A. Håkansson et al. (Eds.): KES-AMSTA 2009, LNAI 5559, pp. 542–549, 2009. © Springer-Verlag Berlin Heidelberg 2009
Enterprise Financial Status Synthetic Evaluation Based
on Fuzzy Rough Set Theory
Ming-Chang Lee and Jui-Fang Chang
Department of Business Administration, National Kaohsiung University of Applied Sciences
Abstract. Enterprise financial status synthetic evaluation is an important issue. The weight of synthesis evaluation is determined by expert, lending to subjec-tivity and without considering the redundancy of attributes exists in traditional synthetic evaluation. Recently, an attempt of integration between the theories of fuzzy set and rough sets has resulted in providing a roughness measure for fuzzy sets. Therefore, in this study, we firstly define the attribute reduction based on rough set theory. Secondly, we create membership function of each attributes. Using membership function, we can easily create the judgment matrix. Thirdly, we discuss the weight of attribute and measure of information. Finally, the methods of the synthesis evaluation are present with an example.
Keywords: Enterprise financial status, fuzzy rough set theory, Synthetic evaluation.
1 Introduction
Enterprise financial status analysis is an important issue. A synthetic evaluation method is R。W, where R is called judgment matrix and W is called weight value. In ordering to simplify the calculation, a new approach of synthetic evaluation is discussed.
Recently, the theory of rough sets has emerged as another method for dealing with uncertainty using from inexact or incomplete information (Pawlak, 1991; Pawlak, 1982). Incorporating fuzziness and uncertainty into decision marking problems can generally generate promising alternatives (Yu, 1984), such as a fuzzy technique has been applied vague data in synthetic evaluation (Zimmerman, 1991). Theories of fuzzy sets (Zadeh, 1965) and rough sets (Pawlak, 1982: Pawlak, 1985) are generalizations of classical set theory for modeling vagueness and uncertainty. Therefore, in this re-search, we use fuzzy set theory to create membership function (Wei et al. 2003) for obtain judgment matrix. We use the definition of weigh of attributes on rough sets theory, and create the set of weight value.
2 Preliminaries
The basic concepts, notations and results of rough sets as well as their extensions are briefly reviewed.
Enterprise Financial Status Synthetic Evaluation 543
2.1 Attribute Reduction Algorithm Based on Rough Set Theory
Given an information system (a data set), S = {U, A, V, f}, where U and A are finite and nonempty sets called the universe, and the sets of attributes, respectively. In informa-tion system, there exists a funcinforma-tion, such that f: U×A V. A is the union of C and D, the intersection of C and D is empty. C is called as conditional attributes, and D is called as decision attributes. The information system is also called decision system, or knowledge system (Zhang and Wu, 2001).
Definition 1. Let P be attribute set and P
⊆
C
, with any P⊆
C
there is an associated equivalence relation INP (P).Definition 2. Let R be equivalence relation in U and X is subset of U, then X is called
positive domain in R. it write as PosR (X) and
PosR (X) = {
x U
∈
∣[u]R⊆
x
}.Definition 3. Let{U，A, V, f} be decision system, with A =C∩D =ψ and A = C∪D.
Where, C is the set of conditional attribute s and D is the set of decision attributes. If B
⊆
A
and IND (B, D) = IND (A, D) then B is called the minimum attributes set.Definition 4. Let{U，A, V, f} be decision system, with A = C∩D =ψ and A = C∪D.
Where, C is the set of conditional attributes and D is the set of decision attributes. If a
∈
A
, a is conditional attribute and IND (A- {a}) = IND(A), then a can be reduced from set of A.Definition 5. The interaction of all reduce sets (red (A)) in A is called the core, it write
as Core (A), we have Core (A) =∩ red (A).
2.2 Create Membership Function of Each Attributes
The membership function of a fuzzy set is a generalization of the indicator function in classical sets. In fuzzy logic, it represents the degree of truth as an extension of valua-tion. Degrees of truth are often confused with probabilities, although they are con-ceptually distinct, because fuzzy truth represents membership in vaguely defined sets, not likelihood of some event or condition. Membership functions were introduced by Zadeh in the first paper on fuzzy sets (1965). We use the threshold value (b), low bound (a), and upper bound (c) and create the triangular membership function.
Triangular membership function is:
0
( )
1
x
a
x
a
a
x
b
b
a
x
x
c
b
x
c
b
c
x
c
μ
≤
⎧
⎪
−
⎪
≤ ≤
⎪
−
=
⎨
−
⎪
≤ ≤
⎪
−
⎪
≥
⎩
(1)544 M.-C. Lee and J.-F. Chang
2.3 The Weight of Attributes Acquisition Method Based on Measure of Information
Given an information system, S = {U, A, V, f}, where U and A (A = C∪D) are finite and nonempty sets called the universe, and the sets of attributes, respectively. Let A be {a1, a2, …, am}.
Definition 6. The weight
w
iof ai, is:1
( )
(
{ })
( )
(
{ })
i i m j jI A
I A
a
w
mI A
I A
a
= ∑−
−
=
−
−
(2)Definition 7. Let U/ IND (p) be {X1, X2, …., Xn}. The measure information of p definite as
1
(
)
(
)
( )
(1
)
( )
( )
n i i icard X
card X
I p
card U
card U
= ∑=
−
2 2 11
1
[
(
)]
[
( )]
n i icard X
card U
∑== −
(3)Where Card (Xi) denotes the cardinality of Xi
2.4 Synthetic Evaluation
Firstly, we obtain the judgment matrix R by membership function. Second, use fuzzy operator M (• , +), we calculate the R.
B = W•R (4)
3 The Proposed of Evaluation Process Are
Step 1: Determine financial evaluation indexes.
In financial reporting analysis, it has fifty factors for enterprise failure or distress (Ahn et al., 2000; Hawley et al., 2000). In this study, we selected 12 financial indexes. The evaluation process based on rough set theory can only handle discrete data, so it need to transform the sign data into discrete data, the continuous data into discrete data. The simplest method is to establish a table with one-to-one correspondence between the sign data and the discrete numerical data. In this study, we used threshold value, and the continuous data transform into discrete data.
Step 2: Attribute Reduction Algorithm based on Rough Set Theory.
Using section 2.1, we calculate IND (C), IND(C-{r}), where r
∈
C. From the defini-tion 4, we can find the minimum attribute set.Enterprise Financial Status Synthetic Evaluation 549
Fourth, we use measure information to calculate the weight of attribute. Finally, we apply fuzzy operator M (•, +), to obtain the result of synthetic evaluation. Our future will find more effective method for weight generation..
References
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[2] Pawlak, A.: Rough Classification. International Journal of Man-Machine Studies 20, 469–483 (1984)
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Dordrecht (1991)
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[6] Yu, P.R.: Dissolution of Fuzziness for Better Decision Perspective and Techniques. Man-agement Sciences 20, 171–207 (1984)
[7] Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)
[8] Zhang, W.X., Wu, W.Z.: Rough sets Theory and methodology. The Press of Science (2001) [9] Zimmermann, H.J.: Fuzzy Set Theory and Its Applications, 2nd edn. Kluwer Academic
Publishers, Boston (1991)
[10] Ahn, B.S., Cho, S., Smkim, C.Y.: The integrated methodology of rough sets and artificial neural network for business failure prediction. Expert system with application 18(4), 65–74 (2000)
[11] Hawley, D.D., Johnson, J.D., Rsina, D.: Artificial Neural Network Systems: A Network tool for financial Decision Making. Financial Analysis Journal, 63–72 (Novem-ber/December 2000)
