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The Geometric Bonferroni Mean (GBM), is an extension of The Bonferroni mean (BM), that combines both BM and the geometric mean, allowing for the representation of correlations among the combined factors while acknowledging the inherent uncertainty within the decision-making process. Within the framework of Pythagorean neutrosophic set (PNS) that encompasses truth, indeterminacy, and falsity-membership degrees, each criterion can be integrated into a unified PNS value, portraying the overall evaluation of that criterion by employing the Geometric Bonferroni mean. This study aims to enhance decision-making in Pythagorean neutrosophic framework by introducing an aggregation operator to PNS using the Geometric Bonferroni Mean. Additionally, it proposes a normalized approach to resolve decision-making quandaries within the realm of PNS, striving for improved solutions. The novel Pythagorean Neutrosophic Normalized Weighted Geometric Bonferroni Mean (PNNWGBM) aggregating operator has been tested in a case of multicriteria decision-making (MCDM) problem involving the selection of Halal products suppliers with several criteria. The result shows that this aggregating operator is offering dependable and pragmatic method for intricate decision-making challenges and able to effectively tackle uncertainty and ambiguity in MCDM problem. [ABSTRACT FROM AUTHOR]

We introduce the notion of q-neutrosophic cubic vague subbisemiring (q-NSCVSBS) and level set of q-NSCVSBS of a bisemiring. The q-NSCVSBS is a new concept of subbisemirings of bisemirings. Let Ξ be a neutrosophic vague subset of Λ. Then 0 = ([T-Ξ, T+Ξ ], [I-Ξ, I+Ξ ], [F-Ξ, F+Ξ ]) is a q-NSCVSBS of Λ if and only if all non empty level set 0(ϱ1,ϱ2,s) is also a SBS of Λ for every ϱ1, ϱ2, s ∈ [0, 1]. Let Ξ be the q-NSCVSBS of Λ and Υ be the strongest cubic q-neutrosophic vague relation of Λ. Then Ξ is a q-NSCVSBS of Λ × Λ. Let Ξ be the q-NSCVSBS of Λ, show that pseudo cubic q-neutrosophic vague coset (ςΞ)p is also a q-NSCVSBS of Λ, for all ς ∈ Λ. Let Ξ1,Ξ2, ...,Ξn be the any family of q - NSCV SBSs of Λ1,Λ2, ...,Λn respectively, then Ξ1 × Ξ2 × ... × Ξn is also a q-NSCVSBS of Λ1 × Λ2 × ... × Λn. The homomorphic image of every q-NSCVSBS is also a q-NSCVSBS. The homomorphic pre-image of every q-NSCVSBS is also a q-NSCVSBS. [ABSTRACT FROM AUTHOR]

In actual life, dealing with uncertain information has become a challenge for researchers who strive day after day to develop more accurate mathematical tools for better dealing with this information. The Q-Fuzzy soft model can process uncertain information in two dimensions by dealing with the subjective judgments of users effectively. Therefore, this article aims to increase the effectiveness of the Q-fuzzy soft model and address the challenges of design-making under uncertain information by proposing a new model called the interval-valued Q-fuzzy soft (IVQ-FSS) model. Under the IV-Q-FSSs, we discuss strongly set-theory operations such as subset, union of two IVQ-FSSs, intersection of two IV-Q-FSSs, complement of IV-Q-FSS, AND operation, and OR operation for IV-QFSSs, and some operations like the possibility and necessity operations of an IV-Q-FSS. In addition, we hand over numerous properties held up by numerical examples that describe how they toil. Finally, this recently developed model has been successfully trying out in dealing with one of the design-making problems based on hypothetical data for a respiratory disease. This algorithm is built based on the aggregation operator for IV-Q-FSS data to break this issue (i.e., selecting the optimal alternative). [ABSTRACT FROM AUTHOR]

