International Journal of Neutrosophic Science

This study offers a comprehensive analysis of the perceptions regarding the gaps in traffic injury laws and the level of judicial security in Ecuador. By employing a neutrosophic approach, which incorporates degrees of truth, indeterminacy, and falsity, the study synthesizes data from legal professionals to assess the need for legislative reform. The use of the Indeterminate Likert Scale and the Triple Refined Indeterminate Neutrosophic Sets (TRINS) enriches the evaluation of nuanced opinions on traffic injuries that result in minimal disability. The resulting insights reveal a significant recognition of the inadequacies within the current legal framework and highlight a societal demand for enhanced legal measures and improved trust in judicial processes. This study underscores the urgency for legal reforms that would bridge the current legislative voids, ensuring justice and protection for traffic injury victims, thereby strengthening the legal system’s accountability and public confidence.

Macroeconomic factors in general are crucial for developing a country's economy. This analysis takes into account the chosen macroeconomic factors for the years 2015 to 2019 including inflation, interest rate, GDP, and GDP per capita. The present study considered the new method of Neutrosophic environment in terms of the Fuzzy CETD matrix to determine the impact of the stock market for a particular year. This article describes a technique for examining how macroeconomic factors affect the stock market in a specific year. The proposed method reveals that the impact of the stock market is higher in 2015 than in 2016.

The fast spread of COVID-19 has been a problem for several nations since February 2020. Computer-aided diagnostic technologies that are both effective and affordable are urgently needed to help ease the burden on healthcare systems. Researchers are delving further into the feasibility of using image analysis to detect COVID-19 in X-ray and CT-scan pictures of patients. In the past ten years, deep learning has surpassed every other method for classifying images. However, deep learning-based approaches' effectiveness is very sensitive to the design of the underlying deep neural network. In recent years, metaheuristics and neutrosophic sets have become more popular as a means of fine-tuning the structure of deep networks. Because of their adaptability, simplicity, and task dependence, metaheuristics have been extensively employed to tackle many difficult non-linear optimization problems. To correctly identify COVID-19 patients from their chest X-rays, the authors of this research made a review of a neurotrophic model and metaheuristics methods.

Breast cancer has emerged as a major killer in recent years. With a yearly rate of about one million new cases, it is the most prevalent among women in the world's poorest countries. Grading of cellular images has emerged as a key prognostic factor during the past decade. Neutrosophic sets used to enhance medical images in the last decade. Neutrosophic sets can overcome the uncertainty and indeterminacy of information. In recent years, metaheuristics have integrated with neutrosophic sets. Because of their adaptability, simplicity, and task independence, metaheuristics have been extensively employed to tackle many difficult non-linear optimization problems. The purpose of this research is to investigate several approaches to image classification for breast cancer pictures. This includes the use of metaheuristics and neutrosophic sets for optimization and image enhancement. This research was undertaken to better understand the current state of the art in breast cancer identification from medical pictures and to provide insight into the difficulties that lie ahead. We hope that this will encourage academics to investigate hitherto understudied facets of breast cancer identification.

According to its definition, a topological space could be a highly unexpected object. There are spaces (indiscreet space) which have only two open sets: the empty set and the entire space. In a discrete space, on the other hand, each set is open. These two artificial extremes are very rarely seen in actual practice. Most spaces in geometry and analysis fall somewhere between these two types of spaces. Accordingly, the separation axioms allow us to say with confidence whether a topological space contains a sufficient number of open sets to meet our needs. To this end, we use bipolar hypersoft (BHS) sets (one of the efficient tools to deal with ambiguity and vagueness) to define a new kind of separation axioms called BHS Ti-space (i = 0, 1, 2, 3, 4). We show that ee BHS Ti-space (i = 1,2) implies BHS Ti−1-space; however, the converse is false, as shown by an example. e For i = 0, 1, 2, 3, 4, we prove that BHS Ti -space is hypersoft (HS) Ti -space and we present a condition so that eee HS Ti-space is BHS Ti-space. Moreover, we study that a BHS subspace of a BHS Ti-space is a BHS Ti-space for i = 0,1,2,3.

In this era of the commercialization of sports, various sports leagues are organized across the globe. At the end of the Series, players are awarded for their performances. These awards are decided by human experts or are based on just one performance indicator. However, human decisions are subjective and error-prone, and decisions based on just one criterion are incomplete and inconsistent. This paper identifies the decision-making problem in sports. It proposes a Neutrosophic TOPSIS approach for performance evaluation and recommendation of the best batsman and bowler of the Series. The approach is well-structured, robust, and efficient in handling vagueness, inconsistency, indeterminacy, and imprecision in real-life problems. We present a case study using the data of IPL 2021. In the case study, we calculate the ranks of the players using neutrosophic TOPSIS with two objective weight calculation methods. Then we evaluate and compare the obtained rank lists using Kendal Tau (). The values of  for bowling-ranked lists is 0.83 and for batting-ranked lists is 0.72, which are impressive and prove the efficiency and effectiveness of the proposed approach. We believe that the proposed approach can be applied to identify and recommend the best resources in other domains of life.

In this paper, “we first define the belief of direct product from neutrosophic sets in INK algebras, neutrosophic set, neutrosophic h-ideals, neutrosophic INK-subalgebra and direct product of neutrosophic h-ideals in INK algebras. Let's prove some theorems that show that there is some connection between these principles. Finally, we define the INK subalgebra of the INK algebra and then offer the ideal theorem approximately the connection between its pix and the direct product from the neutrosophic h-ideals.

