Quality function deployment (QFD) is a focused methodology for carefully listening to the voice of the customer and then effectively responding to those needs or customer requirements, (CRs) and expectations through design requirements (DRs). In classical QFD, exact numbers are used to determine the priorities of the CRs and the position of the company among the competitors. However, vagueness and impreciseness are inevitable uncertainties in those kinds of human evaluations, which are generally realized by linguistic terms. In this paper, the uncertainty in design processes is captured by a relatively new extension of ordinary fuzzy sets, Pythagorean fuzzy sets (PFS), aiming at presenting a larger domain to experts for assigning a membership degree and a non-membership degree together with their hesitancy. We perform all the evaluation processes in the house of quality (HOQ) based on interval-valued PFS (IVPFS) and present some novel definitions for measuring and prioritizing CRs, DRs, and determining the position of the company among the competitors. We give an application of the proposed IVPF-HOQ model for solar photovoltaic technology development.