This study investigates the challenges to the digitalization technology adoption in Malaysia agriculture sector by using the DEMATEL (Decision-Making Trial and Evaluation Laboratory) approach, which will give a complete knowledge of the interdependencies among the barriers. The research objectives are to determine the cause and effect of digital agriculture using DEMATEL and to recommend the best way to overcome the obstacles in using digital technology. The findings from this study reveals the cause and effect from the barriers which is lack of skills, lack of technology, high cost, infrastructure and connectivity, and resistance to change are in the cause group while limited locality, data privacy and security concerns, low level of education, market access and regulatory and policy are in the effect group. The research findings are utilized to give policymakers and stakeholders with practical recommendations aimed at addressing the identified barriers and promoting the adoption of digital technologies in Malaysian agriculture. Thus, this study offers recommendations for the most important obstacles found, which are an improvement in infrastructure and the implementation of financial assistance mechanisms. All things considered, this research makes a significant contribution to the subject of agriculture and sheds light on the difficulties associated with implementing new technologies in Malaysia's agriculture industry. [ABSTRACT FROM AUTHOR]

This study employs a Pythagorean Neutrosophic Bonferroni Mean (PNBM) - Decision Making Trial and Evaluation Laboratory (DEMATEL) approach to analyze barriers faced by young entrepreneurs in Digital Social Innovation (DSI). Pythagorean Neutrosophic Set (PNS) enriches the analysis, accommodating uncertainties in the complex socio-economic context. Limited Access to Funding emerges as the most influential barrier, showcasing its pivotal role in impacting other DSI challenges. Regulatory and Compliance Challenges are identified as interdependent, emphasizing their interconnected nature with broader barriers. Neutrosophic elements elucidate the uncertainties surrounding financial constraints, regulatory frameworks, and mentorship dynamics. The study contributes to a nuanced understanding of DSI challenges and pioneers the application of neutrosophic logic in socio-economic research. It advocates for a more inclusive decision-making methodology, fostering adaptability in addressing the indeterminate nature of barriers faced by young entrepreneurs navigating the digital social innovation landscape. The findings aim to enhance support systems, fostering a conducive environment for DSI initiatives and encouraging future research in neutrosophic decision-making methodologies. [ABSTRACT FROM AUTHOR]

A soft expert set is a concept that combines elements of soft sets and expert systems. It aims to incorporate expert knowledge and uncertainty-handling capabilities into the analysis and decision-making processes. On the other hand, the idea of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) are imported models for handling the uncertainty data. In this work, the authors combine the critical features of FSs and SVNSs under expert systems in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given distance measures (DM) between two SVNFSESs to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications. [ABSTRACT FROM AUTHOR]

A soft expert set(SES) is a concept that combines elements of soft sets and expert systems. It aims to incorporate expert knowledge and uncertainty-handling capabilities into the analysis and decision-making processes. On the other hand, the idea of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) are imported models for handling the uncertainty data. In this work, the authors combine the critical features of FSs and SVNSs under expert systems in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given an Orthogonal Distance and Similarity for SVNFSESs to construct a new algorithm to demonstrate the method's effectiveness in handling some real-life applications. [ABSTRACT FROM AUTHOR]

This research employs DEMATEL analysis as a methodological approach to thoroughly examine the adverse consequences of implementing Artificial Intelligence (AI) among students enrolled at Universiti Teknologi MARA (UiTM) Negeri Sembilan, Malaysia. The analysis encompasses three distinct professional cohorts: student representatives, academic staff, and upper management. Through a systematic analysis of causal relationships between multiple factors, this study aims to identify and prioritize the fundamental elements contributing to the negative consequences associated with integrating artificial intelligence. The prominence of privacy and security concerns as a causal factor highlights the importance of implementing strong data protection measures and adhering to ethical practices related to AI. Furthermore, various factors connected with personal disconnection, restricted adaptability, dependance on technology, and insufficient emotional intelligence influence the adverse outcomes of artificial intelligence implementation among students. The results underscore the necessity of implementing focused interventions and strategies to tackle these difficulties and guarantee a harmonious and advantageous integration of artificial intelligence in students' educational journeys. Higher education institutions can effectively harness the advantages of AI while ensuring their students' welfare and educational achievements by recognizing and proactively addressing any potential limitations. [ABSTRACT FROM AUTHOR]

We introduce the new type neutrosophic set (NS) problems relevant to multiple attribute decision making (MADM). Pythagorean fuzzy set (PFS) and neutrosophic set (NS) can be extended into new type neutrosophic set. We discusses new type neutrosophic weighted averaging (New type NWA), new type neutrosophic weighted geometric (New type NWG), generalized new type neutrosophic weighted averaging (new type GNWA) and generalized new type neutrosophic weighted geometric (new type GNWG). A number of algebraic properties of new type NSs have been established such as associativity, distributivity and idempotency. [ABSTRACT FROM AUTHOR]