In this research article, we introduce the notions of interval valued Q-neutrosophic subbisemirings (IVQNSSBSs), level sets of an IVQNSSBS and interval valued Q-neutrosophic normal subbisemirings (IVQNSNSBSs) of bisemirings. Let Y ⃗ be an interval valued Q-neutrosophic set (IVQNS set) in a bisemiring 〆. Prove that Y ⃗ is an IVQNSSBS of S if and only if all nonempty level set Ξ(t,s) ⃗ is a subbisemiring (SBS) of S for t, s ∈ D[0, 1]. Let Y ⃗ be an IVQNSSBS of a bisemiring 〆 and V ⃗ be the strongest interval valued Qneutrosophic relation of 〆. Prove that Y ⃗ is an IVQNSSBS of S if and only if V ⃗ is an IVQNSSBS of 〆 × 〆. We illustrate homomorphic image of IVQNSSBS is an IVQNSSBS. Prove that homomorphic preimage of IVQNSSBS is an IVQNSSBS. Examples are given to demonstrate our findings.

The theory of type-II generalized Pythagorean neutrosophic interval valued soft set (Type-II PyNSIVS) and its application to real problems are introduced in this study. Additionally, we define a few operations using the type-II PyNSIVS set. The Pythagorean neutrosophic interval valued soft (PyNSIVS) set and Pythagorean fuzzy soft set are both generalized to form the type-II PyNSIVS set. Complement, union, intersection, AND, and OR are some examples of operations that we define. In particular, we demonstrate the applicability of De Morgan’s laws, associative laws, and distributive laws in type-II PyNSIVS set. The proposed similarity measure of type-II GPyNSIVS sets serves as the foundation for a strategy we provide for a medical diagnosis challenge. This method of comparing two type-II GPyNSIVS sets can be used to determine if a sick person has a particular disease or not. We support a method using the type-II generalized soft set model to tackle the decision making (DM) problem. We describe the use of a similarity measure between two type-II GPyNSIVS sets in a medical diagnosis situation. To demonstrate how they can be utilized to successfully address issues with uncertainties, illustrative examples are given.

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.

The following paper introduces a methodology to calculate the least cost for a directed network through Travelling salesman problem. Dynamic programming method is used to find the minimum Cost. The recursion formula is used. The edge weights of the networks are being taken in terms of Triangular, Trapezoidal and Pentagonal Neutrosophic set. Score function for the Triangular, Trapezoidal and Pentagonal Neutrosophic sets are being defined for deneutrosophication. The least cost is estimated using all the above said Neutrosophic sets and the result is compared

The Neutrosophic number is defined to solve the vagueness of the real-life problem and to analysis the indeterminacy of the problem, the paper defines a special single valued Decagonal Neutrosophic number and De-Neutrosophication formula are formulated using the removal area method and a numerical practical example is illustrated of network path edges using Neutrosophic number.

We introduce the notions of (τ1, τ2)-interval valued Q1 neutrosophic subbisemirings (IVQ1NSBSs), level sets of a (τ1, τ2)-IVQ1NSBS, and (τ1, τ2)-interval valued Q1 neutrosophic normal subbisemirings ((τ1, τ2)- IVQ1NNSBS) of a bisemiring. Let cZ1 be a (τ1, τ2)-IVQ1NSBS of a bisemiring M and bV be the strongest (τ1, τ2)-interval valued Q1 neutrosophic relation of M. To illustrate cZ1 is a (τ1, τ2)-IVQ1NSBS of M if and only if bV is a (τ1, τ2)-IVQ1NSBS of M ⋇ M. We show that homomorphic image of (τ1, τ2)-IVQ1NSBS is again a (τ1, τ2)-IVQ1NSBS. To determine homomorphic pre-image of (τ1, τ2)-IVQ1NSBS is also a (τ1, τ2)- IVQ1NSBS. Examples are given to strengthen our results.

In this paper, Neutrosophic definitions and properties of some special number sequences which are frequently found in the science literature, called Neutrosophic Number Sequences (NNSq) via Horadam sequence are studied for the first time. Especially for Neutrosophic Fibonacci (NFNq) and Neutrosophic Lucas (NLNq) number sequences, fundamental properties and identities such as Ruggles, Honsberger, Cassini, Catalan, d’Ocagne, and Tagiuri are given. In addition, Neutrosophic definitions of the sequences of Pell (NPNq), Pell-Lucas (NPLNq), Jacobsthal (NJNq), Jacobsthal-Lucas (NJLNq), Mersenne (NMNq), Mersenne-Lucas (NMLNq), Balancing (NBNq), and Lucas-Balancing (NLBNq) numbers are introduced. Besides defining these numbers and their sequences, since fuzzy and intuitionistic fuzzy sets are restrictions of neutrosophic sets, sequences of numbers within these sets are naturally and indirectly revealed.

In this paper, we introduce new sets  in neutrosophic crisp topology called neutrosophic crisp frontier, neutrosophic crisp border and neutrosophic crisp exterior with the help of neutrosophic crisp open sets in neutrosophic crisp topological space. Also, we discuss the basic and important properties of them and the relations between them. Finally, many examples are presented.