The inclusion of nanoparticles has the potential to improve the thermal efficiency of the base fluid. The field of nanofluid (NF) dynamics has attracted important attention due to its extensive range of practical uses like fuel cells, solar energy, medication administration, heat transfer, microfabrication, coolant applications, and other related domains. The aim of this study is to scrutinize the impact of Lorentz force, thermal energy, joule heating, heat source and injection parameters, and Brownian and thermoporetic diffusions on the hybrid nanofluid over the moving wedge. The stability inquiry is reported for the existing work in order to confirm the stable solutions that make the study unique. Novelty of the existing work is to investigate the hybrid nanofluid flow and its stability. The nanoparticles MoS2 and Ag are suspended in ethylene glycol and water used as host fluids. The numerical solution is obtained from the dimensionless first-order differential equations, which are achieved from the basic flow phenomena through similarity alteration variables. The influence of emerging factors on flow phenomena is reported via graphs. The positive eigenvalues report stable solutions, while the negative eigenvalues designate unstable solutions. It is perceived that due to Lorentz force, the rate of the fluid declines while the temperature inside the flow channel enhances. The velocity profile decreases while the temperature and concentration increase with increasing quantities of permeable factors. Similarly, the Forchheimer number causes to enhance the flow rate and decrease the heat and concentration outlines. The current analysis is validated by the published work.

In this paper, we introduce the notion of single-valued neutrosophic soft uniform spaces as a view point of the entourage approach. We investigate the relationship among single-valued neutrosophic soft uniformities, single-valued neutrosophic soft topologies and single-valued neutrosophic soft interior operators. Also, we study several single-valued neutrosophic soft topologies induced by a single-valued neutrosophic soft uniform space.

In the real word, in most cases, everything (an attribute, event, proposition, theory, idea, person, object, action, etc.) is evaluated in general by many sources (called experts), not only one. The more sources evaluate a subject, the better accurate result (after fusioning all evaluations). That’s why, in this paper, we straightforwardly extend the Refined Neutrosophic Set to the MultiNeutrosophic Set, and we show that the last two are isomorphic. A MultiNeutrosophic Set is a Neutrosophic Set whose all elements’ degrees of truth/indeterminacy/falsehood are evaluated by many (Multi) sources. Afterwards, we introduce a total order on the set of n-plets of the form (p, r, s), we build the operators on the (p, r, s)-plets, and show several applications of the MultiNeutrosophic Sets. Several particular cases of the MultiNeutrosophic Sets are presented: such as MultiFuzzy Set, MultiIntuitionistic Fuzzy Set, MultiPicture Fuzzy Set, and other Multi(Fuzzy Extension) Set.

The goal of this short note is to expand the concepts of ‘pluralism’, ‘neutrosophy’, ‘refined neutrosophy’, ‘refined neutrosophic set’, ‘multineutrosophic set’, and ‘plithogeny’ (Smarandache 2002, 2013, 2017, 2019, 2021, 2023a, 2023b, 2023c), into a larger category that I will refer to as MultiAlism (or MultiPolar). As a straightforward generalization, I propose the conceptualization of a MultiPolar System (different from a PluriPolar System), which is formed not only by multiple elements that might be random, or contradictory, or adjuvant, but also by accepting features from more than one basic system (UniPolar, BiPolar, TriPolar, or PluriPolar systems). PluriAlism is a closed dynamic system without neutralities nor indeterminacies, while MultiAlism is an open dynamic system with neutralities and indeterminacies. PluriAlism is a uni-system (formed by elements from a single system), while MultiAlism is a MultiSystem (formed by elements from many systems).

In order to calculate the indefinite integrals of the symbolic plithogenic field, we used the substitution method, which was provided in this article. We also established a theorem that allowed us to locate the majority of the integrals for the symbolic plithogenic functions, in addition to the condition that must be met for the integration operation to be possible.

Graph labelling is the assignment of labels to the edges, vertices, or both. The issue of limiting the spread of non-interfering frequencies allotted to radio transmitters serves as the motivation for the research on labelling graphs according to different limitations. However, compared to classical models, fuzzy labelling models provide the system with greater accuracy, adaptability, and compatibility. The definition of the neutrosophic fuzzy magic labelling graph and a detailed discussion of its properties using numerical examples for the path, cycle, and star graphs in a neutrosophic environment are presented in this study. The proposed work has also been used in decision-making situations to choose the optimal subject combinations based on student interests for the best academic performance. In order to demonstrate the validity of the suggested work, a comparative analysis with the current methodology has also been conducted.