This article considers a bi-level linear programming with single valued trapezoidal fuzzy neutrosophic cost coefficient matrix and Pythagorean fuzzy parameters in the set of constraints both in the right and left sides. Based on the score functions of the neutrosophic numbers and Pythagorean fuzzy numbers, the model is changed to the corresponding crisp bi-level linear programming (BLP) problem. This problem is designated as a Pythagorean fuzzy bi-level linear programming (PFBLP) problem under neutrosophic environment. Kuhn-Tucker's conditions for optimality are necessary and sufficient for the existence of the optimal solution to a BLP problem. Using the suggested methodology, the problem is formulated as a single-objective non-linear programming problem with several variables and constraints. Two typical numerical examples are examined to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

The incorporation of expert opinions and handling of data uncertainty are addressed by Al-Alkhazaleh through the introduction of a soft expert set. This extension of the soft set framework aims to enhance the analysis and decision-making processes by incorporating expert knowledge. On the other hand, the utilization of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) has been introduced as models to effectively handle uncertain data. In this work, the authors propose a model that combines the essential characteristics of fuzzy sets (FSs) and single neutrosophic sets (SVNSs) within expert systems. Consequently, this model aims to offer decision-makers increased flexibility when interpreting uncertain information, empowering them in the decision-making process. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given an aggregation operator (AO) for SVNFSESs to construct a new algorithm to demonstrate the method's effectiveness in handling some real-life applications. [ABSTRACT FROM AUTHOR]

This paper aims to introduce and explore the innovative concept of T-spherical fuzzy valued neutrosophic sets (T-SFVNSs) in the context of multi-attribute decision making (MADM). The T-SFVNSs are utilized to develop two key aggregation operators: the T-spherical fuzzy valued neutrosophic weighted average operator (T-SFVNWAO) and the T-spherical fuzzy valued neutrosophic weighted geometric operator (T-SFVNWGO). These operators are defined based on the operational rules of T-SFVNNs. The properties of these operators, including idempotency, boundedness, and monotonicity, are rigorously examined and established. To demonstrate the practicality and relevance of the T-SFVN operators, an algorithm and a numerical application are presented. The algorithm illustrates the step-by-step implementation of these operators, while the numerical application showcases their effectiveness in real-world scenarios. Additionally, a comparative analysis is conducted to evaluate the accuracy and performance of the proposed operators in relation to existing ones. [ABSTRACT FROM AUTHOR]

From fuzzy to neutrosophy, multiple hybrid models have been innovated, with each introduced model surpassing its predecessor. Due to the inherent indeterminacy in the world, a more precise form of imprecision is required. As a result, more sophisticated variants of the neutrosophic set have been created. Examples of these amalgamations include fuzzy neutrosophic sets, intuitionistic fuzzy neutrosophic sets, Pythagorean fuzzy neutrosophic sets, neutrosophic vague sets, and neutrosophic rough sets. The main objective of this paper is to present another variant of the neutrosophic set called T-spherical fuzzy-valued neutrosophic set (T-SFVNS). Serving as a generalization of the aforementioned combinations, T-SFVNS allows for the representation of indeterminacy and inconsistency in a more nuanced manner. In this paper, we define the T-SFVNS and Tspherical fuzzy-valued neutrosophic numbers (T-SFVNNs). Additionally, we propose several types of score and accuracy functions to compare the T-SFVNNs. We also present the basic operations of T-SFVNSs and the algebraic operations of T-SFVNNs, supported by proofs and illustrative examples.. [ABSTRACT FROM AUTHOR]

This article considers a stochastic multi-objective linear programming problem in a neutrosophic framework. The righthand sides of the constraints are random variables associated with their means and variances, and the single-valued trapezoidal neutrosophic numbers are included in the coefficients of the objective functions to investigate the problem. The problem is successfully converted into the related deterministic programming model based on the formulation of the scoring function and several distributions, such as the Uniform, Exponential, and Gama distributions. Applying fuzzy goal programming, the deterministic problem is solved. An example is then solved to demonstrate the solution methodology. [ABSTRACT FROM AUTHOR]

