Neutrosophic Logic Research Articles

Retraction Note: Hybrid intelligent model for classifying chest X-ray images of COVID-19 patients using genetic algorithm and neutrosophic logic.

[This retracts the article DOI: 10.1007/s00500-021-06103-7.].

A novel technique for dental radiographic image segmentation based on neutrosophic logic

Oral diseases are very prevalent worldwide and affect people of all ages. Dentists depend on x-rays to study the characteristics of oral diseases. The segmentation and analysis of dental X-ray images pose various challenges compared to other medical images. This makes dental X-ray imaging more challenging because of poor resolution, which makes the segmentation of different parts of teeth and their abnormalities unreliable. It has been shown that Dental X-ray Image Segmentation (DXIS) is a primary and critical step in obtaining relevant and important details about oral diseases. DXIS plays a crucial role in practical dentistry to help identify various periodontal diseases. The proposed methodology automatically segments the teeth regions and assists in further analysis. It works on both peri-apical and panoramic types of dental radiographic images. Neutrosophic logic is used to select the initial region of interest. The best way to improve the performance and make the system faster is to restrict the computation within the foreground regions. The input dental radiographic image is mapped into the neutrosophic domain using the patch level feature, gradient feature, entropy feature, and local binary pattern. Applying neutrosophic logic helps to localize the initial region of interest. Subsequently, a fuzzy c-means algorithm is applied to segment a more accurate region of interest. The proposed methodology has been evaluated on publicly available data sets, ‘Panoramic Dental X-rays with Segmented Mandibles’ and ‘Digital Dental X-ray Database for Caries Screening,’ with the result that the accuracy of the proposed methodology is as high as 93.20%. This performance level confirms that the proposed segmentation technique highly correlates with the manual system.

Zeroing Neural Network Based on Neutrosophic Logic for Calculating Minimal-Norm Least-Squares Solutions to Time-Varying Linear Systems

Zeroing Neural Network Based on Neutrosophic Logic for Calculating Minimal-Norm Least-Squares Solutions to Time-Varying Linear Systems

Identifying Indoor Objects Using Neutrosophic Reasoning for Mobility Assisting Visually Impaired People

Indoor object detection is a fundamental activity for the development of applications of mobility-assistive technology for visually impaired people (VIP). The challenge of seeing interior objects in a real indoor environment is a challenging one since there are numerous complicated issues that need to be taken into consideration, such as the complexity of the background, occlusions, and viewpoint shifts. Electronic travel aids that are composed of the necessary sensors may assist VIPs with their navigation. The sensors have the ability to detect any obstacles, regardless of whether they are static or dynamic, and offer information on the context of an interior scene. The characteristics of an interior scene are not very clear and are subject to a great deal of variation. Recent years have seen the emergence of methods for dealing with issues of this kind, some of which include the use of neural networks, probabilistic methods, and fuzzy logic. This study describes a method for detecting indoor objects using a rotational ultrasonic array and neutrosophic logic. A neutrosophic set has been seen as the next evolution of the fuzzy set because of its indeterminate membership value, which is absent from conventional fuzzy sets. The suggested method is constructed to reflect the position of the walls (obstacle distance) and to direct the VIP to move freely (ahead, to the right, or to the left) depending on the degree of truthiness, the degree of indeterminacy, and the degree of falsity for the reflected distance. The results of the experiments show that the suggested indoor object detecting system has good performance, as its accuracy rate (a mean average precision) is 97.2 ± 1%.

Inspection Assignment Form for Product Quality Control Using Neutrosophic Logic

During the production process, production companies need to monitor the finished products and ensure their quality, which imposes on them the appointment of inspectors for auditing, and this appointment costs the company amounts that affect the general profit, so it strives to make this cost as low as possible and that the audit process is carried out with high accuracy because in case that the finished products do not conform to the basic specifications of the product, the company is required to pay a fine. In this research, we will formulate the text of the problem appropriately for such a case and then we will build the appropriate mathematical model through which we can obtain the lowest possible cost of inspection, and we will present the study using classical values and neutrosophic values, and we will demonstrate them through an example that shows us the difference between them.

