In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.
<abstract><p>Simulation software replicates the behavior of real electrical equipment using mathematical models. This is efficient not only in regard to time savings but also in terms of investment. It, at large scale for instance airplane pilots, chemical or nuclear plant operators, etc., provides valuable experiential learning without the risk of a catastrophic outcome. But the selection of a circuit simulator with effective simulation accuracy poses significant challenges for today's decision-makers because of uncertainty and ambiguity. Thus, better judgments with increased productivity and accuracy are crucial. For this, we developed a complex probabilistic hesitant fuzzy soft set (CPHFSS) to capture ambiguity and uncertain information with higher accuracy in application scenarios. In this manuscript, the novel concept of CPHFSS is explored and its fundamental laws are discussed. Additionally, we investigated several algebraic aspects of CPHFSS, including union, intersections, soft max-AND, and soft min-OR operators, and we provided numerical examples to illustrate these key qualities. The three decision-making strategies are also constructed using the investigated idea of CPHFSS. Furthermore, numerical examples related to bridges and circuit simulation are provided in order to assess the validity and efficacy of the proposed methodologies. The graphical expressions of the acquired results are also explored. Finally, we conclude the whole work.</p></abstract>
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