The goal of this research is to investigate fuzzy multiobjective dynamic programming issues with fuzzy parameters in the objective functions and single valued trapezoidal neutrosophic numbers in the left hand side of the constraints. Piecewise quadratic fuzzy numbers characterize these fuzzy parameters. In addition, applying the score function of the neutrosophic numbers to convert the constraints parameters into its crisp. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique is presented for obtaining a subset of the parametric space that has the same α-pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided. [ABSTRACT FROM AUTHOR]

In this paper, the concept of bipolar Pythagorean fuzzy neutrosophic sets (BPNSs) will be introduced which represents an innovative synthesis, incorporating bipolarity, Pythagorean fuzzy sets, and neutrosophic sets to provide a comprehensive solution to the multifaceted issues encountered in decision-making challenges. BPNS is proposed to enhance the expressiveness and flexibility of the model by incorporating both positive and negative preferences that can lead to more accurate and realistic modeling of complex decision scenarios. The essential idea of BPNSs is defined and some definitions for instance complement, intersection, and union are described. The basic operation, the derivation of its properties, and the numerical example of the method are integrated to execute the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, a bi-level chance constrained programming problem is considered when the coefficients of the objective function is presented as neutrosophic numbers and the right-hand side of the constraints is normal variables and the constraints have a joint probability distribution. While the probability problem and applying the score and accurate functions the problem is converted into an equivalent deterministic non-linear programming problem, a fuzzy programming approach is applied by defining membership function. A linear membership function is used for obtaining optimal compromise solution. A numerical example is given to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Hypersoft sets (HSSs) have gained popularity because of their ability to formulate data in the form of several trait-valued disjoint sets that blend various traits. Motivated by this idea, in this study, we present a new hyper-approach referred to as bipolar neutrosophic hypersoft sets (BNHSSs) by a generalization of neutro-sophic hypersoft sets (NHSSs) and bipolar fuzzy hypersoft sets (BFHSSs) or by merging and subjecting both HSSs and neutrosophic sets (NSs) to a bipolarity property of real numbers. By utilizing positive and negative neutrosophic structures, we construct different notions and operations on the basis of BNHSSs, such as an absolute BNHSS, a null BNHSS, a complement, subset-hood, a restricted and extended union, and a restricted and extended intersection, along with their related properties. Also, some operations like OR and AND on BNHSS have been initiated. In addition, some properties are displayed paired together, and some numerical hypothetical examples are given to clarify the mechanism of using these instruments. Finally, to prove the efficiency and applicability of the proposed model, we established two novel algorithms based on mathematical techniques (aggregation operator and score function) applied to our model (BNHSS). The aforementioned meth-ods have been utilized in the resolution of a multi-attribute group decision-making (MAGDM) problem. Some discussions and comparisons between the given techniques are also presented to demonstrate their effectiveness and applicability. [ABSTRACT FROM AUTHOR]

A field is a fundamental algebraic structure that finds extensive applications in algebra and various mathematical domains. On the other hand, a Q-complex neutrosophic soft set (Q-CNSS) is a unique hybrid model that combines the characteristics of soft sets and neutrosophic sets within a complex number framework. It utilizes the effectiveness of Q-set as a powerful tool in the domain of this particular model. In this article, we leverage this model to define fields under uncertainty. We present the Q-complex neutrosophic soft field (Q-CNSF) and examine the unique algebraic properties associated with this model. Additionally, we explore the relationships between Q-CNSF and Q-neutrosophic soft field (Q-NSF). Furthermore, we define the Cartesian product of QCNSFs and delve into the relevant properties. Through this comprehensive exploration, our aim is to enhance the understanding of Q-CNSFs and their properties, ultimately contributing to the field of algebraic analysis and its practical applications in handling uncertainty and vagueness. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to investigate the algebraic structures within the Q-complex neutrosophic soft model. We introduce two fundamental concepts: the Q-complex neutrosophic soft ring (Q-CNSR) and the Q-complex neutrosophic soft ideal (Q-CNSI). Q-CNSRs combine the properties of Q-complex neutrosophic soft sets (Q-CNSSs) with ring theory, effectively capturing uncertainty and indeterminacy present in ring operations through the incorporation of Q-complex neutrosophic membership values. Additionally, we define Q-CNSIs as subsets of Q-CNSRs that possess distinctive properties and hold significant roles in ring theory. Furthermore, we discuss and verify the specific algebraic properties of Q-CNSR and Q-CNSI. By examining these properties, we gain a deeper understanding of the algebraic behavior of Q-CNSR and Q-CNSI. In particular, we shed light on the relationship between Q-CNSRs and soft rings. This provides insights into how Q-CNSR relates to the broader framework of soft ring, highlighting the unique features and contributions of Q-complex neutrosophic soft structures in the realm of algebraic analysis. We have also verified the relations between Q-CNSR and Q-neutrosophic soft ring (Q-NSR), as well as between Q-CNSI and Q-neutrosophic soft ideal (Q-NSI). Through this comprehensive exploration, our objective is to advance the understanding of Q-CNSR and Q-CNSI, thereby contributing to the field of algebraic analysis and its application in handling uncertainty and vagueness. [ABSTRACT FROM AUTHOR]