Improvement of Unconstrained Optimization Methods Based on Symmetry Involved in Neutrosophy

The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we propose and investigate an improvement of line search methods for solving unconstrained nonlinear optimization models. The improvement is based on the application of symmetry involved in neutrosophic logic in determining appropriate step size for the class of descent direction methods. Theoretical analysis is performed to show the convergence of proposed iterations under the same conditions as for the related standard iterations. Mutual comparison and analysis of generated numerical results reveal better behavior of the suggested iterations compared with analogous available iterations considering the Dolan and Moré performance profiles and statistical ranking. Statistical comparison also reveals advantages of the neutrosophic improvements of the considered line search optimization methods.

A few little steps beyond Knuth’s Boolean Logic Table with Neutrosophic Logic: A Paradigm Shift in Uncertain Computation

The present article delves into the extension of Knuth’s fundamental Boolean logic table to accommodate the complexities of indeterminate truth values through the integration of neutrosophic logic (Smarandache Christianto, 2008). Neutrosophic logic, rooted in Florentin Smarandache’s groundbreaking work on Neutrosophic Logic (cf. Smarandache, 2005, and his other works), introduces an additional truth value, ‘indeterminate,’ enabling a more comprehensive framework to analyze uncertainties inherent in computational systems. By bridging the gap between traditional boolean operations and the indeterminacy present in various real-world scenarios, this extension redefines logic tables, introducing neutrosophic operators that capture nuances beyond the binary realm. Through a thorough exploration of neutrosophic logic's principles and its implications in computational paradigms, this study proposes a novel approach to logic design that accommodates uncertain, imprecise, and incomplete information. This paradigm shift in logic tables not only broadens the spectrum of computing methodologies but also holds promise in fields such as decision-making systems and data analytics. This article amalgamates insights from over twelve key references encompassing seminal works in boolean logic, neutrosophic logic, and their applications in diverse scientific and computational domains, aiming to pave the way for a more robust and adaptable logic framework in computation.

Solving Thermal System Problem Via Fuzzy Mohand Transform under Neutrosophic Initial Conditions

In this paper, a new fuzzy integral transform is introduced and called “fuzzy Mohand transform” which is based on a mathematical formula of the classical Mohand transform. The fuzzy technique that is well-established from fuzzy Laplace transform, agrees with the neutrosophic logic. In fact, in mathematical field, neutrosophic logic, which is based on the idea of indeterminacy, is introduced as a generalization of fuzzy logic. In Neutrosophic logic, there are three values, grade of membership of Truth values (T), Indeterminate values (I) and False values (F). To demonstrate this mixed technique, a realistic example about heating system is discussed as an illustrative example for solving an ordinary differential equation of first order using fuzzy Mohand transform with neutrosophic numbers as an initial condition.

Analyzing and Evaluation of Quick Switching System using Neutrosophic Poisson Distribution

In Statistical Quality Control (SQC), the judgement of the accepting the lot or rejecting the lot s carried out with the help of acceptance sampling plans in the inspection process of any manufacturing industry. Based on the predefined risk the output is attained with minimum inspection cost based on the optimum sample size. Generally Classical statistics is used based on the deterministic nature of the information and measurements. In some circumstances, the quality characteristics may not be certain enough leading to vagueness or impreciseness situation. Accordingly, in past few decades Fuzzy logic is one of the most popular techniques to model the uncertainty in the manufacturing industries. As an advent of technology and knowledge data era, an extension of Fuzzy, a new concept known as Neutrosophic Logic is in progress to apply to achieve these uncertainties. In this, such vagueness, imprecise is called as indeterminants. Thus, Neutrosophic Logic taken its role in Acceptance Sampling Plans with Probability distributions for various plan parameters such as AQL, LQL and Neutrosophic defection status are offered for Poisson distribution in the first time. The chief formulations of Acceptance Sampling plans for Single Sampling were derived based on Neutrosophic Statistics. As an advanced step the mixture of Acceptance Sampling plans with the shifting ruling for swapping from one plan to another plan are named as Sampling System and one such system is Quick Switching System the most widely applicable to safeguard from bad quality which give high level protection as well as to reduce the cost of inspection and time. In this study, Quick Switching System (QSS) with Single Sampling Plan (SSP) as reference plan is constructed based on Neutrosophic sets on Poisson distribution as baseline distribution. The procedures, OC Curves and tables have been redesigned and presented with numerical example.

