International Journal of Neutrosophic Science

This paper presents a novel approach for ranking the issues experienced by female employees across various industries using the nonagonal single-valued neutrosophic soft set framework. By leveraging an extensive database of multi-observer data, we evaluated the challenges faced by women in diverse work environments. The Neutrosophic Soft Set proved to be a robust tool for addressing decision-making complexities within the neutrosophic domain, facilitating a comprehensive understanding of these issues. We established a comparative table to categorize the identified problems, enabling effective organization based on attributes, capabilities, and outcomes. Our findings underscore the utility of advanced mathematical frameworks in analyzing gender-specific workplace challenges, providing valuable insights for developing targeted interventions. This research contributes to the ongoing discourse on gender equity in the workplace and lays the groundwork for future studies aimed at enhancing the experiences of female employees across sectors.

We studied and introduced a concept SIVFT then present the concept of SIVF subspace and SIVF product topology in SIVF topological spaces. W-Hausdorff Separation Axiom in SIVF topological spaces and its basics are studied.

This work adds to the burgeoning knowledge of soft topology. First, we continue the study of soft locally closed sets. We present several characterizations of soft locally closed sets. Also, we investigate their behaviors using specialized soft topologies as product and subspace soft topologies. Then, we define and investigate the concept of soft dense-in-itself spaces. In particular, we characterize soft dense-in-itself subspaces in terms of locally closed sets. Given a soft topological space pN, ρ, Mq, the collection of soft locally closed sets of pN, ρ, Mq forms a soft topology on N relative to M which is denoted by ρl. We obtain several symmetries between the pN, ρ, Mq and pN, ρl, Mq. In particular, we show that pN, ρ, Mq is soft T0 (resp. soft TD, soft indiscrete) iff pN, ρl, Mq is soft T0 (resp. soft discrete, soft connected). Moreover, we show that if pN, ρl, Mq is soft T1 (resp. soft Alexandroff), then pN, ρl, Mq is soft discrete (resp. soft Alexandroff) but not conversely. In addition to these, we obtain several characterizations and relationships of both soft locally indiscrete spaces and soft submaximal spaces. In particular, we show that pN, ρ, Mq is soft locally indiscrete if and only if ρ “ ρl. In the last section, via the soft locally closed sets, we define and investigate soft lc-regularity as a stronger form of soft regularity. Finally, the paper deals with the correspondence between some concepts in soft topology and their analog concepts in classical topology.

Decision-making procedures frequently encounter disputes or contradictions between expert perspectives, and thus we need ways to resolve them. When working with many viewpoints in a decision-making environment, this method enables dynamic, changing input from different experts, which may be particularly helpful in real- world situations like expert systems and group decision-making. In this work, we provide multiple opinions in the fuzzy soft expert set and their application to decision-making issues (MO-FSES), which is an extension of the fuzzy soft set, and multiple opinions in time fuzzy soft expert set. The characteristics of its primary operations complement, union intersection, AND, and OR will also be defined and examined by me. Lastly, we will use this strategy for decision-making challenges.

