How arithmetically fuzzy are we? An empirical comparison of human imprecise calculation and fuzzy arithmetic

Abstract

This paper proposes an experimental comparison between human imprecise calculation and fuzzy arithmetic: an empirical study has been conducted to collect real intervals resulting from products and additions with imprecise operands from participants. Fuzzy intervals are elicited from these data and fuzzy arithmetic is applied to the collected imprecise operands. Comparisons show that the fuzzy product and addition differ from the way human beings perform these operations. Moreover, they show that the participants, rather than taking into account the imprecisions in the calculations, realise exact calculation and in the end approximate the exact result.