Enhancing Crime Cluster Reliability Using Neutrosophic Logic and a Three-Stage Model

Enhancing Crime Cluster Reliability Using Neutrosophic Logic and a Three-Stage Model

An effective Decision making model through Fusion Optimization and risk associated with flash flood hazards: A case study Asyut, Egypt

One of the most dangerous natural disasters, which causes massive damage all over the world, is flash floods. Therefore, the assessment of flash floods disasters is considered increasingly urgent and important. The widely used techniques for studying and analyzing the causes and impact of natural hazards are multi-criteria techniques. Several researchers used traditional multi-criteria decision-making techniques in the estimation process of flash floods problems as the analytical hierarchy process, decision making trial and evaluation laboratory and analytic network process. The main disadvantage of these traditional models is the incapability of simulating and reflecting uncertain human thoughts. Since neutrosophic logic has a great ability for simulating human’s thoughts and increase the flexibility of expert's preferences in real world problems, we applied it in this study. There are different locations in Egypt that are at a serious risk of flooding, especially in Upper Egypt. Asyut has suffered from frequent flash floods, with some flood events that lead to mortality, damages, and economic losses in the last decades. The intensity of floods in Egypt varies from year to year, according to several climatic and hydrological variables. This study focuses on using a Neutrosophic Decision making trial and evaluation laboratory (N-DEMATEL) technique with remotely sensed data and geographical information system (GIS) for producing a flash floods hazard map. The N-DEMATEL technique is applied to determine the weights of various factors that related to flash flooding, including elevation, slope, topographic wetness index, distance from the stream, flow accumulation, aspect, flow direction, soil, land cover, watershed, curvature, drainage density , total population , population density and precipitation. The obtained weight of selected criteria used then to produce the flood hazard map (FHM) using a raster calculator tool in geographic information system.

The State of Risk and Optimum Decision According to Neutrosophic Rules

In light of the current circumstances and the momentary fluctuations that we live in all domains of life, which have transformed most decision-making cases into risky cases, this study was necessary. In this research, we present a new study for decision-making in the event of risk, by formulating some rules according to the neutrosophic logic starting from the data of the problem, where we replaced the classical values in the matrix of profit and probabilities with neutrosophic values that have a margin of freedom thanks to the indeterminacy provided by the neutrosophic logic, and we got more accurate solutions than the solutions that we obtained when using the classical rules which reduces the occurrence of losses, especially if the decisions are fateful and the decision issues are huge and complex and helps us to achieve the greatest profits by adopting a rational decision based on modern quantitative ways and methods.

Modern Elementary School: Neutrosophic and Education

Elementary school is a stage of primary education, it's the most critical stage of education in general, and teaching during the elementary stage is one of the most influential periods for children. In this stage, pupils can develop their basic skills and information through elementary education. In this study, we hope to insert the concept of neutrosophic logic in elementary school curriculum to clearly define the logic for pupils using shapes, figures, games, graphs, or mathematics problems that contain some indeterminacy. These neutrosophic examples include some indeterminacy which is the basic compound for neutrosophic logic. The basic difference from classical logic, further to other compounds (truth, falsehood).

