International Journal of Neutrosophic Science

The notion of complex interval-valued q-neutrosophic subbisemiring (CIVqNSBS) is developed and examined. Additionally, we examine the homomorphic features and significant attributes of CIVqNSBS. We suggest the CIVqNSBS level sets for bisemirings. Consider a complex neutrosophic subset of bisemiring Δ, denoted as ℵ if and only if every non-empty level set Z(∂,♭) is a subbisemiring, where ∂, ♭ ∈ D[0, 1], then Z= )Z,Z, Z) is a CIVqNSBS of Δ. Let ℵ be the strongest complex neutrosophic relation of bisemiring Δ, and let Ψ be a CIVqNSBS of bisemiring Δ, if and only if Ψ is a CIVqNSBS of Δ × Δ, then ℵ is a CIVqNSBS of bisemiring Δ. We show that homomorphic images of all CIVqNSBSs are CIVqNSBSs, and homomorphic pre-images of all CIVqNSBSs are CIVqNSBSs. There are examples given to illustrate our results.  

This study introduces the Spherical Fermatean Neutrosophic Sets (SFNSs), representing a significant advancement in the realm of Neutrosophic Sets (NSs) and Fermatean neutrosophic sets (FNSs). In decision making scenarios involving diverse perspectives, a mere average of decision values may fail to capture the entire spectrum of viewpoints. To address this limitation, the SFNS is proposed as a comprehensive solution. It features a spherical representation that encompasses membership, non-membership and indeterminacy functions at its core, complemented by a defined radius. This spherical construct facilitates the encapsulation of all decision makers’ opinions within its bounds, providing a holistic perspective. Leveraging its geometric structure, the SFNS excels in resolving ambiguity and risk with greater accuracy and effectiveness compared to conventional FNSs. This innovative approach aims to better accommodate the complexities of decision making involving diverse perspectives. Selecting the best material for a structural engineering project is given as numerical example at the end.

This study presents an innovative approach to cloud service provider selection using the spherical Fermatean neutrosophic Bonferroni mean. As organizations increasingly rely on cloud services, selecting the optimal provider becomes critical, necessitating robust multi criteria decision making methods. Traditional approaches often fall short in capturing the diverse perspectives of decision-makers, leading to suboptimal choices. The spherical Fermatean neutrosophic Bonferroni mean addresses this gap by integrating a spherical representation that encompasses membership, non-membership and indeterminacy functions, enhanced by the Bonferroni mean. This structure effectively encapsulates the opinions of all decision makers, offering a comprehensive and balanced perspective. The study evaluates six cloud service providers based on four criteria: cost (nonbeneficiary), performance, security and scalability (beneficiary). Three decision makers with distinct priorities participate in the evaluation, ensuring a thorough assessment. The proposed spherical Fermatean neutrosophic Bonferroni mean method excels in resolving ambiguity and managing risk with greater precision than conventional FNSs, providing a more accurate and effective decision-making framework. A numerical example illustrates the practical application of spherical Fermatean neutrosophic Bonferroni mean, demonstrating its utility in selecting the optimal cloud service provider for an organization.

In this article, we define secondary generalized inverse of a neutrosophic fuzzy matrices whenever exists. . Also, the S-ordering for the set of neutrosophic fuzzy matrices are defined and characterized. A necessary and sufficient condition for the existence of secondary generalized inverse of neutrosophic fuzzy matrices with the help of S-ordering is obtained.

Over the last few years development of Internet of Things (IoT) devices and communication technologies have resulted in the massive generation of health-related data. In the context of healthcare, IoT offers several advantages, including being able to observe patients very closely and using data for analytics. A major challenging issue that exists in the usage of IoT and big data in the medical field is security. As healthcare data is highly vulnerable and becomes a target for attacks, there are significant privacy issues related to the usage of big data analytics. Besides, implementing new data analysis tools and strategies for handling big data decision-making is a major issue. The capability to examine this amount of data is a significant aspect of big data in health care.  For resolving these issues, this paper presents a new intelligent deep learning-based trust management with decision making tool (IDLTM-DMT) for IoT healthcare big data environments, incorporating Neutrosophic Set Analysis (NSA). The proposed IDLTM-DMT model enables IoT devices to gather healthcare data. The IDLTM-DMT model involves a DL based bidirectional long short-term memory (BiLSTM) model for vulnerability detection and thereby identifies the malicious traffic in the Network. Hadoop MapReduce is used for handling big data and a decision-making tool using Deep Stacked Auto Encoder (DSAE) is used for the classification of diseases that exist in big data. To optimize the DSAE model's hyperparameters and improve classification performance, the Sandpiper Optimization (SPO) Algorithm is employed. Neutrosophic Set Analysis is integrated to manage the indeterminacy and inconsistency of the data, enhancing the decision-making process. Extensive experimental analysis is conducted on the EEG Eye State Dataset, with results analyzed using various performance measures. The findings indicate that the proposed method achieves improved accuracy compared to existing methods, demonstrating the effectiveness of incorporating Neutrosophic Set Analysis in IoT healthcare big data environments.

