International Journal of Neutrosophic Science

In this paper, we continue to discuss the concept of harmonized fuzzy subgroups. We present the harmonized fuzzy coset and harmonized fuzzy normal subgroup and their properties. We also study the effect of group homomorphism on harmonized fuzzy subgroups. Finally, we define and study the cartesian product of two harmonized fuzzy subgroups.

The purpose of this paper is to introduce and study fuzzy hypersoft θ continuous maps, fuzzy hypersoft θ semi continuous maps, fuzzy hypersoft θ pre continuous maps and fuzzy hypersoft θ irresolute maps in fuzzy hypersoft topological spaces with examples. Further, we derived some useful results and properties related to them.

The article aims to introduce the Linguistic Fermatean Neutrosophic set (LFNS) which is an important mathematical tool that helps to solve decision-making problems. LFNS is a generalization of the Linguistic Fermatean Fuzzy set (LFFS), by adding the truth, falsity and indeterminacy membership degrees to denote the uncertain information. Score and Accuracy functions are introduced to distinguish any two or more linguistic Pythagorean Neutrosophic Numbers. Weighted averaging and geometric aggregation operators with respect to linguistic Pythagorean neutrosophic weighted average and geometric, ordered weighted average are proposed. OEE (Overall Equipment Effectiveness) is the industry standard for measuring manufacturing productivity. It defines the percentage of manufacturing time that is productive. A 100% OEE score means that you are creating only high-quality products as soon as possible, with no downtime. By measuring OEE and the underlying losses, you will gain critical insights on how to systematically optimize your manufacturing process. OEE is the single most effective measure for detecting losses, assessing progress, and improving manufacturing equipment productivity (i.e., reducing waste). To adopt OEE practices in manufacturing industries, we must first understand, measure, and enhance OEE. The purpose of this research is to better understand OEE practices and their crucial aspects. The Human Arena, Engineering, Management, and Social elements are assessed, with sub-factors aggregated by similarity and analyzed using a LFNN. This method helps to comprehend the impact of each factor and ranks the group based on their influence in implementing the OEE practices effectively in an organization. The Engineering aspects and the Management aspects contribute a major role in the success of OEE. In this study, the assessment of numerous components and sub-factors involving determining the influence factor leading to OEE is translated into a Multi-Attribute Group Decision Making (MAGDM) problem and illustrated in the last section utilizing LFNN.

We introduce new methods for the trigonometric Pythagorean neutrosophic set (TPNSS) via interaction aggregating operator in this study. A combination of the trigonometric operator and the Pythagorean neutrosophic set. The universal aggregation function is used to study the novel averaging and geometric interaction operations of Pythagorean neutrosophic numbers. The TPNSS are commutative, associative, idempotent, and boundedness compatible. TPNSS interaction weighted averaging, TPNSS interaction weighted geometric, generalized TPNSS interaction weighted averaging, and generalized TPNSS interaction weighted geometric are the four new interaction aggregating operators that are introduced. The Euclidean distance, Hamming distance, and score values are often assumed to represent the aggregation functions.

In this manuscript, we elegantly delineate the concept of JSφ-contractions within the realm of JS-metric spaces, as articulated by Jleli and Samet. Utilizing these contractions, we have formulated a groundbreaking fixed point theorem that paves the way for a diverse array of fixed point results. Additionally, we demonstrate a fixed point result specifically for P-contractions in JS-metric spaces. To further enrich our discourse, we provide several examples that vividly illustrate the essence of our principal theorem.

This paper introduces the concept of Pentapartitioned Neutrosophic Numbers (PNNs) and proposes score and accuracy functions to effectively rank PNNs based on their score values. Utilizing the adaptability of Dombi operators to accommodate various parameters, the study applies these operators to address complex Multicriteria Attribute Group Decision Making (MAGDM) problems. To achieve precise aggregation under neutrosophic conditions, Dombi T-norm and T-conorm operations for two PNNs are defined. Building upon these Dombi operations, the paper presents two weighted aggregation operators—PNDWAA (Pentapartitioned Neutrosophic Dombi Weighted Arithmetic Average) and PNDWGA (Pentapartitioned Neutrosophic Dombi Weighted Geometric Average)—and investigates their properties within the pentapartitioned neutrosophic environment. Furthermore, the study explores a Multicriteria Attribute Decision Making (MADM) approach that utilizes either the PNDWAA or PNDWGA operators for decision-making.An illustrative example is provided to demonstrate the proposed method, offering a detailed step-by-step process that highlights the effectiveness of the approach in determining the optimal alternative based on ranking order.

This study is an attempt to explore the value of the teachers’ critical thinking skills with fuzzy expert systems. The study employed this system to obtain an objective and authentic evaluation in an abstract or ambiguous assessment. The working group consisted of 275 teachers working in public schools in Antalya central districts during the 2021-2022 academic year. This study deployed The Critical Thinking Appraisal (CTA) developed by Özelçi (2012). In the first stage, the data obtained from the teachers' critical thinking skill scale were analyzed through classical logic. Validity (explanatory and confirmatory factor analysis) and reliability analyzes (Cronbach Alpha) were performed during data analysis. Besides, the data regarding the teachers' critical thinking skill scale were also examined through the fuzzy logic approach. Different results emerged when comparing both methods. The findings revealed that the result on the fuzzy logic approach, which underpins artificial intelligence applications and which is used in various decision-making applications, is more consistent and objective. This study may shed light onto the researchers to obtain results that are more objective by conducting studies based on fuzzy logic-based survey. Besides, the validity and reliability analyzes made through the classical method with a similar method may also be carried out through the fuzzy logic method. These new results may be compared with those of the classical method. Thus, the objectivity of classical validity and reliability analyzes may also be examined.

