International Journal of Neutrosophic Science

We construct and analyze the concept of complex cubic neutrosophic subbisemiring (ComCNSBS). We analyze the important properties and homomorphic aspects of ComCNSBS. For bisemirings, we propose the ComCNSBS level sets. A complex neutrosophic subset of bisemiring S is represented by the symbol G if and only if each non-empty level set R(p,x), where R is a ComCNSBS of S. We show that homomorphic images of all ComCNSBSs are ComCNSBSs, and homomorphic pre-images of all ComCNSBSs are ComCNSBSs. There are examples given to illustrate our results.

This article proposed a novel method to categorize the best student in all progressive studies by using the single valued Neutrosophic soft set-in variable sense. An ambivalence set of multi-observer data which is related to analyse the students, taken as input for categorizing the best student identification. Neutrosophic soft set is an immense application to find out the choice-making problem in the Neutrosophic area. The creation of an analogous table has shaped the classification investigation. It helps to put up things, people into groups according to their quality, ability, performance etc., in Neutrosophic environment.

Quadripartitioned neutrosophic set is an extension of neutrosophic set and n-valued neutrosophic logic for solving real-world issues. In order to demonstrate the validity of the suggested idea, this paper's major goal is to provide several quadripentapartition neutrosophic probability distributions with numerical examples.  Neutosophic probability has up till now been obtained from traditional statistical distributions, with less contributions to the statistical distribution's creation. With the help of numerical examples, we introduced the quadripartition neutrosophic binomial distribution, the quadripartitioned Poisson distribution, and the quadripartitioned Poisson distribution as a limiting case of the neutrosophic binomial distribution. We also proposed the quadripartitioned exponential distribution and the quadripartitioned uniform distribution.  This paper paves the door for addressing problems that adhere to the classical distributions while still include inaccurately stated data.

In this paper, we introduce the notion of $\flat,\ell$-neutrosophic subsemigroup (NSS), neutrosophic left ideal(NLI), neutrosophic right ideal(NRI), neutrosophic ideal (NI), neutrosophic bi-ideal(NBI), $(\epsilon, \epsilon \vee q)$-neutrosophic ideal, neutrosophic bi-ideal of an ordered $\Gamma$-semigroups and discuss some of their properties. The concept of $\flat,\ell$-neutrosophic ideal is a new extension of neutrosophic ideal over ordered $\Gamma$-semigroups $\mathcal{Z}$. A non-empty subset $\xi_{\flat}$ is a $(\flat, \ell)$-NSS (NLI, NRI, NBI, (1,2)-ideal) of $\mathcal{Z}$. Then the lower level set $\Delta_{\flat}$ is an subsemigroup $(LI, RI, BI, (1,2)-ideal)$ of $\mathcal{Z}$, where $\Delta_{\flat}=\{\varrho\in \mathcal{Z}|\Delta(\varrho)> \flat\}$, $\Psi_{\flat}=\{\varrho\in \mathcal{Z} |\Delta(\varrho)> \flat\}$ and $\mho_{\flat}=\{\varrho\in \mathcal{Z}|\Delta(\varrho)< \flat\}$. A subset $\xi=[\Delta,\Psi,\mho]$ is a $(\flat, \ell)- NSS[NLI,NRI,NBI,(1, 2)-ideal]$ of $\mathcal{Z}$ if and only if each non-empty level subset $\xi_{t}$ is a subsemigroup $[LI,RI,BI,(1,2)-ideal]$ of $\mathcal{Z}$ for all $t\in(\flat, \ell]$. Every $(\epsilon, \epsilon \vee q)$NBI of $\mathcal{Z}$ is a $(\flat,\ell)$NBI of $\mathcal{Z}$, but converse need not be true and examples are provided to illustrate our results.

In this study, a new notion of m-polar neutrosophic set (MPNS) and m-polar neutrosophic topology is introduced. To achieve this goal, first, we explore numerous representations of the concept of MPNS and deliberate its definitive characteristics. Some operations on MPNS were established. A score function is proposed for comparing the MPN numbers (MPNNs). Next, an MPN topology is introduced and closure, frontier, interior, and exterior for MPNS are defined with representative examples. Depression is a popular mental health problem that disturbs a broad range of individuals worldwide. Generally, people who undergo from this attitude have problems like mood swings, low concentration, suicide, and dementia. A social media platform such as Twitter enables to interact and share videos and photos that express their moods. Hence, the studies on social media content present an overview of personal sentiments, such as depression. Research has been undertaken on depression recognition in English and less in Arabic. The recognition of depression from Arabic social media falls after owing to the lack of resources and techniques and the available difficulty of the Arabic language. This article presents a novel Applied Linguistics with m-Polar Neutrosophic Set Mood Change and Depression on Social Media (MPNS-MCDSM) technique on Arabic Text Analysis. To accomplish this, the MPNS-MCDSM method undertakes a data pre-processing stage to convert the input dataset into a beneficial format. In addition, the Glove word embedding method is applied to the feature extraction from the preprocessed dataset. For the classification process, the m-Polar Neutrosophic Set (MPNS) classifier can be applied. Finally, the Whale Optimization Algorithm (WOA) is applied for optimum adjustment of the hyperparameters related to the MPNS classifier. The simulation outcomes of the MPNS-MCDSM technique are verified on the benchmark dataset. The experimental result analysis of the MPNS-MCDSM technique shows its promising solution over other existing approaches.

