The proposed multiple inputs and outputs (MIO) classification method designated as the FVM-index method integrates fuzzy set theory (FST), variable precision rough set (VPRS) theory, and a modified cluster validity index (MCVI) function, and is designed specifically to filter out the uncertainty and inaccuracy inherent in the surveyed MIO real-valued dataset; thereby improving the classification performance.

The results confirm that the proposed FVM-index method provides a good MIO classification performance even in the presence of inaccuracy and uncertainty. As a result, it provides a robust approach for the extraction of reliable decision-making rules.

The proposed FVM-index method could effectively applied to the real applications of augmented reality product design and data envelopment analysis.