OWA rough set model for forecasting the revenues growth rate of the electronic industry

Expert Systems with Applications 37 (2010) 610–617

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OWA rough set model for forecasting the revenues growth rate of the electronic industry Jing-Wei Liu a, Ching-Hsue Cheng a,*, Yao-Hsien Chen a,b, Tai-Liang Chen c a

Department of Information Management, National Yunlin University of Science and Technology, 123, Section 3, University Road, Touliu, Yunlin 640, Taiwan, ROC Department of Information Management, WuFeng Institute of Technology, 117, Section 2, Jianguo Road, Minsyong, Chiayi 621, Taiwan, ROC c Department of Information Management and Communication, Wenzao Ursuline College of Languages, 900, Min-Tzu 1st Road, Sanming District, Kaohsiung 807 Taiwan, ROC b

a r t i c l e

i n f o

Keywords: Attribute selection OWA (ordered weighted averaging) Rough set theory Revenue growth rate Electronic industry

a b s t r a c t Business operation performance is related to corporation profitability and directly affects the choices of investment in the stock market. This paper proposes a hybrid method, which combines the ordered weighted averaging (OWA) operator and rough set theory after an attribute selection procedure to deal with multi-attribute forecasting problems with respect to revenue growth rate of the electronic industry. In the attribute selection step, four most-important attributes within 12 attributes collected from related literature are determined via five attribute selection methods as the input of the following procedure of the proposed method. The OWA operator can adjust the weight of an attribute based on the situation of a decision-maker and aggregate different attribute values into a single aggregated value of each instance, and then the single aggregated values are utilized to generate classification rules by rough set for forecasting operation performance. To verify the proposed method, this research collects the financial data of 629 electronic firms for public companies listed in the TSE (Taiwan Stock Exchange) and OTC (Over-the-Counter) market in 2004 and 2005 to forecast the revenue growth rate. The results show that the proposed method outperforms the listing methods. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Besides the financial index, the business operation performance of listed companies is the most important factor of investment, which deeply affects the long-term portfolio of investors in the stock market. Investors will select some adequate performance indices to evaluate the development capability of companies as investment targets. Due to advances in electronic techniques and international growth of economics, the manufacturers in the electronic industry have continuously designed and produced more and more advanced electronic components and products. Furthermore, people have had more economic ability in pursuit of a comfortable life via consuming the latest advanced electronic products, such as computer, communication, and common consumer electric appliances that are so-called 3C products for short. Accommodating the global trend of development in the electronic industry and supported by governments under Regulations of Encouragement, that makes the electronic industry substantially grown up in the last decades in Taiwan. Compared with other traditional

* Corresponding author. Tel.: +886 5 534 2601x5312; fax: +886 5 531 2077. E-mail addresses: [email protected] (J.-W. Liu), chcheng@yuntech. edu.tw (C.-H. Cheng), [email protected] (Y.-H. Chen), [email protected]. edu.tw (T.-L. Chen). 0957-4174/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2009.06.020

industries in Taiwan, the proportion of export and gross national product in the electronic industry have been raising ceaselessly. Concurrently, Taiwan has become one of the major electronic products producers, and the electronic industries have had the greatest number of listed companies in the Taiwan stock market. Trade in the electronic section has become one of the most important choices of investment in the Taiwan stock market. Moreover, the stock price fluctuation of the electronic section often essentially affects the whole price index and even the cycle of the stock market in Taiwan. For these reasons, accurately forecasting the operation performances of those electronic companies will be deeply related with the investment benefits for stock investors. For performance analysis, it is the major step to select a set of proper input and output attributes as measure attributes, because more adequate input and output attributes identified will bring more suitable results of evaluation in the respective condition (Charnes, Cooper, & Rhodes, 1984). Thore, Philips, Ruefli, and Yue (1996) adopted six input attributes and three output attributes to rank the efficiency of US computer companies. Reynolds and Biel (2007) used seven attributes as input and four attributes as output to measure productivity index. Both researches introduced revenue as a major output indicator to measure the business operation performance of industrial comparators. This paper employs 12 attributes as input of the developed forecasting model and revenue