Inventory management plays an important role in production and marketing processes, especially in production facilities and commercial institutions that have warehouses in which they store their equipment and goods. Inventory management is considered one of the most important management functions in terms of determining the ideal volume of inventory and calculating its costs, as this affects the facility’s efficiency and achieves either large profits or it causes huge losses, so warehouse managers in production facilities or institutions must determine the appropriate and ideal volume of inventory, especially when they are presented with price offers from companies seeking to market their products.

Impostor syndrome or Impostor phenomenon is a belief that a person thinks their success is due to luck or external factors, not their abilities. This psychological trait is present in certain groups like women. In this paper, we propose a neutrosophic trait measure to represent the psychological concept of the trait - antitrait using refined neutrosophic sets. This study analysed a group of 200 undergraduate students for impostor syndrome, perfectionism, introversion and self-esteem: after the COVID pandemic break in 2021. Data labelling was carried out using these neutrosophic trait measures. Machine learning models like Support Vector Machine(SVM), K-nearest neighbour (K-NN), and random forest were used to model the data; SVM provided the best accuracy of 92.15%.

In this paper, we were keen to present the concept of the symbolic plithogenic differentials calculus, Where the symbolic plithogenic differentiable is defined. In addition, properties of the symbolic plithogenic differentiation are introduced. Also, we prove the derivation rules of the symbolic plithogenic functions.

Abstract The entropy generation analysis for the nanofluid flowing over a stretching/shrinking curved region is performed in the existence of the cross-diffusion effect. The surface is also subjected to second-order velocity slip under the effect of mixed convection. The Joule heating that contributes significantly to the heat transfer properties of nanofluid is incorporated along with the heat source/sink. Furthermore, the flow is assumed to be governed by an exterior magnetic field that aids in gaining control over the flow speed. With these frameworks, the mathematical model that describes the flow with such characteristics and assumptions is framed using partial differential equations (PDEs). The bvp4c solver is used to numerically solve the system of non-linear ordinary differential equations (ODEs) that are created from these equations. The solutions of obtained through this technique are verified with the available articles and the comparison is tabulated. Meanwhile, the interpretation of the results of this study is delivered through graphs. The findings showed that the Bejan number was decreased by increasing Brinkman number values whereas it enhanced the entropy generation. Also, as the curvature parameter goes higher, the speed of the nanofluid flow diminishes. Furthermore, the increase in the Soret and Dufour effects have enhanced the thermal conduction and the mass transfer of the nanofluid.

A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2 − SPR.

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer’s rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

The linear programming method is one of the important methods of operations research that has been used to address many practical issues and provided optimal solutions for many institutions and companies, which helped decision makers make ideal decisions through which companies and institutions achieved maximum profit, but these solutions remain ideal and appropriate in If the conditions surrounding the work environment are stable, because any change in the data provided will affect the optimal solution and to avoid losses and achieve maximum profit, we have, in previous research, reformulated the linear models using the concepts of neutrosophic science, the science that takes into account the instability of conditions and fluctuations in the work environment and leaves nothing to chance. While taking data, neutrosophic values carry some indeterminacy, giving a margin of freedom to decision makers. In another research, we reformulated one of the most important methods used to solve linear models, which is the simplex method, using the concepts of this science, and as a continuation of what we did in the previous two researches, we will reformulate in this research. The graphical method for solving linear models using the concepts of neutrosophics. We will also shed light on a case that is rarely mentioned in most operations research references, which is that when the difference between the number of unknowns and the number of constraints is equal to one, two, or three, we can also find the optimal solution graphically for some linear models. This is done by taking advantage of the conditions of non-negativity that linear models have, and we will explain this through an example in which the difference is equal to two. Also, through examples, we will explain the difference between using classical values and neutrosophic values and the extent of this’s impact on the optimal solution.

This study provides an innovative approach to neutrosophic algebraic structures by introducing a new structure called Neutrosophic Soft Cubic T-ideal (NSCTID), which combines T-ideal (TID) and Neutrosophic Soft Cubic Sets (NSCSs) within the framework of PS-Algebra. Within the already-existing neutrosophic cubic structures, the addition of soft sets with the characteristics of TID makes this structure more desirable. The theoretical development of the proposed structure includes the application of fundamental ideas as union, intersection, the Cartesian product, and homomorphism. We also introduce the notions of NSCTID-translation and NSCTID-multiplication to further enhance the structure of NSCTID. By applying the idea of translation and multiplication, we offer improved algorithm for neutrosophic cubic sets to deal with different parameters that are satisying the TID’s distinctive characteristics. Through this thorough research, we offer an elementary understanding of NSCTID and its capabilities, providing the way to new algebraic structures.