The Sustainable Development of a country is a relatively new concept, where the right of each country to achieve decent economic and social development is accepted, and where there is well-being for the population. At the same time, the environment is respected. On the other hand, the Circular Economy is another recent concept where the efficient and effective use of resources and products is proposed, where the fundamental principle is the reuse of waste as far as possible and its rational use, to reduce environmental pollution, and providing economic savings for the country. This paper aims to study the relationship between the concepts of Circular Economy and Sustainable Development contextualized in the Peruvian department of Junín. To examine this relationship and its future behavior, there are challenges such as the existence of indirect relationships between these two concepts, dependent on other concepts; and relationships between concepts that are unknown, at least partially. Taking all this into account, a group of three experts on the subject in Junín was asked for their opinion to determine the relationship between the selected concepts. This allowed the representation of knowledge with the help of a Neutrosophic Cognitive Map (NCM) and the study of the dynamic behavior of concepts with the help of the Method for Hidden Patterns.

In this paper, we extend statistical hypothesis testing to data represented as neutrosophic sets, encompassing membership, indeterminacy, and non-membership components. Two distinct scenarios are considered: first, where all three components are independent, and second, where all three components are dependent.

In this paper, fuzzy γ-open sets, and fuzzy γ-irresolute functions are used to define and investigate a new class of functions called fuzzy completely γ-irresolute functions, fuzzy completely weakly γ-irresolute between fuzzy topological spaces. We obtain their characterizations and their basic properties.

The university's mission as established in the World Declaration on Higher Education is to contribute to sustainable development and improve society, which implies training highly qualified professionals. This paper aims to determine to what extent Project Management is related to Social Responsibility at the Universidad Peruana Los Andes, 2024. For the study, a survey is applied to a sample of 384 graduates from a total population of 5823 distributed by faculties, in 2024 regarding the attitude of this university's Center on Project Management and University Social Responsibility. For data representation, we use an Indeterminate Likert Scale. This type of scale consists of the quantitative score of each of the possible nominal values, in this way the opinion of each respondent is captured more faithfully. On the other hand, we use the Plithogenic Statistics, because there are several variables to study, some of them with indeterminacies.

This paper introduces the concept of -(3,2) ƒuzzy ᵴemigroups within an -ᵴemigroup and explore their characterizations. Various comparable conditions for -(3,2) ƒuzzy normal subᵴemigroups are established. Additionally, the -(3,2) ƒuzzy coset, -(3,2) ƒuzzy ideal, -(3,2) ƒuzzy symmetric ᵴemigroup and -(3,2) ƒuzzy normal subᵴemigroups are defined. The idea of conjugate -(3,2) ƒuzzy ᵴemigroups is also introduced, and the order of an -(3,2) ƒuzzy ᵴemigroup is determined. The (3,2) ƒuzzy semigroup condition applied to decision making process also.

Fuzzy differential equations (FDEs) are used to represent dynamical systems under uncertain environments. Finding solutions for fuzzy differential equations (FDEs) is highly challenging. This work employs the neutrosophic version of the Sumudu transform method to determine the solution to fuzzy differential equations (FDEs) that incorporate Neutrosophic Numbers (NNs). By utilising a novel fuzzy arithmetic operations on the parametric representations of NNs, significant theorems are established to demonstrate the characteristics of Neutrosophic Sumudu Transform (NST). The proposed NST approach is efficient in approximating the solutions of FDEs without converting them into their crisp equivalent forms. An illustrative numerical example is provided to demonstrate the efficacy of the proposed methodology.

Domination and graph energy are fundamental concepts in graph theory for addressing unpredictable phenomena, and they have attracted considerable interest from researchers. In recent developments, the concept of dominating energy has become increasingly significant in the study of graph energies. While fuzzy graphs (FG) sometimes fall short in delivering optimal results, the neutrosophic set (NS) as well as neutrosophic graphs (NG) offer a robust alternative, effectively managing the uncertainties linked with inconsistent and indeterminate information in real-world scenarios. Most existing research on domination energy in the fuzzy environment focus solely on a single membership function. In contrast, bipolar neutrosophic models, which account for both positive and negative influences, provide a more versatile and applicable approach. This paper focuses on advancements in NG theory to address scenarios where imprecision is represented by both positive and negative membership functions. It introduces a new concept called the double dominating energy graph, relying on the currently developed bipolar single-valued neutrosophic graphs (BSVNG). The study further explores the energy of double domination within the BSVNG framework. Specifically, it develops the adjacency matrix of a dominating BSVNG, analyzes the spectrum of this matrix, and elaborates on the associated theoretical aspects using illustrative examples. Additionally, the double domination energy of BSVNG is calculated to demonstrate its applicability. At the end of this study, conclusions are drawn and avenues for future research are discussed.

The manuscript dealt with the problem of the initial value, especially in second-order differential equations with three degrees of Neutrosophic conditions, which are truth, falsity, and indeterminacy. In addition, we exploited the Kamal transformation to solve it.