Neutrosophic normed linear spaces are the main significant notion in the study of classical functional analysis under a neutrosophic environment to handle indeterminate and inconsistent information. Where the neutrosophic norm function assigns to each vector in the linear space a neutrosophic number, which is a number with a truth, indeterminacy, and falsity component. The main aim of this work is to study and discuss the important properties of proximinality of specific sets and new results for a large class in neutrosophic normed space. Moreover, we show some results closely related proximainality of classes to the normed construction in the space. Also, we prove achieved for generalized sets in neutrosophic normed space, most marks on convexity and Cheby-shevity classes are considered.

Medical image processing is indispensable for correct diagnosis and planning of treatment. However, it is susceptible to many errors due to noise, artifacts, and the variability innate in anatomical structures themselves. Traditional image analysis methods hence suffer from these complexities in the images themselves and lead to probable inaccuracies in image analysis. This paper probes into the role of neutrosophic logic in the domain of medical image processing to seek better handling of these problems. The main objectives of the work were to optimize the noise reduction, image segmentation, feature extraction, and classification using the special capabilities of neutrosophic logic directed toward handling uncertainty and indeterminacy. Contributions The contributions of this study are multifaceted: it contributes by introducing detailed support for applying neutrosophic logic in a number of medical image processing tasks and integrates neutrosophic logic with prior techniques and evaluates their performance with traditional methods. The experimental results in the study are complete and demonstrate significant improvements in key metrics. For example, applying neutrosophic logic in noise reduction increased the peak signal-to-noise ratio of MRI images from 25 dB to 35 dB. In some segmentation tasks, the Dice coefficient for liver CT scans increased from 0.85 to 0.92. It increases the accuracy of feature extraction in breast cancer detection from 88% to 95%, while integrating neutrosophic logic with convolutional neural networks improves the accuracy in retinal image classification from 92% to 97%. All these results underline the strong role that neutrosophic logic can play in enhancing accuracy, robustness, and reliability in the processing of medical images. The result of the study concludes that neutrosophic logic not only improves the current limitations but also holds great promise for handling uncertainty in many medical fields, opening a promising way for future advancements in the field of medical imaging and health applications.

Mentoring and entrepreneurship management are characteristics that must be promoted in the organization because the success of a business depends on them. Entrepreneurship is an innate quality of personality; however, it can be developed through education. This paper aims to show the initial steps to develop entrepreneurship and mentoring programs within today's Peruvian universities. For this, we count on the support of four specialists who determined the essential factors for designing academic entrepreneurship programs in Peru. They also serve to evaluate the importance of these concepts. From a quantitative point of view, we use the Neutrosophic AHP technique to calculate the weights to measure the importance of each of these factors in the teaching of these concepts on the university campuses of Peru. The Neutrosophic AHP method is the generalization to the neutrosophic framework of the well-known AHP, where indeterminacy is included within decision-making.

Business sustainability has become a global imperative in response to the environmental, social, and economic challenges facing our world. In this context, the measurement and evaluation of business sustainability have become crucial to guide the actions of organizations towards more responsible and sustainable practices. However, the lack of specific measurement instruments for specific regional contexts may limit the ability of companies to evaluate and improve their sustainability performance. In this paper, we present the design of a business sustainability measurement method adapted to the context of Tarma, Peru. Tarma, a region located in the heart of the Peruvian Andes, is characterized by its cultural, environmental, and economic diversity, making it a unique context to address business sustainability. This article proposes a method for measuring business sustainability based on the Neutrosophic 2-tuple Linguistic Model, which includes an aggregation operation based on a NeutroAlgebra generated by Combining Functions in Prospector.  

