Effective vague soft environment-based decision-making

The soft idea has a crucial impact on facing uncertainty, but extending soft, fuzzy soft, and vague soft settings is more comprehensive in expressing the problem ambiguity parameters than the soft set. Despite this advancement, the vague soft set falls short in addressing certain decision-making issues. This occurs when we have some external factors that can impact our final decision. These external factors can be represented in the effective parameter set. So, the objective of the current article is to incorporate the new concept of effectiveness into the concept of vague sets. This approach leads the researchers to create a novel and expanded framework for effective decision-making, surpassing any previously introduced methods in applicability. The article also provides an exploration of the types, concepts, and operations of effective vague soft sets, each illustrated with examples. Furthermore, the study delves into the examination of properties like De Morgan's laws, distributive, commutative, absorption, and associative properties for those new sets. Moreover, the framework of effective vague soft sets is used to develop a decision-making methodology. This technique simplifies the process of determining whether a student meets the requirements for a particular level of education or if a patient has a specific disease, among other applications. Additionally, to clarify the proposed algorithm, a detailed case study representing how to classify students toward specializations is examined in detail. Using matrix processes in this example, in addition to $ Wolfram \; Mathematica^{\circledR} $, not only renders computations simpler and quicker but also results in more precise optimum effective decisions. In the end, a detailed comparison with existing techniques is performed and summed up in a chart to illustrate the difference between them and the present one.