Measurement, imprecision and uncertainty in financial accounting: Can double entry be understood with fuzzy numbers?

The concepts of measurement and information are central to the accountancy model of the representation of business. The classical financial accounting remains based on elementary arithmetic (groups of differences constructed on the commutative and cancelling monoid of the real positives supplied by addition), and it is not conceived to take into account the imprecision which can vitiate the information with which it is dealing. The underlying measurement is purely quantitative and precise at the same time. In the face of the emergence of a certain number of dysfunctions, it is possible to extend the system of financial accountability in double entry to a treatment of a quantitative report which is imprecise, indeed, subjective. The fuzzy-sets theory creates a general framework in theory in order to explore the principle of the limits of such an extension. However, this step, apparently direct, needs a profound re-examination of its own semantic with the accounting context of measuring the assets and the profit or loss.