In this short note we show that the so-called Ambiguous Set (2019) is a subclass of the Double Refined Indeterminacy Neutrosophic Set (2017) and is a particular case of the Refined Neutrosophic Set (2013). Also, the Ambiguous Set is similar to the Quadripartitioned Neutrosophic Set (2016), and Belnap’s Four-Valued Logic (1975).

Operations research methods focus on formulating decision models, models that approximate the real work environment to mathematical models, and their optimal solution helps the decision maker to make optimal decisions that guarantee the greatest profit or the lowest cost. These models were built based on the data collected on the practical issue under study, and these data are classic values, specific values that are correct and accurate during the period in which these data are collected, which means that they remain ideal if the surrounding conditions remain the same as those in which they were collected. Data, and since the aim of this study is to make ideal decisions and to develop future plans through which we achieve the greatest profit or the least cost, It was necessary to search for a study that fits all the conditions in which the work environment passes in the present and the future. If we take data, neural values, indeterminate values - uncertain - leave nothing to chance, and take into account all conditions from worst to best. In this paper, we will present a complementary study to what we have done in previous research, the purpose of which was to reformulate some operational research methods using neutrosophic data. We will reformulate the assignment problem and one of the methods for its solution, which is the Hungarian method, using neutrosophic concepts, and we will explain the difference between using classical and neutrosophic data through examples.

In this paper we recall the six new types of topologies, and their corresponding topological spaces, that we introduced in the last years (2019-20223), such as: NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. The nth-PowerSets ( ) n P H and * ( ) n P H , that the SuperHyperTopology and respectively Neutrosophic SuperHyperTopology are based on, better describe our real world, since a system H (that may be a set, company, institution, country, region, etc.) is organized in sub-systems, which in their turn are organized each in sub-sub-systems, and so on.

Utilizing two ideas of neutrosophic subsets (NS) and triangular norms, we introduce a new type of graph as valued-inverse Dombi neutrosophic graphs. The valued-inverse Dombi neutrosophic graphs are a generalization of inverse neutrosophic graphs and are dual to Dombi neutrosophic graphs. We present the concepts of (complete) strong valued-inverse Dombi neutrosophic graphs and analyze the complement of (complete) strong valued-inverse Dombi neutrosophic graphs and self-valued complemented valued-inverse Dombi neutrosophic graphs. Since the valued-inverse Dombi neutrosophic graphs depend on real values, solving the non-equation and the concept of homomorphism play a prominent role in determining the complete, strong, complementarity and self-complementarity of valued-inverse Dombi neutrosophic graphs. We introduce the truth membership order, indeterminacy membership order, falsity membership order, truth membership size, indeterminacy membership size and indeterminacy membership size of any given valued-inverse Dombi neutrosophic graph, which play a major role in the application of valued inverse Dombi neutrosophic graphs in complex networks. An application of a valued-inverse Dombi neutrosophic graph is also described in this study.

Multi-criteria decision making (MCDM) is concerned about coordinating as well as looking after selection as well as planning problems which included multi-criteria. The neutrosophic soft set cannot handle the environment which involved more than one attribute. To overcome those hurdles neutrosophic hypersoft set (NHSS) is defined. In this paper, we proposed the generalized aggregate operators on NHSS such as extended union, extended intersection, OR-operation, AND operation, etc. with their properties. Finally, the necessity and possibility operations on NHSS with suitable examples and properties are presented in the following research.

Plithogenic sets coined by Smarandache in the year 2018 has unveiled new research opportunities in the field of Multi criteria decision making (MCDM). The contributions and developments of new decision making approaches based on plithogeny is gaining high momentum presently. The theoretical conceptualization of different phenomenon with plithogenic sets are also applied in designing optimal solutions to the decision making problems. This review paper presents the applications of plithogenic MCDM from the year 2018 to till date in almost all the spheres of decision making scenario. The literature works of the researchers presented in this paper will certainly portray the compatibility and flexibility of plithogenic sets, operators and other decision making tools. Though the time span considered for counting on the plithogeny based works is short, the applications of plithogenic sets are growing many in number and also plithogeny based theories are amplifying in a speedy manner. This has motivated the authors to investigate on the proliferation of plithogeny applications in decision making. This review paper has focused on the dimensions of different fields to which plithogeny is applied, new plithogeny based theories, extension of plithogeny, plithogenic based operators and measures. In addition to it the data on the publications of plithogeny based articles and interests of researchers are also presented as a part of this review work. The overall impact of plithogeny in the arena of decision making science and on the researchers of the same field is well sketched in this paper with the intention and hope of inspiring plithogenic researchers.