The idea of interval-valued neutrosophic soft sets (IVNSSs) is a new generalization of the neutrosophic soft sets to the neutrosophic sets when the authors combine the critical features of IVNS and soft sets (SSs) in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this highperformance IVNSS disappears. Therefore, in this paper, we initiated a new approach known as possibility interval-valued neutrosophic soft sets (PIVNSSs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on PIVNSSs along with their basic properties. Also, we investigate AND and OR operations between two PIVNSSs as well as several numerical examples to clarify the above fundamental operations. Finally, we have given aggregation operators (AO) to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications. [ABSTRACT FROM AUTHOR]

Soft set(SS) is a powerful tool to handle the vagueness of information in a parametric environment. In other hand the idea of interval-valued neutrosophic soft sets (IVNSSs) is a new generalization of the neutrosophic soft sets to the neutrosophic sets when the authors combine the critical features of IVNS and soft sets (SSs) in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this highperformance IVNSS disappears. Therefore, in this paper, we initiated a new approach known as possibility interval-valued neutrosophic soft sets (PIVNSSs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on PIVNSSs along with their basic properties. Also, we investigate AND and OR operations between two PIVNSSs as well as several numerical examples to clarify the above fundamental operations. Finally, we have given similarity measure (SM) between two PIVNSSs to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications. [ABSTRACT FROM AUTHOR]

Soft set(SS) is one of the soft computing techniques that plays an important role in addressing the hiddenness and uncertainty associated with uncertain data. In other hand the idea of interval-valued neutrosophic soft sets (IVNSSs) is a new generalization of the neutrosophic soft sets to the neutrosophic sets when the authors combine the critical features of IVNS and soft sets (SSs) in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this high-performance IVNSS disappears. Therefore, in this paper, we initiated a new approach known as possibility interval-valued neutrosophic soft sets (PIVNSSs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on PIVNSSs along with their basic properties. Also, we investigate AND and OR operations between two PIVNSSs as well as several numerical examples to clarify the above fundamental operations. Finally, we have given distance measures (DM) between two PIVNSSs to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications. [ABSTRACT FROM AUTHOR]

DEMATEL serves as a tool for addressing multi-criteria decision-making problems, primarily by identifying critical factors that exert the most significant influence on a specific system. To enhance its capabilities in handling contextual decision problems, DEMATEL has been further developed through integration with various other MCDM methods. The inherent reliance on direct input from experts for initial decision information in DEMATEL raises concerns about the potential limitations imposed by experts' domain knowledge and bounded rationalities. The effectiveness of decision-making can be compromised if the initial information provided by experts is deemed unreliable, leading to debatable outcomes. To address these challenges, this study proposes the incorporation of a Bonferroni mean aggregation operator within a Pythagorean neutrosophic environment, illustrated through a numerical example applied to DEMATEL. This integration is intended to fortify decision accuracy by introducing a more enhanced decision framework by developing a new normalized weighted Bonferroni mean operator for Pythagorean neutrosophic set aggregation (PN-NWBM). By integrating this operator, this study aims to alleviate the impact of unreliable initial information and enhance the overall reliability of decision outcomes thereby contributing to its improvement in decision making. Through the implementation of the Bonferroni mean aggregation operator, the study anticipates achieving a more comprehensive and accurate representation of decision factors as illustrated in the numerical example. This research includes a comparative and sensitivity analysis to thoroughly examine the implications and effectiveness of the proposed integration. [ABSTRACT FROM AUTHOR]