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

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

Utilizing Neutrosophic Logic in a Hybrid CNN-GRU Framework for Driver Drowsiness Level Detection with Dynamic Spatio-Temporal Analysis Based on Eye Aspect Ratio

Driver drowsiness has been identified as a major cause of roadway accidents globally. Efficiently determining the extent of drowsiness can greatly enhance preventive measures. This study proposes a novel approach, combining convolutional neural networks (CNN) and Gated Recurrent Units (GRU) to dynamically evaluate both the presence of drowsiness and its severity based on the Eye Aspect Ratio (EAR). By bridging spatial features extracted by CNNs with temporal sequences through GRU, our model offers a robust and real-time assessment of drowsiness levels, paving the way for enhanced safety measures in vehicular systems. Incorporating Neutrosophic Logic enables a more robust representation of uncertainty and ambiguity in the data and enhances the accuracy of driver drowsiness level detection within the Hybrid CNN-GRU framework. The model’s hybrid CNN-GRU structure combines CNN layers to extract spatial information from Human eye Images and GRU units to represent temporal correlations between frames. In-car cameras and sensors must be integrated to implement the suggested system in real-time and enable continuous driver behavior monitoring. The system alerts early warnings and takes action when drowsiness is detected, lowering the likelihood of accidents caused by weary drivers. The CNN-GRU hybrid architecture accurately detects fatigue during real-time driving. Performance metrics, including accuracy, recall, and F1-score, are provided for comparative research utilizing baseline models. Model behavior may be understood by visualizing tiredness detection and carefully examining false positives and negatives. The proposed CNN-GRU framework outperforms traditional methods such as SVM, KNN, and BPNN by achieving a significantly higher accuracy of 99.5%. It increases the recognition of driver tiredness by proposing a trustworthy and adaptable hybrid CNN-GRU deep learning system. This project is implemented in Python; it offers a practical and versatile solution for real-time driver drowsiness level detection. The proposed technology has the potential to dramatically increase traffic safety by sending out early warnings and taking steps to lessen the risks related to driver fatigue.

Beyond Negation and Excluded Middle: An exploration to Embrace the Otherness Beyond Classical Logic System and into Neutrosophic Logic

As part of our small contribution in dialogue toward better peace development and reconciliation studies, and following Toffler Toffler’s War and Antiwar (1993), the present article delves into a realm of logic beyond the traditional confines of negation and the excluded middle principle, exploring the nuances of Otherness that transcend classical and Nagatomo logics. Departing from the foundational premises of classical Aristotelian logic systems, this exploration ventures into alternative realms of reasoning, specifically examining Neutrosophic Logic and Klein bottle logic (cf. Smarandache, 2005). The study challenges conventional boundaries and explores the implications of embracing paradoxes and self-reference in logic systems, aiming to redefine approaches to understanding truth and reasoning. The paper investigates how these alternative logics open avenues for philosophical inquiry, redefining entropy, and potentially influencing innovative perspectives in free energy systems. Through this exploration, it seeks to expand the discourse on logic, welcoming a broader spectrum of thought beyond established frameworks; and we also discuss shortly a number of possible implementations including in risk management and also Klein bottle entropy redefinition (Tang et al, 2018).

An Extended Neutrosophic Stepwise Weight Assessment Ratio Analysis Technique Based on GIS for Analysing Flash Floods

Flash floods are a sudden natural hazard caused by successive heavy rains in a short period of time. The world suffers from heavy and frequent rains due to climate change. So, the risk assessment of flash floods is considered increasingly important and urgent. Egypt is considered one of the countries exposed to sudden floods resulting from heavy rains, especially in Upper Egypt. Multi-criteria techniques are widely used to study and analyze the causes and effects of natural hazards. In contrast to the traditional multi-criteria techniques used in the process of estimating flood problems, we applied neutrosophic logic in this study that has a great ability for simulating and reflecting uncertain human’s thoughts in real world problems. Our study area sits in Southeast Sohag, and it is one of the most flash floods prone regions of Egypt's Eastern Desert. This area of Sohag has suffered from frequent flash floods, with some flood events resulting in human casualties in the last decades. This study focuses on using a neutrosophic stepwise weight assessment ration analysis (N-SWARA) technique with remotely sensed data and geographical information system (GIS) for producing a flash floods hazard map. The N-SWARA technique is applied to determine the weights of various factors that related to flash flooding, including elevation, slope, topographic wetness index, distance from the stream, flow accumulation, aspect, and flow direction. The obtained weight of selected criteria used then to produce the flood hazard map (FHM) using a raster calculator tool in geographic information system. The weight of each factor calculated by using the N-SWARA multi criteria analysis method and obtained the following results: 0.39 for slope, 0.21 for elevation, 0.12 for distance, 0.08 for flow direction, 0.05 for flow accumulation, 0.09 for TWI and 0.03 for aspect.