The softmax function is a well-known generalization of the logistic function. It has been extensively applied in various probabilistic classification methods such as softmax regression, linear discriminant analysis, naive Bayes classifiers, and artificial neural networks. Inspired by the advantages of the softmax function, we have developed the softmax function-based single-valued neutrosophic aggregation operators. Then we have es tablished some essential properties of aggregation operators based on the softmax function with the neutrosophic set. Additionally, we have defined a multi-attribute decision-making method based on the proposed aggregation operators. Using the proposed MCDM method, we have developed a novel algorithm. This algorithm helps to examine FD-risk assessment problems. Also, the proposed algorithm process is a reasonable strategy for the decision-making problem. It is easy to recognize when choosing a neutrosophic set of information for a practical decision problem. We used this proposed MADM method to exercise a realistic MADM problem with neutrosophic information. Finally, we have considered one numerical illustration to show the validity and reliability of the proposed methods.

In this paper, we extend, for the first time, the Law of Included Multiple-Middles to the Law of Infinitely-Many-Middles. And we present several practical applications. Also, we discuss Aristotle's Syllogism, Principle of Identity, and Principle of NonContradiction.

This paper presents novel concepts including stratified single-valued neutrosophic soft topogenous (stratified svns-topogenous), stratified single-valued neutrosophic soft filter (stratified svns-filter), stratified single-valued neutrosophic soft quasi uniformity (stratified svnsq-uniformity) and stratified single-valued neutrosophic soft quasi proximity (stratified svnsq-proximity). Additionally, we present the idea of single-valued neutrosophic soft topogenous structures, formed by integrating svns-topogenous with svns-filter, and discuss their properties. Furthermore, we explore the connections between these single-valued neutrosophic soft topological structures and their corresponding stratifications.

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function and a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems.

The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.

The neutrosophic automorphisms of a neutrosophic groups G (I) , denoted by Aut(G (I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G (I) which is also a neutrosophic homomorphism. Moreover, suppose that X1 = X(G (I)) is the neutrosophic group of inner neutrosophic auto-morphisms of a neutrosophic group G (I) and Xn the neutrosophic group of inner neutrosophic automorphisms of Xn-1. In this paper, we show that if any neutrosophic group of the sequence G (I), X1, X2, … is the identity, then G (I) is nilpotent.

It is well known that the unpredictable speech production brought on by stress from the task at hand has a significant negative impact on the performance of speech processing algorithms. Speech therapy benefits from being able to detect stress in speech. Speech processing performance suffers noticeably when perceptually produced stress causes variations in speech production. Using the acoustic speech signal to objectively characterize speaker stress is one method for assessing production variances brought on by stress. Real-world complexity and ambiguity make it difficult for decision-makers to express their conclusions with clarity in their speech. In particular, the Neutrosophic speech algorithm is used to encode the language variables because they cannot be computed directly. Neutrosophic sets are used to manage indeterminacy in a practical situation. Existing algorithms are used except for stress on Neutrosophic speech recognition. The creation of algorithms that calculate, categorize, or differentiate between different stress circumstances. Understanding stress and developing strategies to combat its effects on speech recognition and human-computer interaction system are the goals of this recognition.

This article introduces the notion of duplex elements of the finite rings and corresponding neutrosophic rings. The authors establish duplex ring and neutrosophic duplex ring by way of various illustrations.

For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only partially true (and partially indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical space that has some item that are totally (100%) false. While the Non-Euclidean Geometries [hyperbolic and elliptic geometries] resulted from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom [and in general: theorem, concept, idea etc.] and even of more axioms [theorem, concept, idea, etc.] and in general from any geometric axiomatic system (Euclid’s five postulates, Hilbert’s 20 axioms, etc.), and the NeutroAxiom results from the partial negation of any axiom (or concept, theorem, idea, etc.). Clearly, the AntiGeometry is a generalization of Non-Euclidean Geometries.

In this paper, we propose the introduction of a neutrosophic chi-square-test for consistency, incorporating neutrosophic statistics. Our aim is to modify the existing chi-square -test for consistency in order to analyze imprecise data. We present a novel test statistic for the neutrosophic chi-square -test for consistency, which accounts for the uncertainties inherent in the data. To evaluate the performance of the proposed test, we compare it with the traditional chi-square -test for consistency based on classical statistics. By conducting a comparative analysis, we assess the efficiency and effectiveness of our proposed neutrosophic chi-square -test for consistency. Furthermore, we illustrate the application of the proposed test through a numerical example, demonstrating how it can be utilized in practical scenarios. Through this implementation, we aim to provide empirical evidence of the improved performance of our proposed test when compared to the traditional chi-square-test for consistency based on classical statistics. We anticipate that the proposed neutrosophic chi-square -test for consistency will outperform its classical counterpart, offering enhanced accuracy and reliability when dealing with imprecise data. This advancement has the potential to contribute significantly to the field of statistical analysis, particularly in situations where data uncertainty and imprecision are prevalent.