The main purpose of this evaluation is to analyze the economic viability of the implementation of circular models in agriculture in Tarma, Peru. This involves examining the costs and benefits associated with the adoption of circular practices, as well as identifying possible barriers and opportunities for their implementation at the local level. By better understanding the economic landscape, it will be possible to inform decision-making both at the government level and at the level of individual farmers. For the analysis, we have a committee of 30 experts who will evaluate the relationship between variables that positively or negatively affect the implementation of these models in the town. The tool selected for the analysis is Neutrosophic Cognitive Maps, which includes an indeterminacy component within the calculations. This allows greater accuracy in the results since indeterminacy is an inherent part of prediction.

We introduce the new type neutrosophic interval-valued set (NIVS) problems relevant to multiple attribute decision making (MADM). Pythagorean interval-valued fuzzy set (PIVFS) and neutrosophic set (NS) can be extended into new type neutrosophic interval-valued set. We discusses new type neutrosophic interval-valued weighted averaging (new type NIVWA), new type neutrosophic interval-valued weighted geometric (new type NIVWG), generalized new type neutrosophic interval-valued weighted averaging (new type GNIVWA) and generalized new type neutrosophic interval-valued weighted geometric (new type GNIVWG). A number of algebraic properties of new type NIVSs have been established such as associativity, distributivity and idempotency. Using expert judgments and criteria, we will be able to decide which options are the most appropriate. Several of the proposed and current models are also compared in order to demonstrate the reliability and usefulness of the models under study. Additionally, the findings of the study are fascinating and intriguing.  

YouTube is moving towards personalized media. In 2011, Enchufe TV became an Ecuadorian online comedy series known for its witty humor. Taking advantage of the openness of the Internet, the video is currently available to watch on the YouTube platform. The purpose of this study is to conduct an unbiased analysis of the factors that determine the development of humorous discourse in TV Antufe's YouTube videos using the TOPSIS method. To understand the growth of the show and its audience, we compared its premiere year to 2022 across 10 years. At the same time, data such as comedy type, language level, audio-visual narrative, and humorous discourse were collected to quantitatively understand the popularity and influence of the play at the time. There. Variables such as views, audience engagement, and subscriber base growth are analyzed, as well as objective measures of content relevance and influence within the platform environment. Enchufe TV's decline in user activity can also be explained by several factors, such as the emergence of new platforms and content saturation. We also found that blue spoken words were the most widely used, with popularity varying by year of study.  

The aim of this article is to establish two new and qualitative subfamilies F(ε, κ, ℵ) and G(ε, κ, ℵ) of biunivalent functions. For functions in these subfamilies, we determine the first two Maclaurin coefficient estimations |C2| and |C3|, and address the Fekete–Szeg¨o problem. Additionally, we mention some corollaries related to the main results.  

In this paper, we introduce the notion of the intrinsic product of neutrosophic sets, and some related properties are investigated. Characterizations of neutrosophic subrings, neutrosophic ideals, neutrosophic quasi-ideals, and neutrosophic bi-ideals are given.

An early cancer diagnosis is carried out for adequate management of diseases. Magnetic resonance imaging (MRI) is most commonly preferred method for cancer diagnosis. Due to the uncontrolled and rapid growth of cells, brain tumor is occurred. If not treated at a preliminary phase, it may lead to death. Thus, a noteworthy prerequisite for a successful treatment outcome is an early and precise diagnosis.Many conventional methods are discussed for performing efficient tumor detection. But, conventional classification methods not distinguish MRI as primary and metastases tumors in an accurate manner. Therefore, the performance comparison of deep learning-based classification (i.e., Differential Quadri-Partitioned Neutrosophic Interval-valued Polynomial Attention-based Deep CNN (DQNI-PADCNN) method and Canonical Quadri-Partitioned Neutrosophic Set based Otsuka–Ochiai Deep Recurrent Neural Network (CQNS-ODRNN) method) is introduced to provide exact image classification results. The brain MRI images are considered as an input. MRI image classification is carried out through CNN and RNN to find the brain tumor disease. Before the classification process, input images are de-noised. The noise-removed images are get segmented to identify the region of interested regions. Later, the images are classified into four classes such as glioma, meningioma, no tumor, and pituitary classes to detect the brain tumor. Both classification methods use Quadri-Partitioned Neutrosophic set for categorizing the images. Depending on CNNs and RNNs achievement in handling intricate tasks, an optimal multi-class brain tumor diagnosis is carried out. Experimental evaluation is implemented using MATLAB 2017 for brain tumor detection with the Brain Tumor MRI dataset. To the total number of MRI images, the various performance metrics are calculated in terms of sensitivity, specificity, accuracy, and time for the detection of brain tumors.