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growth rate (RGR) as output attribute, which synthesizes related the literature above and the opinions of investment consultants of the stock market in Taiwan. How to extract useful information from vast amounts of data has proven extremely challenging. Often, traditional data analysis tools and techniques cannot be useful because of the massive size or the imprecise meaning of a data set. Data-mining is a technology that blends traditional data analysis methods with sophisticated algorithms for processing large volumes of data (Tan, Steinbach, & Kumar, 2006). Moreover, intelligent technologies utilize fuzzy concept and processing models for resolving imprecise meaning of data. Soft computing is a new paradigm that seamlessly integrates different, seemingly unrelated, intelligent technologies in various permutations and combinations to exploit their strengths (Kumar & Ravi, 2007; Kurt, Ture, & Kurum, 2008). Zadeh (1994) stated that soft computing views the human mind as a role model and builds upon a mathematical formalization of the cognitive processes that those humans take for granted. Further, the resulting hybrid architectures tend to minimize the disadvantages of the individual technologies while maximizing their advantages. Increasingly, the soft computing method is coming into popular use as a tool to measure the relative operation performance of industrial corporations. This paper proposes an OWA rough set model to show that the soft computing method could be further extended to improve the forecasting of the operation performance in the Taiwan electronic industry. However, previous related researches have never made orderings for attributes based on their importance and applied the aggregated value of these attributes for decisions. Hence, this research proposes a hybrid model with three processes to enhance forecasting function: (1) rank attributes by the OWA method; (2) aggregate attribute values into one single value; and (3) classify the aggregated value by rough set theory to generate classification rules. Accordingly, this study proposes a new method for forecasting the RGR of corporations, which combines OWA and rough set classifier to improve classification methods and provides some suggestions for investing in stocks. The rest of this paper is organized as follows. Section 2 is literature reviews. Section 3 details the proposed method. In Section 4, an experiment is conducted to evaluate the proposed method and compare classification accuracy with other existing methods. In Section 5, conclusions are given.

In this section, we describe briefly about selecting attributes methods, OWA, and rough set theory. 2.1. Selecting attributes methods (1) Chi-Squared (Anderson, 1996; Huang, Yang, & Chuang, 2008) This method measures the importance of a feature by computing the value of the X2-statistic with respect to the class. (2) Information Gain (Huang et al., 2008) This method measures the importance of a feature by measuring the information gain with the respect to the class. Information gain is given by:

InfoGain ¼ HðXÞ  HðYjXÞ

ð1Þ

where X and Y are features and pðYÞ X

log2 ðpðyÞÞ

ð2Þ

y2Y

HðYjXÞ ¼ 

GainRðAÞ ¼

gainðAÞ entropyðAÞ

ð4Þ

Its gain part tries to maximize the difference of entropy before and after the split. To prevent excessive bias towards multiple small splits, the gain is normalized with the attribute’s entropy. (4) Symmetrical Uncertainty (Huang et al., 2008; Karnik, Mendel, & Liang, 1999) Information gain is based in favor of features with more values. Furthermore, the values have to be normalized to ensure they are comparable and have the same effect. Therefore, we choose symmetrical uncertainty (Chouchoulas & Shen, 2001), defined as follows:

SUðX; YÞ ¼ 2



IGðXjYÞ HðXÞ þ HðYÞ

 ð5Þ

Symmetrical uncertainty (5) compensates for information gain’s bias toward features with more values and restricts its values to the range [0, 1], where the value 1 means that the knowledge of discriminator values induces the value of the other, while 0 suggests that attributes X and Y are independent. (5) ReliefF (Kononenko, Šimec, & Robnik-Šikonja, 1997; RobnikSikonja & Kononenko, 2003)Relief-F is based on the estimation of relevance of features according to their ability to distinguish between instances near to each other, situated in the same or in different classes. Specifically, it tries to find a good estimate of the following probability to assign the weight for each feature f:

wf ¼ Pðdifferent value of f j different classÞ  Pðdifferent value of f j same classÞ

ð6Þ

This approach has shown good performance in various domains (Robnik-Sikonja & Kononenko, 2003). 2.2. OWA operator

2. Related works

HðYÞ ¼

Both the information gain and the X2-statistic are biased in favor of features with higher dispersion. (3) Gain Ratio (Marko, David, & Igor, 2003) In the C4.5 decision tree algorithm, a splitting criterion known as gain ratio is used to determine the goodness of a split. It is an entropy-based measure defined as

pðXÞ pðYjXÞ X X x2X

y2Y

log2 ðpðyjXÞÞ

ð3Þ

Ordered weighted averaging (OWA) operator was proposed by Yager (1988), which was used to deal with multi-decision-making problems and aggregate information into a single integrated value. Many related studies were published in last two decades. The aims of these studies were trying to improve some drawbacks of Yager’s OWA operator. For example, Fuller and Majlender (2001) used the Lagrange multipliers to improve Yager’s OWA operator. OWA operators have been used in a wide range of applications, such as neural network database systems (Yager, 1987, 1991b, 1995), fuzzy logic controllers (Yager, 1991a), group decision-making problems with linguistic assessments (Herrera, Herrera-Viedma, & Verdegay, 1996), and data-mining (Torra, 2004; Yager, 1992, 1993; Yager & Dimitar, 1994). To determine the associated weights of the OWA operator is the most important task. Many methods have been developed to compute the associated weights. The research describes two of these methods, which play the important roles of the research as follows. 2.2.1. Yager’s OWA Yager had proposed the OWA operator in 1988 (Yager, 1988), and he suggested that the associated weights of the OWA operator