The study examined the shortcomings of conventional statistical techniques in managing unclear or ambiguous data and emphasized the necessity of implementing neutrosophic statistical techniques as a more enhanced remedy. Advanced techniques like neutrosophic statistics (NS) were developed since traditional statistical methods are unable to handle the uncertainty present in ambiguous data. In order to tackle this problem, the study suggested an innovative and novel sampling method called "neutrosophic stratified ranked set sampling (NSRSS)" in addition to specialized neutrosophic estimators for precisely predicting the population mean in the proximity of uncertainty. This novel strategy adjusted ranked set sampling (RSS) techniques to allow the special features of neutrosophic data. Furthermore, the study improved the precision of estimating the population mean in uncertain situations by introducing neutrosophic estimators that use subsidiary information inside the structure of stratified ranked set sampling (SRSS). The work provided theoretical insights into the performance of these estimators by presenting comprehensive formulations of bias and mean squared error (MSE). To illustrate the efficacy of the suggested techniques, the study includes simulation studies, numerical examples conducted using the computer language R. Evaluations utilizing MSE, and percentage relative efficiency (PRE) demonstrated the higher accuracy of the suggested estimators over conventional alternatives. The findings demonstrated the NSRSS's applicability, particularly for predicting population means in situations where heterogeneity and uncertainty are prevalent. Furthermore, it was demonstrated that the estimators and technique produced interval-based findings, which provided a more accurate depiction of the uncertainty related to population parameters. The reliability of the estimators in estimating population means was greatly improved by this interval estimation in combination with a lower MSE. A significant vacuum in the field of statistical research is filled by the study's introduction of estimators and a customized sampling approach made especially for neutrosophic data. This research significantly advances statistical theory and practice by extending traditional statistical approaches to efficiently handle ambiguous data, especially for applications where exact data is few, heterogeneous, or uncertain. The empirical validation through numerical illustrations and simulations conducted in R further solidifies the practicality and robustness of the proposed techniques, reinforcing their applicability to real-world scenarios.

The goal of this study is to introduce fuzzy neutrosophic -closed sets, a novel notion of collections in fuzzy neutrosophic topology. In this research, we use certain novel concepts, theories, and hypotheses to explore and analyze other innovative characteristics of these classes. In order to make clear the connections among the new research of -closed sets and other sets, a collection of instances is given and explored.

Pentagonal Neutrosophic Set is a powerful technique for modelling situation in real life where there is uncertainty, indeterminacy, and inconsistency, the PNTP is an advanced version of classical transportation problems. Traditional transportation models do not perform well with imprecise data unlike PNTP that offers a powerful framework that can handle truth, indeterminacy, falsity, non-membership, and membership parameters resulting in a more realistic decision about logistics. In this work, we present a novel Topologized Graphical Method (TGM) for resolving the PNTP, which uses graphical notations to visualize and analyse intricate interactions in transport networks under neutrosophic circumstances. In this paper, an efficient and structured solution methodology has been developed for optimization of PNTP, with TGM incorporated to provide a systematic approach to the PNTP while significantly reducing computational burden. To improve the pragmatism of the method, an algorithm is established in Python to convert the neutrosophic transportation model into a classical transportation problem, which contributes to computing efficiency and helps the decision-makers get the optimal solutions with little efforts. Solutions to numerical examples and case studies, which show that our method achieves better performance than conventional approach in minimizing transportation cost, optimizing resources allocation, and reducing the burden of calculation, provide validation of the proposed method. This research employs Pentagonal Neutrosophic Sets with the TGM as well as the use of the Python programming language to offer an effective and accurate decision-support instrument, improving transportation planning in uncertain dynamic environments. In addition, the findings provide tangible insights into how PNTP could be beneficial in real-world applications, particularly in fields like logistics, SCM, and network design, where managing uncertain information is essential. The next step of this work will be analysing the integration of AI and ML techniques with the presented method to gain improvements on predictive analytics, automation, and real-time decision-making abilities in transportation problems.

This paper aims to introduce various operations in the context of the Rough Single-Valued Pentapartitioned Neutrosophic Set (RSVPNS) environment. Then, based on Grey Relational Analysis (GRA), we propose a Multi-Attribute Decision-Making (MADM) technique. Additionally, we present a practical numerical example to validate the proposed MADM technique in the context of selecting a tourist place for government initiatives aimed at enhancing its attractiveness to tourists.

In this paper, we researched and confirmed some of the axioms of NOPCMS (Neutrosophic orthogonal pentagonal controlled metric space). We used NOPCMS to translate the Banach contraction principle in the formerly defined spaces. Several cases were numerically evaluated, and certain findings were supported, in or- der to review what we found. Furthermore, by demonstrating their existence with a unique and comprehensive solution, we deliver proof of usage and implementation.

