Fuzzy logic in accounting and auditing

Corresponding Author: mohsen.imeni86@yahoo.com
http://dx.doi.org/10.22105/jfea.2020.246647.1002
E-ISSN: 2717-3453 | P-ISSN: 2783-1442
|
Abstract
1 | Introduction
Ambiguity and imprecision in human judgments are in many scientific disciplines. Accountants in
dealing with the issue of ambiguity and imprecision, they behave there is no ambiguity or it is a random
[1]. In recent years, fuzzy logic has gained wide acceptance in the field of accounting and business.
This acceptance is due to the ability to management in situations of ambiguity and lack of consistency
that does not exist within other approaches to dual value logic. In dual value logic, the proposition is
true or false. Also, accounting has ambiguous in many important respects [2]. The problem of
ambiguity and imprecision in accounting and auditing is related to the rules and accounting system
[3]. Ro [4] argues that the concept of materiality is not essentially two-dimensional, such as black or
white and good or bad, but that there are degrees of materiality that are overlooked in accounting.
However, ambiguity and imprecision is different from being random. Randomness refers to the
uncertainty about the occurrence or non-occurrence of an event and is expressed in the form of
probabilities. While, ambiguity and imprecision are related to the inaccuracy and lack of clarity in the
Journal of Fuzzy Extension and Applications
www.journal-fea.com
J. Fuzzy. Ext. Appl. Vol. 1, No. 1 (2020) 66–72.
Paper Type: Review Paper
Fuzzy Logic in Accounting and Auditing
Mohsen Imeni *
Department of Accounting, Ayandegan Institute of Higher Education, Tonekabon, Iran; mohsen.imeni86@yahoo.com.
Citation:
Imeni, M. (2020). Fuzzy logic in accounting and auditing. Journal of fuzzy extension and application, 1
(1), 66-72.
Accept: 02/03/2020
Revised: 01/02/2020
Reviewed: 11/12/2019
Received: 04/11/2019
Many areas of accounting have highly ambiguous due to undefined and inaccurate terms. Many ambiguities are generated
by the human mind. In the field of accounting, these ambiguities lead to the creation of uncertain information. Many of
the targets and concepts of accounting with binary classification are not consistent. Similarly, the discussion of the
materiality or reliability of accounting is not a two-part concept. Because there are degrees of materiality or reliability.
Therefore, these ambiguities lead to the presentation information that is not suitable for decision making. Lack of
attention to the issue of ambiguity in management accounting techniques, auditing procedures, and financial reporting
may lead to a reduced role of accounting information in decision-making processes. Because information plays an
important role in economic decision-making, and no doubt, the quality of their, including accuracy in providing it to a
wide range of users, can be useful for decision-making. One of the features of the fuzzy set is that it reduces the need
for accurate data in decision making. Hence this information can be useful for users.
Keywords: Fuzzy logic, Accounting, Auditing, Ambiguity.
Licensee Journal
of Fuzzy Extension and
Applications. This
article is an open access
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Attribution (CC BY)
license
(http://creativecommons.
org/licenses/by/4.0).

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Fuzzy
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and
auditing
definition of words, the occurrence of events and judgments [2]. Zariffard [1] argues that neglect of
ambiguity and imprecision in decision models can limit the usability of accounting models due to reduced
usefulness and predictive power. Therefore, it is important attention to ambiguity. The purpose of this
study is to introduce fuzzy logic and also is examine its major applications in accounting and auditing. The
importance of this research is that considering that information is the main component of any decision
making today, it has economic value.
2| Literature Review
2.1| Fuzzy Set Theory
In 1965, Zadeh discussed the existence of ambiguity and fuzziness in many human systems. According to
Zadeh [5], the need to be very careful in decision analysis causes the analyst to ignore some related issues
and consider only a part of this relationship with the real world. Fuzzy thinking followed the objection to
Aristotelian logic about the distance between logic and reality. Aristotelian logic forms the basis of classical
mathematics. This logic assumes that the world is black and white or two values one or 0. Zadeh [6]
proposed the theory of fuzzy sets as a method for modeling in ambiguity and uncertainty. Sets can be
divided into finite sets and fuzzy sets. In finite set, is there a member in a set or not? That is, it has no more
than two values, one or 0. But not in the fuzzy set.
In fact, Aristotelian logic sacrifices accuracy for ease. But the real phenomena are not just black or white,
they are somewhat gray. In other words, real phenomena are always fuzzy, that is, ambiguity and
imprecision [7]. Fuzzy set theory reduces the possibility of making personal judgments by expressing
qualitative and subjective information, and leads to more rational decisions [8].
2.2| Definition of Fuzzy Set
Let U be a classical (or ordinary) set of objects, called the universe, whose generic elements are denoted by
x. That is, U={x}. A fuzzy set A in U is characterized by a membership function µA(X) which associates
with each element in U a real number in the interval (0–1) [9]. The fuzzy set, A, is usually denoted by the
set of pairs [10].
For an ordinary set, A
When U is a finite set {x1,…, xn}, the fuzzy set on U may also be represented as
When U is an infinite set, the fuzzy set maybe represented as
 
