The q-rung orthopair fuzzy set is a powerful tool for depicting fuzziness and uncertainty. This paper proposes a new tool, called interval-valued bipolar q-rung orthopair fuzzy sets to deal with vagueness and impreciseness encountered in real-world scenes. These proposed sets take full advantage of the q-rung orthopair fuzzy set and comprehensively reflect quantitative and qualitative assessments. Moreover, we describe some prevailing similarity measures in the surroundings of the interval-valued bipolar q-rung orthopair fuzzy set. The prominent advantage of the proposed similarity measures is that the interrelationship between interval-valued bipolar q-rung orthopair fuzzy numbers can be considered. Further, we establish a multicriteria decision-making algorithm based on the proposed similarity measures to determine the best supplier selection in supply chain management and analyze its acquired consequences. We examine the merits and limitations of the new approaches by comparing them with some existing similarity measures based on fuzzy extensions. Some graphical interpretations are also discussed to demonstrate the reliability and effectiveness of the explored measures.