One of the most effective devices to model uncertainty in decision-making difficulties is the Neutrosophic set (NS) and its extensions, like interval NS (INS), interval complex NS (ICNS), and complex NS (CNS). Predicting the result of sales benefits is the essential element of effective business management. Traditionally, undertaking this prediction has depended generally on individual human analyses in the sales decision-making process. A model of business-to-business (B2B) sales predicting is a difficult decision-making procedure. There are several methods for supporting this procedure; however, generally it is even established on the individual judgments of the decision-maker. The B2B sales predicting problem is represented as the prediction problem. Presently, intelligible predictive methods were analyzed and studied utilizing the technique of machine learning (ML) to increase the upcoming sales prediction. This paper presents an Adaptive Intelligent Business to Business Sales Estimation using Neutrosophic Fusion of Rough Set Theory (AIB2BSE-NFRST) model. The main intention of AIB2BSE-NFRST technique is to enhance prediction analysis for B2B sales estimation using advanced techniques. Initially, the data pre-processing performs min-max normalization to prepare raw input data for analysis by transforming it into a structured format. Furthermore, the proposed AIB2BSE-NFRST technique utilizes NFRST method for the prediction process. To further optimize model performance, the seagull optimization algorithm (SOA) is utilized for hyperparameter tuning to ensure that the best hyperparameter is selected. To exhibit the enhanced performance of the presented AIB2BSE-NFRST model, a comprehensive experimental analysis is made under the E-commerce sales dataset. The AIB2BSE-NFRST model outperforms existing techniques with a superior MSE of 0.0033, highlighting its exceptional accuracy in B2B sales estimation.

Neutrosophic logic is a neonate research field in which all propositions are anticipated to have the percentage (proportion) of truth in a sub-set T, the proportion of falsity in a sub-set F, and the proportion of indeterminacy in a sub-set I. Neutrosophic set (NS) is efficiently applied for indeterminate information processing and provides assistance to address the indeterminacy information of data. Demand Forecasting, undoubtedly, is the only most significant element of some organization's Supply Chain. It defines the predictable demand for the future and sets the preparedness level that is needed on the supply side to match the demand. Business intelligence (BI) plays a significant part in helping the decision maker obtain the understanding for increasing productivity or improved and faster decisions. Furthermore, it improves and helps the efficacy of functional rules and its influence on corporate-level decision-making that provides improved strategic options in dynamic business environments. Within the period of data-driven demand forecasting, the integration of artificial intelligence (AI) technologies in BI models has transformed the system groups that utilize and analyze data. In the manuscript, a Business Intelligence Framework for a Data-Driven Demand Forecasting Model Using a Pentapartitioned Neutrosophic Vague Soft Set (BIFDDF-PNVSS) technique is proposed. The main goal of the BIFDDF-PNVSS technique is to progress the accurate BI structure for the demand forecasting method. The data pre-processing stage is initially applied for converting input data into a beneficial format by the Z-score normalization method. Moreover, the PNVSS technique is utilized for the data-driven demand prediction model. Finally, to improve the prediction performance of the PNVSS model, the parameter tuning process is performed by implementing the cheetah optimization algorithm (COA) model. A comprehensive experimentation is performed to verify the performance of the BIFDDF-PNVSS methodology under the demand forecasting dataset. The BIFDDF-PNVSS methodology outperforms existing techniques with a superior MSE of 0.0008, demonstrating its exceptional accuracy in demand forecasting compared to other models.