As a generalization of fuzzy set (FS) and intuitionistic FS (IFS), neutrosophic sets (NS) were proposed to signify imprecise, uncertain, inconsistent and imperfect data present in real-time. Moreover, the interval NS (INSs) were developed just to find out the problems with an array of statistics in the actual unit interval. Then, there are least consistent processes for INSs, along with the decision-making process and INS aggregation operator. The vital operations are presented on n-valued interval NSs like intersection, union, multiplication, addition, scalar division, scalar multiplication, false-favorite and truth favorite. Bankruptcy prediction was a major concern in the areas of finance and management science that appealed to the attention of practitioners and researchers. With the great progress of up-to-date information technology, it has been developed to utilize machine learning (ML) or deep learning (DL) techniques to perform the prediction, from the primary analysis of financial statements. If ML methods have adequate interpretability, they might be employed as effectual analytical methods in bankruptcy calculation. This manuscript presents a Bankruptcy Prediction using Cutting-Edge N-Valued Interval Neutrosophic Sets (BP-CENVINS) mechanism. The projected BP-CENVINS method is a complicated approach to bankruptcy forecast that affects radical data preprocessing, classification, and hyper parameter optimization approaches. Initially, the Z-score normalization regularizes the fiscal details to increase the comparability and stability throughout the information. Next, it employs the CENVINS for the classification, skillfully detecting the subtle communication amongst variables to differentiate between creditworthy and bankrupt organizations. Finally, the Grasshopper Optimization Algorithm (GOA) is applied for parameter tuning to improve the predictive outcomes of the CENVINS classifiers, systematically purifying design parameters to achieve finest efficiency. An extensive experiments is made to illustrate the betterment of the BP-CENVINS technique. The simulation outcomes of the BP-CENVINS method have exhibited better performances than other existing methodologies.

An interval neutrosophic set (INS) is an example of a NS, which is simplified from the theory of fuzzy set (FS), classical set, paradoxist set, intuitionistic FS, paraconsistent set, interval-valued FS, interval-valued intuitionistic FS, and tautological set. The association of an element to an INS is stated by 3 values such as t, i, and f. These values signify memberships of truth, indeterminacy, and false, correspondingly. Bankruptcy prediction is also called a corporate failure or bankruptcy prediction, which is a major focus in the area of finance and accounting, as the condition of a business is extremely substantial to its partners, shareholders, investors, creditors, even its suppliers, and buyers. Practitioners and researchers were reserved for emerging models and approaches to forecast the bankruptcy of companies more rapidly and precisely. With the excessive growth of contemporary information technology, it has developed to use machine learning (ML) or deep learning (DL) techniques to perform the prediction, from the preliminary study of economic statements. This study introduces an Optimized Bankruptcy Prediction using Feature Selection with m-Polar Neutrosophic Topological Spaces (OBPFS-MPNTS) method. The projected OBPFS-MPNTS system uses the parameter tuning and DL method to forecast the presence of bankruptcy. To achieve this, the OBPFS-MPNTS approach uses min-max normalization to convert input data into a uniform format. The OBPFS-MPNTS method begins with a grey wolf optimization (GWO) for selecting feature subsets. In addition, the OBPFS-MPNTS algorithm applies the m-polar neutrosophic topological space (MPNTS) system for bankruptcy prediction. To upsurge the performance of the MPNTS system, the whale optimizer algorithm (WOA) is employed. The experimentation outcome study of the OBPFS-MPNTS system is verified on a benchmark database and the outcomes pointed out the developments of the OBPFS-MPNTS algorithm over other current methodologies.

Neutrosophic set (NS) is a prevailing logic aimed at facilitating the understanding of inconsistent and indeterminate data; several kinds of complete or incomplete data can be described as interval-valued NS (IVNS). This study presents aggregation operator for IVNSs and prolongs the generalized weighted aggregation (GWA) operations to congruently work with IVNS information. Also, these results are formulated as IVNSs that are represented by indeterminate, truth, and false degrees. The tremendous growth of financial innovation offers a several convenience to people’s lives and production and brings many security risks to financial technology. To avoid financial risk, an improved way is to construct an accurate warning mechanism before the financial risk takes place, not to solve this matter after the risk outbreak. Recently, deep learning (DL) has delivered outstanding results in the natural language processing and image recognition areas. Thus, researcher used DL techniques for the financial risk prediction and obtained satisfactory results. This study develops a new Pythagorean Neutrosophic Normal Interval-Valued Weighted Averaging for Financial Risk Prediction (PNNIVWA-FRP) method using sustainable development. The objective of the PNNIVWA-FRP method is to have two dissimilar stages of processes. Initially, financial data are classified by the PNSNIVWA technique. This method is used for its highest proficiency in managing imprecision and uncertainty in financial data, containing incomplete and ambiguous data. Second, the classified parameter is fine-tuned by means of Glowworm Swarm Optimization (GSO) technique. Based on the luminescent communication of glowworms, GSO is proficient at navigating multidimensional, complex search spaces for identifying better solutions. The empirical findings on benchmark dataset demonstrate the effectiveness of the PNNIVWA-FRP method, showcasing significant development in prediction results than classical approaches.