The objective of this study is to incorporate topological space into the realm of n- Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-cylindrical Fuzzy neutrosophic topological spaces (n-CyFNTS), n- CyFN Open sets, and n-CyFN Closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.

This paper is devoted to Plithogeny, Plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of the principal concepts derived from plithogeny, and relate them to complex problems.

One of the disadvantages of the point estimate in survey sampling is that it fluctuates from sample to sample due to sampling error, as the estimator only provides a point value for the parameter under discussion. The neutrosophic approach, pioneered by Florentin Smarandache, is an excellent tool for estimating the parameters under consideration in sampling theory since it yields interval estimates in which the parameter lies with a very high probability. As a result, the neutrosophic technique, which is a generalization of classical approach, is used to deal with ambiguous, indeterminate, and uncertain data. In this investigation, we suggest a new general family of ratio and exponential ratio type estimators for the elevated estimation of neutrosophic population mean of the primary variable utilizing known neutrosophic auxiliary parameters. For the first degree approximation, the bias and Mean Squared Error (MSE) of the suggested estimators are computed. The neutrosophic optimum values of the characterizing constants are determined, as well as the minimum value of the neutrosophic MSE of the suggested estimator is obtained for these optimum values of the characterizing scalars. Because the minimum MSE of the classical estimators of population mean lies inside the estimated interval of the neutrosophic estimators, the neutrosophic estimators are better than the equivalent classical estimators. The empirical investigation, which used both real and simulated data sets, backs up the theoretical findings. For practical utility in various areas of applications, the estimator with the lowest MSE or highest Percentage Relative Efficiency (PRE) is recommended.

In this paper, we recall and study the new type of algebraic structures called Symbolic Plithogenic Algebraic Structures. Their operations are given under the Absorbance Law and the Prevalence Order.

It is well known that Hv-groups and groups are connected through regular relations. The purpose of this paper is to find a similar connection between neutrosophic Hv-groups and neutrosophic groups by using the concept of fundamental relations on Hv-groups. First, we characterize the complete parts of neutrosophic Hv-groups. Then we study their (strongly) regular relations. Finally, we find their fundamental group.

The research objective of the paper is to propose a model, based on the Multiple-Criteria Decision-Making (MCDM) methods, that facilitates a selection process of an adequate strategy directed to the development of e-commerce. For that aim, the MEthod based on the Removal Effects of Criteria (MEREC) is applied for defining the criteria weights. The recently proposed COmprehensive Distance Based RAnking (COBRA) method is used for the final assessment and ranking of the considered alternatives. The applicability of the proposed model is tested by using an example borrowed from the literature. Three alternative development strategies are assessed against five evaluation criteria. The final results proved the applicability and reliability of the proposed MCDM model.

The Vehicle Routing Problem (VRP) has been extensively studied by different researchers from all over the world in recent years. Multiple solutions have been proposed for different variations of the problem, such as Capacitive Vehicle Routing Problem (CVRP), Vehicle Routing Problem with Time Windows (VRP-TW), Vehicle Routing Problem with Pickup and Delivery (VRPPD), among others, all of them with deterministic times. In the last years, researchers have been interested in including in their different models the variations that travel times may experience when exposed to all kind of phenomena, mainly vehicle traffic. This article addresses the VRP from this perspective, proposing the design and implementation of a genetic algorithm based on neutrosophic theory for calculating the fitness function of each route, considering the variability and uncertainty present in travel times. A deterministic genetic algorithm is also implemented with the average travel times to compare it with the neutrosophic algorithm using simulation. As conclusion, a deterministic algorithm does not necessarily generate the best solution in the real world, full of uncertainty. Also, the quantification of uncertainty using neutrosophic theory can be used in route planning, opening a broad and interesting field of research for future investigations.

In this paper we define the Soft Set Product as a product of many soft sets and afterwards we extend it to the HyperSoft Set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft Set. We also present several applications of the Soft Set Product to Fuzzy (and fuzzy-extensions) Soft Set Product and to IndetermSoft Set and IndetermHyperSoft Set.