A Novel Decision-Making Algorithm Based on Interval-Valued Bipolar Neutrosophic Soft Sets

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.