To ensure the traceability of testing and diagnostic equipment it is necessary to provide a chain of comparisons connecting the equipment with primary standards of the SI units based on fundamental physical constants. The values of the constants are regularly determined by an adjustment procedure which requires consistency of input data and an assumed statistical model. In this paper, it is proposed to apply the developed interval fusion with preference aggregation (IF&PA) method for combining data and determining a consensus value of a fundamental constant. Due to its high robustness, accuracy and reliability confirmed by the numerical experimental results, the IF&PA does not require a consistency check and works well without using any statistical assumptions. Usage of the IF&PA is demonstrated by example of processing the simulated interval data and real values of the Planck constant used in the adjustment in 2006 and 2017. The outcome comparison with the estimates obtained by other methods, including the procedures based on Birge ratio, modified Birge ratio, random effects model and fixed effects model, is carried out.