Neutrosophic Logic is an offspring study region in which every intention is projected to hold the proportion of indeterminacy in a subset I, the percentage of truth in a subset T, and the percentage of falsity in subset F. Neutrosophic set (NS) has been effectively used for indeterminate data processing, and establishes benefits to handle with the indeterminacy information of data and is quite a method stimulated for classification application and data analysis. NS delivers an effective and precise method to describe imbalanced data as per the features of the data. Recently, the usage of the Internet of Things (IoT) has enlarged rapidly, and cyber security effects have enlarged beside it. On the state-of-the-art of cyber security is Artificial Intelligence (AI), which employed for the progress of intricate techniques to defense systems and networks, containing IoT systems. Though, cyber-attackers have determined how to develop AI and have started to utilize adversarial AI for accomplishing cybersecurity threats. Therefore, this study designs a new Interval-Valued Neutrosophic Set using Optimization Algorithm-Based Intrusion Detection System (IVNSOA-IDS) technique in IoT cybersecurity. The key objective of the IVNSOA-IDS method rests in the automatic identification of intrusion detection in IoT cybersecurity. In the IVNSOA-IDS technique, data pre-processing is executed to convert the raw data into a compatible format. Besides, the interval-valued neutrosophic set (IVNS) model has been utilized for the automated identification of intrusion detection. Finally, an improved whale optimization algorithm (IWOA) is employed for the better hyperparameter tuning of the IVNS classifier. To demonstrate the enhanced performance of the IVNSOA-IDS technique, an extensive of simulations take place and the performances are inspected under distinct aspects. The experimental outcome reported the advancement of the IVNSOA-IDS methodology under various metrics.

Our study focusses on the concept of the kernel with in neutrosophic crisp sets (NCS_s) and its relationship with the separation axioms of NCTS, coinciding, and shedding light on the properties that characterize them.

In this paper, we have put forward the SH-homo and 0−preserving SH-homo to compare two SH groupoids along with few examples. Some properties of SH-homo and 0−preserving SH-homo are explored. Also, we proved the SH-homo between two SuperHyper BCI-Algebra is 0−preserving SH-homo. Finally, the category of SuperHyper Groupoid, SuperHyper BCI-Algebra and Neutrosophic SuperHyper BCI-Algebra were investigated.

The notion of the complex Q bipolar neutrosophic subbisemiring (CQBNSBS) is a fundamental notion to be considered for tackling tricky and intricate information. Here, in this study, we want to expand the notion of CQBNSBS by giving a general algebraic structure for tackling bipolar complex fuzzy (BCF) data by fusing the conception of CQBNSBS and subbisemiring. Keeping in view the importance of fuzzy algebraic structures, in this manuscript, we develop the concept of CQBNSBS. We analyze the important properties and homomorphic aspects of CQBNSBS. For bisemirings, we propose the CQBNSBS level sets. We also develop the notions of homomorphic images of all CQBNSBSs is also CQBNSBS and homomorphic pre-images of all CQBNSBSs is also CQBNSBS. Examples are provided to demonstrate our findings.

We introduce the concept of complex cubic Q neutrosophic subbisemiring (CCQNSBS) is a new extension of cubic Q neutrosophic subbisemiring. We examine the characteristics and homomorphic features of CCQNSBS. We communicate the CCQNSBS level sets for bisemirings. A cubic complex Q neutrosophic subset G if and only if each non-empty level set R is a ComCQNSBS of S. We show that the intersection of all CCQNSBSs yields a CCQNSBS ofS. If S1, S2, …,Sn be the finite collection of CCQNSBSs of respectively. Then S1* S2* …* Sn is a CCQNSBS of S1* S2* …* Sn. If F : S1 --- S2 is a homomorphism, then F is a subbisemiring of CCQNSBS  of S2. Examples are provided to show how our findings are used.

The BE-Algebra was presented by Kim in 2007. After that, several authors studied this type of logic concept in algebra. In this paper, we introduce more properties and remarks of BE-Algebra. Note that (A,*,1) is called BE-algebra if   ∀ a ∈A, b, c ∈A: collect a*a=1, a*1=1, 1*a=a and a*(b*c)=b*(a*c). In addition, a Neutrosophic BE-filter FI subset of the Neutrosophic BE-algebra is Neutrosophic BE-algebra AI is Neutrosophic BE-subalgebra AI.  Some new results and the criterion to determine some properties of BE-algebra and several relationships with another algebra namely Hibert algebras (H-algebra).

The main goal of this work is to study the effect of applying Lagrange's polynomials on finding the numerical solutions of many different neutrosophic boundary value problems, where we use those polynomials to solve three different neutrosophic boundary value problems numerically, and we present many numerical tables to compare the accuracy of the solutions obtained by Lagrange's polynomials with other famous methods such as Adomian's method.