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.accounting: auditing, information system: management, mathematics: sets

Combining Individual Judgments

“…Language designates categories to which things may not belong absolutely, but only to some degree, that is, it designates fuzzy sets. Fuzzy set theory (Kaufmann, 1975) has been proposed as the mathematical basis for aggregation of verbally expressed judgments (Cooley & Hicks, 1983).…”

“…Cooley and Hicks (1983) proposed evaluating the strength of control over accounts in a business firm by aggregation of verbal judgments of all the component parts of the system. They suggest several ways to do this.…”

Dealing with Fuzziness in Cost-Volume-Profit Analysis

“…The methodology is also appropriate for other accounting problems, especially in cases where human judgement is essential. In fact, Fuzzy Set Theory has been applied to internal control judgements (Cooley and Hicks, 1983); materiality judgements (Kelley, 1984); determining the significance of cost variances for investigation (Zebda, 1984); etc. As the theory has provided a mathematical framework wherein imprecise phenomena in decision making can be treated systematically, its application in managerial accounting are numerous, and may include linear programming in product mix decisions, capital budgeting, cost/benefit analysis etc.…”

Assessing risks due to threats to internal control in a computer‐based accounting information system: a pragmatic approach based on fuzzy set theory

“…By and large, fuzzy set methodology has been applied to engineering and computer science problems. Cooley and Hicks (1983), Zebda (1984), Kauffman (1984), Kelly (1984), and Lin (1984) were amongst the earliest to utilize fuzzy set methodology in an accounting context. In recent years, an increasing number of accounting researchers have applied the methodology of fuzzy sets in developing decision models and suggesting improvements in the accounting decision process (e.g.…”