Neutrosophic-based Machine Learning Techniques in the Context of Supply Chain Management: A Survey

Supply Chain Management (SCM) plays a critical role in the success of any business organization. Individuals involved in business activities often have to make decisions regarding different aspects of the supply chain, including planning, procurement, production, inventory management, transportation, distribution, and customer relationship management. The combination of neutrosophic logic and machine learning has gained significant attention in the field of SCM as a means to tackle uncertainties and improve decision-making. This paper highlights the potential benefits and applications of integrating neutrosophic reasoning and machine learning in SCM. Neutrosophic reasoning provides a framework for handling imprecise and uncertain information, while machine learning techniques offer powerful tools for data analysis, pattern recognition, and predictive modeling. By leveraging machine learning algorithms within the context of neutrosophic logic, SCM practitioners can enhance demand forecasting accuracy, optimize inventory management, improve transportation and routing decisions, and strengthen supply chain collaboration. The integration of neutrosophic logic and machine learning enables the handling of complex supply chain data, accommodates dynamic and uncertain environments, and supports proactive decision-making. Furthermore, the combination of these approaches can contribute to improved supply chain resilience, sustainability, and customer satisfaction. This paper applied the neutrosophic AHP method as a feature section to select the highest importance criteria as an input to machine learning. Then we applied two machine learning models named random forest and decision. The results show the random forest has the highest accuracy followed by a decision tree.

A Study of the Movement of a Neutrosophic Material Point in the Neutrosophic Plane by Using a Neutrosophic AH-Isometry

This articles presents a new concept in mathematics according to a neutrosophic logic, which is the first of its kind in applied mathematics, which is the concept of the movement of a neutrosophic point in the neutrosophic plane and determining the path of this point, after determining Cartesian and polar neutrosophic coordinates of this point and also defining the neutrosophic local, velocity and acceleration vectors of these point. We have also determined the relationsships between the motion of a neutrosophic point and its equivalent in the classical plane, through an AH-isometry that connects the neutrosophic and classical plane. We conducted the previous study on three different examples, each example differs from the other in the form of a path and type of movement of the studied point.

A Study of a Support Vector Machine Algorithm with an Orthogonal Legendre Kernel According to Neutrosophic logic and Inverse Lagrangian Interpolation

The decision-making process is greatly affected by the data collection stage. If the data collection process is not well controlled, i.e. there is some data lost due to the poor quality of the devices used or the lack of accuracy in the data entry process...etc., this will affect the work of the SVM algorithm, which is considered one of the best. Most of the workbooks suffer from the problems of missing and anomalous data. In this paper, we propose a method to treat the missing and anomalous data by reshaping the data set defined by the classical method into the neutrosophical data set by calculating the amount of true T, false F, and neutrality I in the neutrosophical set using inverse Lagrangian interpolation. We noticed the superiority of our proposed method for processing missing data over the method of [21], then we trained a support vector machine algorithm with orthogonal legender kernel on a breast cancer dataset taken from the Statistics Department of Al-Bayrouni Hospital in Damascus, where the proposed algorithm achieved a classification accuracy of 97%. The reason we chose a support vector machine classifier with an orthogonal legender kernel has two goals: the first is to eliminate the repetition of support vectors in the feature space. The second is to solve the problem of non-linear data distribution.