Finding an internal optimum in the classification of management accounting information: The role of fuzzy sets

This article contributes to the fuzzy logic application literature in accounting by examining a key issue in the use of fuzzy logic: how to find an optimum number of classes to minimize the decision maker's cost. Two costs are assumed: (1) we assume fuzziness is costly and thus should be minimized and (2) we assume that adding categories is costly. In order to address the issue of finding the optimal number of classes, we define the objective function as being cost minimization. We seek to determine the costs and benefits of increasing the number of classifications and ask whether an internal optimum is identifiable and achievable. We assume, ceteris paribus, less fuzziness is preferable to more fuzziness, but fuzziness can only be reduced through the use of more categories whose creation is costly. More fuzziness is costly, but so is the creation of additional categories to alleviate the fuzziness. When we arrive at the optimal number of clusters that corresponds to a minimal total cost, that number may not be the same as the “natural” number of categories. It is, nonetheless, a useful and practical way of deciding on the number of classifications. The approach we employ in this study is not confined to a management accounting information environment. It can be applied to any information environment where measurable classifications exist.