 
 
A
A x,μ (X) ,x U . (1)
 


  



A
1, x A
μ (X) .
0, x A (2)

 
n
i A i
i 1
A x / μ (x ). (3)
  A
A (x / μ (x))dx. (4)

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2.3| Basic Concepts of Fuzzy Set
The complement, support, a-cut, convexity, normality and cardinality of a fuzzy set are presented in the
following sections [9].
Complement of a fuzzy set. The definition of the complement of fuzzy set A is defined as
Support of a fuzzy set. Those elements which have nonzero membership grades are considered as
support of that fuzzy set
a-Cut of a fuzzy set. a-Cut of a fuzzy set is an ordinary set whose elements belong to fuzzy set A, at least
to the degree of a
It is a more general case of the support of a fuzzy set. If α=0 then Aα=S(A).
Convexity of a fuzzy set. A fuzzy set is convex if
X1 and X2ϵU also λϵ (0–1).
Normality of a fuzzy set. A fuzzy set A is normal only if there are one or more x́ values such that
 
A
μ ( X ) 1.
Cardinality of a fuzzy set. The cardinality of fuzzy set A evaluates the proportion of elements of U
having the property A. When U is finite, it is defined as
For infinite U, the cardinality is defined as
For more details, enormous materials can be found in the literature about fuzzy set theory.
  
A A
μ (X) 1 μ (X) x U. (5)
 
  
A
S(A) x U μ (X) 0 . (6)
 
  
A
Aα x U μ (X) α . (7)
 
A 1 2 A 1 A 2
( X 1 )X min( (X ), (X )).
        (8)
A
A (x), x U.
  
 (9)
A
x
A (x)dx.
 
 (10)

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Fig. 1. Triangular and trapezoidal fuzzy numbers.
Fig. 1 defines a fuzzy and triangular number D as follows [8]:
D= {1, d, u} where 1, d, and u as the lower spread, the middle spread, and the upper spread. In this case
the membership function µ(D) X it is defined as follows:
If the climax of the triangular number D is not unique; the fuzzy number is known as a trapezoid.
3| Fuzzy Set Theory and Accounting and Auditing
For a variety of reasons, fuzzy set theory can be of great value to accountants in practice. First, fuzzy set
theory provides a mathematical framework which fuzzy concepts of accounting can be examined on a
regular basis, for instance, materiality errors. Therefore, using fuzzy set theory, accountants will be able to
apply fuzzy set theory in accounting. As a result, they no longer have to ignore ambiguities in accounting
matters. Also, they will be able to deal with it like random events using probability theory. Accountants
with ignoring the ambiguity cause inaccuracies in accounting matters [1].
In addition, unlike ordinary set theory, fuzzy set theory abandons the rule of excluding the mean and logic
of two values. As a result, there will be no need for a binary classification of accounting objectives that are
generally unrealistic and artificial. Many of the targets and concepts of accounting with binary classification
are not consistent. For example, neutrality is not a debate of being black and white. There are different
degrees of neutrality, or in the discussion of deviation analysis, controllable deviations or uncontrollable
deviations are kinds of unrealistic integration. Similarly, the discussion of the materiality or reliability of
accounting is not a two-part concept. Because there are degrees of materiality or reliability. One of the
features of the fuzzy set is that it reduces the need for accurate data in decision making.
Recently, this theory has been used to solve accounting problems. These studies can be divided into two
groups. The first group deals with audit problems such as internal control, audit sampling, and judgment
of materiality. The second group deals with management accounting issues and problems such as capital
budgeting, cost deviations, and strategic planning. Some applications of fuzzy sets in the audit are
summarized as:
Friedlob and Schleifer [11] argue that auditors usually express risk in the form of probabilities, examining
different types of audit uncertainty. Finally, they introduced the fuzzy logic-based method as a new method
of examining audit uncertainty.
D
0; x 1
(x 1) / (d 1); 1 x d
(x) .
(u x) / (u d); d x u
0; x u