Groups and subgroups are rich algebraic structures, and both of them depend on binary operations in their work. The discussion of this paper is organized into two parts. In the first part, we define the notion of Qcomplex neutrosophic soft sets (Q-CNSSs) by amalgamating two previous models of Q-complex neutrosophic set (Q-CNS) and soft set (SS) to address the issues of two-dimensionality (two variables) in a universal set under a parametric environment. Subsequently, the relation between Q-CNSSs and Q-neutrosophic soft sets (Q-NSSs) is verified. A basic set theory for this hybrid model is developed. In particular, null Q-CNSS and absolute Q-CNSS are defined. The basic operators of the complement, subset, equality, union and intersection are advanced and their properties are examined. Further, the notions of the homogeneous and completely homogeneous Q-CNSSs are proposed along with some illustrated examples. In part two, we move to study some algebraic structures of this model when we define the notions of Q-complex neutrosophic soft groups (QCNSG) and Q-complex neutrosophic soft subgroups (Q-CNSSG). Then, the relation between Q-CNSG and Q-neutrosophic soft group (Q-NSG) is scrutinized. Moreover, the algebraic properties of the Q-CNSG and Q-CNSSG are discussed and verified. Finally, some theories that show the relationship between the Q-CNSG and the soft group are proposed. [ABSTRACT FROM AUTHOR]

Pythagorean neutrosophic sets (PNS) have been recognized as a highly effective mechanism for managing situations characterized by indeterminacy and inconsistency within decision-making procedures. This paper delves into the examination of algebraic operations performed on PNS, thereby expanding their scope of application, and enhancing their utility. In this study, we put forth a set of algebraic operations that can be applied to PNS. These operations encompass addition, multiplication, scalar multiplication, and power. These operations facilitate the efficient manipulation and combination of PNS, thereby enhancing decision-making in scenarios characterized by uncertainty and vagueness. To demonstrate the efficacy of these operations, we will present several illustrative examples accompanied by corroborating proofs. The introduction of algebraic operations enhances the capabilities of PNS, thereby creating opportunities for their practical application. [ABSTRACT FROM AUTHOR]

The implementation of halal certification in Muslim-owned dining establishments in Malaysia faces various obstacles. This research aimed to analyze and investigate these challenges. The study used the DEMATEL approach with the integrated single-valued neutrosophic normalized weighted Bonferroni mean (SVNNWBM) to identify and understand the interrelationships among the obstacles. Three groups comprising academicians, industry professionals, and Muslim owner-restaurant representatives provided their perspectives. The findings highlighted three key obstacles hindering the acceptance and implementation of halal certification: customer perception, halal perception, and inadequate awareness. Fiscal constraints, inadequate awareness, and halal perception were significant barriers in Malaysia's restaurant sector. These obstacles were categorized as causal factors, generating additional barriers in the industry. By identifying these challenges, effective strategies can be developed to overcome them and improve the adoption of halal certification. This research provides valuable insights for policymakers, restaurant owners, and other stakeholders, enabling them to understand the obstacles better and develop targeted interventions. Employing the integrated SVNNWBM-DEMATEL approach and incorporating perspectives from experts in academia, industry, and Muslim owner-restaurant representatives ensures a comprehensive analysis of the obstacles faced in halal certification implementation. [ABSTRACT FROM AUTHOR]

This study proposes a methodology that integrates the Pythagorean Neutrosophic Set (PNS) with the Decision-Making Trial and Evaluation Laboratory (DEMATEL) approach. This integration is intended to effectively handle the challenges of uncertainty and linguistic vagueness that are commonly encountered in multi-criteria decisionmaking scenarios. The PNS-DEMATEL framework comprises eight distinct steps, wherein the fundamental divergence lies in the creation of a linguistic variable within the PNS-DEMATEL framework. The linguistic variable has been formulated utilizing the PNS methodology, thereby enabling a more all-encompassing depiction of the viewpoints of experts. The application of the 7-point linguistic scale is utilized to acquire evaluations from experts, resulting in heightened precision and discernment. The method that has been put forth aims to improve the representation and management of linguistic variables, thereby enhancing the usability and validity of the model. The verification of the linguistic variable's validity is achieved by ensuring that the conditions outlined for the PNS are met. The integration of PNS with DEMATEL can facilitate the exploration of causal relationships in the barriers to halal certification. This approach can provide decision-makers with a more comprehensive and accurate representation of their opinions and judgements, leading to improved effectiveness in decision-making across various application domains. [ABSTRACT FROM AUTHOR]

