A Fuzzy Set Approach to Aggregating Internal Control Judgments

Abstract

Internal control evaluation traditionally has been an integral part of an audit to provide an opinion on an entity's financial statements. Essentially, internal control evaluation is used to determine the substantive testing necessary to render an opinion on the financial statements. With the passage of the Foreign Corrupt Practices Act (FCPA) and recent proposals of the SEC, internal control evaluation has gained new impetus. These events may lead to the independent auditor being required to provide an internal control opinion separate from a financial statement audit. Consequently, the auditor may be required to aggregate the evaluation of system parts into a statement as to the performance of the system or major subsystem as a whole in addition to the reports currently made to management on the adequacy of internal control. Although mathematical models for internal control evaluation have been proposed, these have failed to receive acceptance by auditors. As an alternative to these models, this paper proposes the use of a procedure for aggregating the evaluation of parts of an internal control system employing the linguistic values commonly in use by auditors such as “strong,” “weak,” and “adequate.” The linguistic model (1) uses the theory of fuzzy sets to aggregate these common linguistic values and (2) returns a linguistic aggregate evaluation of the control system under review. A cash receipts and shipping control system is used in a numerical illustration and future research directions are proposed.