    

  
   

 

(11)

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Pathak et al. [12] indicates that in order to reduce the costs of detecting fraud in the claims made in their
insurance companies, they designed fuzzy expert systems to evaluate and express the elements related
to fraud in resolving insurance claims. This system is useful for deciding whether settled insurance claims
are actual or whether there is evidence of fraud.
Comunale and Sexton [13] introduced a fuzzy logic approach to assess the importance of presenting
financial statements. A fuzzy logic-based approach to significance assessment can provide an expert
system for significance assessment compared to traditional approaches, which are based on binary
valuation; In such a way that the importance of presenting financial statements correctly can be shown
between zero and one, and on the other hand, quality criteria can be considered in evaluating the
importance.
Dereli et al. [14] using a fuzzy mathematical programming model, they proposed a strategic algorithm
to shape the quality audit team. In this study, the fuzzy ranking method has been used to determine the
adequacy of the skills and expertise of each auditor in team auditing.
De Korvin et al. [15] examined the risk of internal controls in computer accounting information systems
through a fuzzy set approach. The model presented in this research is used through a risk analysis matrix
in a company active in the chemical industry. This model is useful in evaluating and applying new control
procedures to increase the security of the company's information systems.
Also, some applications of fuzzy sets in the management accounting [16] and [17] are summarized as:
Oderanti and De Wilde [18] used the concepts of fuzzy logic and game theory to model the strategic
decision-making process by business organizations based on uncertain information. In this study,
competition between business organizations is considered as a game and organizations are its actors.
They model their decisions through strategic actions based on uncertain information.
Cassia et al. [19] examined the development of corporate management accounting systems in providing
information to facilitate the strategic decision-making process and its relationship to the shape,
development and size of companies through the general mode of fuzzy logic. The results of the study
indicate that 511 Italian companies are always advances in the evolution of corporate management
accounting system do not meet. In other words, you can find a large number of companies with a simple
organizational structure but with an advanced management accounting system.
Rangone [20] according to strategic management accounting, strategic cost management and non-
financial performance metrics are introduced as strategies to overcome the limitations of traditional
management accounting systems. He provided an analytical framework using fuzzy logic to establish a
relationship between the effectiveness of the organization, key indicators of success and performance
measurement.
Nagasawa [21] using fuzzy set theory, a model for value engineering and cost management was designed.
The existence of different tools and solutions for value engineering, their prioritization as well as the
related ambiguities related to them, have been expressed as reasons for the need to address fuzzy set
theory in value engineering.
Nachtmann and Needy [22] through the application of fuzzy logic concepts in costing, they developed
an activity-based costing system. This study demonstrates the benefits of a fuzzy activity based costing
system and the stages of development and implementation in a pharmaceutical company.
Nachtmann and Needy [23] have introduced and compared methods of overcoming ambiguity and
uncertainty over the input data of the activity-based costing system from the perspective of cost-benefit
analysis. According to the comparison, the use of fuzzy method in activity-based costing to consider the

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conditions of ambiguity and uncertainty is more appropriate than the methods based on each of the
standard models, distance and Monte Carlo with normal input variables.
Yuan [24] Using a fuzzy expert system, designed a model to analyze costs, activity volume and profit in
ambiguous conditions by management. In this new system, unlike the traditional mode, which uses the
break-even point and assumes a state of confidence, the information of experts and the concepts of fuzzy
sets are used to overcome inaccuracies and ambiguities.
4| Conclusion
The purpose of this paper is to introduce fuzzy set theory in accounting and examine its relationship as a
way to solve accounting problems in conditions of ambiguity. Fuzzy theory, unlike traditional quantitative
methods, provides a mathematical framework for inaccurate phenomena in human systems and decision
making that can be applied on a regular basis. This theory does not require accurate measurements. As a
result, fuzzy theory can be invaluable to accountants, especially in times of ambiguity and when care cannot
be taken. Therefore, due to the ambiguities that exist in accounting and auditing issues; accountants and
auditors should not hesitate to use fuzzy set theory. One of the features of the fuzzy set is that it reduces
the need for accurate data in decision making. Because today, information plays an important role in
economic decision-making, and no doubt [25], the quality of their, including accuracy in providing it to a
wide range of users, can be useful for decision-making [26].
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