Smarandache developed the idea of hypersoft set (HSS) theory as an extension of soft set (SS) theory. HSS provides a general mathematical framework for handling data that can be formulated as several trait-valued disjoint sets which blend to various traits. The major goal of this article is to lay the footing for supplying a new model called bipolar fuzzy hypersoft sets (BFHSSs) by linking both fuzzy sets (FSs) and HSSs under bipolarity property. By using positive and negative membership functions and multi-argument functions, these structures work best for testing uncertainty. This makes them better at solving real-world problems, especially ones that have both good and bad sides. This paper also has different operations for BFHSSs, such as absolute BFHSS, null BFHSS, complement, subset, union, intersection, and their related properties. Moreover, operations like OR and AND for BFHSS have been instituted. Some properties are demonstrated, and some numerical examples are given to illustrate the mechanism of using these tools. Finally, these tools are applied in the decision-making process based on an algorithm that is built. [ABSTRACT FROM AUTHOR]

Most complex problems in the real-world typically involve uncertain, incomplete and indeterminate two-dimen sional data i.e. information pertaining to the attributes and the periodicity of the problem parameters. To meet the demand for models that has the ability to handle these information with these characteristics, the introduction of neutrosophic sets (NSs) was followed by their extension to the complex neutrosophic sets (CNSs). In this paper, we introduce the concept of Q- complex neutrosophic set (Q-CNS) by extending the ranges of the membership functions in Q-neutrosophic set (Q-NS) from [0,1] to the unit circle in the complex plane. Q-CNS plays a key role in the decision making theory, where the extra information provided by the elements of the Q-set serve in modeling of some decision making problems. Based on this new concept we define the basic theoretical operations such as complement, equality, subset, union, intersection, Q-complex neutrosophic product and Cartesian product. Some related examples are also given to enhance the understanding of the proposed concepts. The basic properties of these operators are also verified with supporting proofs. [ABSTRACT FROM AUTHOR]

The neutrosophic idea is a fertile environment adaptable to different mathematical tools. This paper aims to introduce the mapping of complex interval neutrosophic soft sets (MI-CNSSs). Further, the images and inverse images of complex interval neutrosophic soft sets and their properties are explored. These will be supported by concrete examples, and this paper will present some theorems about complex interval neutrosophic soft images and inverse images. [ABSTRACT FROM AUTHOR]

In this paper, we study neutrosophic of one important types of algebra namely BCK-algebra. Some new results of a generalization of BCK-algebra (Ω-BCK-algebra) have been introduced. Several facts about neutrosophic Ω-BCK-algebra are presented such as neutrosophic of homomorphic image and neutrosophic of kernel homomorphism. Finally, some definitions, examples, and other properties of neutrosophic BCKalgebra and neutrosophic Ω-BCK-algebra are given. [ABSTRACT FROM AUTHOR]

The idea of an interval complex neutrosophic soft set (I-CNSS) emerges from the interval neutrosophic soft set (I-NSS) by the extension of its three membership functions (T, I, F) from real space to complex space (unit disc) to better handle uncertainties, vagueness, indeterminacy, and imprecision of information in the periodic nature. The novelty of I-CNSS lies in its more significant range of activity compared to CNS. Measures of similarity and distance are important tools that can be used to solve many problems in real life. Hence, this paper presents some interval complex neutrosophic soft similarities based on Hamming and Euclidean distances of I-CNSSs to deal with real-life problems that include uncertain information such as decision-making issues and medical diagnosis stats. Firstly, this paper reviews the definition of an interval complex neutrosophic soft set. Secondly, we defined distance Hamming measures and distance Euclidean measures on I-CNSSs. Next, the axiomatic definition of similarity measures based on Hamming and Euclidean distances of I-CNSSs is proposed. Moreover, a numerical example is given and relations between these measures are introduced and verified. Meanwhile, some applications are given to show how similarity can be used to help the user in making decisions and making medical diagnoses. Finally, a comparison of some current approaches is used to back up this study. [ABSTRACT FROM AUTHOR]