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Business has a massive effect on both people and society as a whole in today's culture. Businesses make significant contributions to humanity's general well-being and progress by promoting economic growth, supporting innovation, producing wealth, and addressing social challenges. However, choosing the right location for a business is a complex task, involving multiple criteria and qualitative and quantitative factors that heavily rely on expert judgement. The researchers propose a unique approach called the SVNZN multi-attributed decision-making method to aid decision-makers in this process. They introduce new operating laws for SVNZNs based on the sine trigonometric (ST) function, known for its periodicity and symmetry over the origin, making it favorable for decision-makers over multi-time phase parameters. Additionally, novel AOs such as SVNZN weighted averaging and geometric operators are defined to combine SVNZNs effectively. Based on these AOs, a decision-making technique for MADM problems is presented, and its applicability is demonstrated through a numerical example of selecting the best location for a business. To validate and enhance the understanding of these proposed techniques, the researchers conducted a comprehensive comparison analysis, including a sensitivity analysis, considering existing literature on MADM difficulties. Figure 1 provides a thorough graphical summary by visually representing all of the contributions and outcomes. [ABSTRACT FROM AUTHOR]

The use of a single-valued neutrosophic set (svns) makes it much easier to manage situations in which one must deal with incorrect, unexpected, susceptible, faulty, vulnerable, and complicated information. This is a result of the fact that the specific forms of material being discussed here are more likely to include errors. This new theory has directly contributed to the expansion of both the concept of fuzzy sets and intuitionistic fuzzy sets, both of which have experienced additional development as a direct consequence of the creation of this new theory. In svns, indeterminacy is correctly assessed in a way that is both subtle and unambiguous. Furthermore, membership in the truth, indeterminacy, and falsity are all completely independent of one another. In the context of algebraic analysis, certain binary operations may be regarded as interacting with algebraic modules. These modules have pervasive and complicated designs. Modules may be put to use in a wide variety of different applications. Modules have applications in a diverse range of industries and market subsets due to their adaptability and versatility. Under the umbrella of the triplet (μ , ν , ω) structure, we investigate the concept of svns and establish a relationship between it and the single-valued neutrosophic module and the single-valued neutrosophic submodule, respectively. The purpose of this study is to gain an understanding of the algebraic structures of single-valued neutrosophic submodules under the triplet structure of a classical module and to improve the validity of this method by analyzing a variety of important facets. In this article, numerous symmetrical features of modules are also investigated, which demonstrates the usefulness and practicality of these qualities. The results of this research will allow for the successful completion of both of these objectives. The tactics that we have devised for use in this article are more applicable to a wide variety of situations than those that have been used in the past. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are some of the tactics that fall under this category. [ABSTRACT FROM AUTHOR]

This study included concepts for (ϖ, ε, ς )-single valued neutrosophic hyperring ((ϖ, ε, ς )-SVNHR) and (ϖ, ε, ς )-single valued neutrosophic hyperideal ((ϖ, ε, ς )-SVNHI). (ϖ, ε, ς )-single valued neutrosophic hyperrings ((ϖ, ε, ς )-SVNHRs) and (ϖ, ε, ς)-single valued hyperideals ((ϖ, ε, ς )-SVNHIs) are examined and validated in terms of algebraic features and of structural characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the notion of γ-single valued neutrosophic subrings and ideals. Also, several properties related to the algebraic structure of rings and ideals are discussed. Moreover, many characterizations are proposed on γ-single valued neutrosophic subrings and ideals. [ABSTRACT FROM AUTHOR]

We use the homotopy perturbation method (HPM) to construct a new iterative system for solving non-linear equations in this article. The criteria for convergence in the scheme developed are also imposed. To show the validity and reliability of our process, we compare our regime with other current procedures by looking at various test problems. [ABSTRACT FROM AUTHOR]