From a philosophical viewpoint, the theory of neutrosophic set (NS) is a simplification of the concept of Fuzzy Set (FS) and intuitionistic FS (IFS). An NS is illustrated by a truth, an indeterminacy, and a falsity membership functions and every membership degree is an actual standard or a non-standard sub-set of the non-standard unit range of] −0, 1+ [.  Customer churn is when clients stop utilizing a company’s service or product. Moreover, it is also named customer retention, which is vastly significant metric as it is much less costly to keep the existing customers than to obtain novel customers. The prediction of churn plays an essential part in customer retention because it forecasts clients who are in danger of leaving the organization. In the banking sector, the customer attrition arises when clients quit utilizing the services and goods provided by the bank for some time. So, customer churn is vital in today’s economic banking industry. This study proposes a Leveraging Bipolar Fuzzy Hypersoft Set with Heuristic Optimization Algorithms-based Customer Retention Prediction (BFHSS-HOACRP) technique in financial sectors. The BFHSS-HOACRP technique applies optimized techniques to predict the customer retention behavior in the industry of bank.  Initially, the mean normalization technique is utilized in the data pre-processing stage to prepare raw data into a suitable format for analysis and modeling. For the selection of feature process, the grasshopper optimization algorithm (GOA) method is employed to identify and select the most relevant features from an input data. In addition, the proposed BFHSS-HOACRP technique implements bipolar fuzzy hypersoft set (BFHSS) method for the classification process. Additionally, the spider monkey optimization (SMO)-based hyperparameter selection process is performed to optimize the classification results of BFHSS model. The efficacy of the BFHSS-HOACRP approach is examined under the bank customer churn prediction dataset. The comparison analysis of the BFHSS-HOACRP approach portrayed a superior accuracy value of 95.41% over existing techniques.

The primary goal of this paper is to study and introduce fuzzy anti-normed linear spaces, as well as, some additional properties concerning these spaces. From this point of view, some theoretical results are obtained; for example, it was proved that the space of all linear and fuzzy bounded operators over fuzzy anti-normed linear spaces is fuzzy complete. Moreover, some additional theoretical results are stated and proved.

A complex linear Diophantine fuzzy (CLDF) set extends a linear Diophantine fuzzy set (LDFS) by handling uncertainty with complex-valued membership degrees within a unit disc. In this paper, we combine the notions of LDFS, BCK-algebra, and complex fuzzy set (CFS) to preface and elaborate the innovative concepts of CLDF subalgebras (CLDF − Subs), CLDF ideals (CLDF − Ids), CLDF implicative ideals (CLDF − IIds), and CLDF positive implicative ideals (CLDF − PIIds) in BCK-algebras, and probe their fundamental characteristics. These new notations of certain kinds of algebraic substructures in BCK-algebras serve as a bridge among CLDFS, crisp set, and BCK-algebra and also demonstrate the influence of the CLDFS on a BCK-algebra. Moreover, we examine some illustrative examples and prevalent features of these innovative notions in detail. Finally, characterizations of these intricate fuzzy structures are given, and related results for ideals, implicative ideals, and positive implicative ideals in the view of CLDFSs are obtained.

Neutrosophic Logic is a neonate research field in which every proposition is assessed to have the proportion (percentage) of truth in a sub-set T, the proportion of indeterminacy in a sub-set I, and the proportion of falsity in a sub-set F. Neutrosophic set (NS) is effectively implemented for undetermined data processing and establishes benefits for handling the indeterminacy data. In the academic industries, early performance prediction of students is significant to the academic community so strategic interference might be planned before students attain the final semester. Forecasting the performance of students has turned into a challenging task owing to the rising number of data in educational procedures. The educational data mining (EDM) models are involved in extracting a pattern to explore hidden data from educational information. Currently, Machine learning (ML) and Artificial intelligence (AI) are implemented in numerous domains generally in the field of education to evaluate and analyze several features of educational datasets gathered from many educational institutions. This study develops a Leveraging Generalized Possibility Neutrosophic Soft Set with Feature Selection for Accurate Students’ Academic Performance Prediction Model (GPNSSFS-SAPPM). The intention of the proposed GPNSSFS-SAPPM system relies on improving the prediction model of students’ higher education performance using metaheuristic optimization algorithms.  The data pre-processing model is employed at first by applying mean normalization for converting input data into a suitable format. In addition, the golf optimization algorithm (GOA) is exploited for the feature selection process. Followed by, the classification process is done by generalized possibility neutrosophic soft set (GPNSS). At last, the parameter tuning process is performed through henry gas solubility optimization (HGSO) algorithm to improve the classification performance of the GPNSS classifier. A wide-ranging experimentation was performed to prove the performance of the GPNSSFS-SAPPM method. The experimental results specified that the GPNSSFS-SAPPM model underlined advancement over other recent techniques.