Bipolar neutrosophic soft sets are powerful tools for modeling data under conditions of uncertainty and imprecision due to their rich parametric structure and the useful mathematical properties of the operations defined on them. In this paper, motivated by the limitations of existing decision‐making algorithms, we introduce a new numerical characteristic, the energy of a bipolar neutrosophic soft set defined using singular values, analogous to the graph energy and nuclear norm. Our goal is to develop an efficient decision‐making algorithm that successfully identifies the optimal alternative even in cases where other algorithms provide inaccurate or inconsistent results. Our research is motivated by the need for more reliable decision‐making methods in complex soft environments and the potential of the energy‐based approach to overcome the weaknesses of existing methods, which we demonstrate through a comparative analysis using concrete examples.

Modeling uncertainty and imprecision in real-world decision-making problems often requires structures that can simultaneously capture interval-valued, bipolar, and parametric information. In this paper, we introduce the concept of an interval-valued bipolar neutrosophic soft set (IVBNSS) as a hybrid structure that combines the expressive power of interval-valued bipolar neutrosophic sets with the parametric flexibility of soft sets. Inspired by graph energy and the nuclear norm, we introduce the notion of the energy of an IVBNSS, establish its fundamental boundedness properties, and develop a novel decision-making algorithm based on this concept. The proposed algorithm is illustrated through two case studies: a sensor selection problem in industrial automation, where the goal is to identify the optimal sensor based on multiple performance criteria, including response time, environmental resistance, accuracy, and sensitivity; and a benchmark engineering problem from the literature concerning the selection of bio-inspired thin-wall structures. A comparative analysis with existing decision-making algorithms in the interval-valued bipolar neutrosophic setting confirms the validity and advantages of the proposed approach.