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could be computed by using linguistic quantifiers. The OWA operator is obtained by the following steps: (1) Reorder the input arguments in descending order. (2) Determine the weights that associate with the OWA operator by using a proper method. (3) Utilize OWA weights to aggregate these reordered arguments. An OWA operator of dimension n is a mapping, OWA: Rn ? R, that has an associated n vector w = (w1, w2, . . . , wn)T such that P wj 2 [0, 1] and nj¼1 wi ¼ 1, such that

OWAw ða1; a2 ; . . . ; an Þ ¼

n X

wi bj ;

ð7Þ

j¼1

where bj is the jth largest element of the collection of the aggregated objects (a1, a2, . . . , an). Yager further introduced two characterizing measures, called orness measure and dispersion measure. Both of them are associated with the weighting vector w of an OWA operator, where the orness measure of the aggregation is defined as

ornessðwÞ ¼

n 1 X ðn  iÞwi n  1 j¼1

ð8Þ

where the orness(w) = a is a situation parameter that lies in unit interval [0, 1] and characterizes the degree to which the aggregation is like an or operation. The second one, the dispersion measure of the aggregation, is defined as

dispðwÞ ¼ 

n X

wi ln wi

ð9Þ

j¼1

which measures the degree to which w takes into account the information in the arguments during the aggregation. O’Hagan (1987, 1988) used orness measure and dispersion measure to develop a new method to generate the OWA weight that has a predefined degree of orness and maximizes the entropy. This procedure is based on the following constrained optimization problem:

Maximize :

n X

wi ln wi

ð10Þ

j¼1

Subject to :

n 1 X ðn  iÞwi ¼ a; n  1 i¼1 n X

wi ¼ 1;

06a61

0 6 wi 6 1; i ¼ 1; 2; . . . ; n

ð11Þ

i¼1

2.2.2. Fuller and Majlender’s OWA Fuller and Majlender (2001) proposed a new method by using Lagrange multipliers to improve the problem in Eq. (5) and got the following: (1) If n = 2, then w1 = a, w2 = 1  a. (2) If a = 0 or a = 1, then the associated weighting vectors are uniquely defined as w = (0, 0, . . . , 1)T and w = (1, 0, . . . , 0)T, respectively, with the value of dispersion zero. (3) If n P 3 and 0 < a < 1, then

wj ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi j1 wn1 1 wn

n1

ð12Þ

ððn  1Þa  nÞw1 þ 1 wn ¼ ðn  1Þa þ 1  nw1 n

ð13Þ n1

w1 ¼ ½ðn  1Þa þ 1  nw1  ¼ ððn  1ÞaÞ

½ððn  1Þa  nÞw1 þ 1 ð14Þ

where wj is weight vector, n is the number of attributes, and a is the situation parameter. The optimal OWA-associated weights are obtained by solving Eqs. (6)–(8). After obtaining the best a value, the principal components scores and OWA-associated weights can aggregate into a single integrated value by the following equation:

ak ¼ w1 x1k þ w2 x2k þ    þ wi xik þ wn xnk

ð15Þ

where wi is ith input of the OWA-associated weight and xik is ith attribute value of kth record. 2.3. Rough set theory The rough set theory was proposed by Pawlak (2002), which has been successfully applied in a great many domains, such as controlling industrial processes (Chan, 1998; Jackson, Pawlak, & LeClair, 1998), diagnosis analysis (Mitra, Mitra, & Pal, 2001; Tay & Shen, 2003), image processing (Pal & Mitra, 2002), market decision-making (Shen & Loh, 2004), environmental problem detection (Che‘vre, Gagne’, Gagnon, & Blaise, 2003), data-mining (Chen, Chang, & Chen, 2003), and web and text categorization (Chouchoulas & Shen, 2001; Jensen & Shen, 2004). The basic concept of the RST is the notion of approximation space, which is an ordered pair A = (U, R), where U: nonempty set of objects, called universe, and R: equivalence relation on U, called indiscernibility relation. If x, y 2 U and xRy then x and y are indistinguishable in A. e where An approximation space can be noted by A ¼ ðU; RÞ, e ¼ U=R. A definable set in A is any finite union of elementary sets R in A. For x 2 U, let [x]R denote the equivalence class of R, containing x. For each x # U, x is characterized in A by a pair of sets – its lower and upper approximation in A, defined respectively as:

Alow ðXÞ ¼ fx 2 Uj½xR # Xg

ð16Þ

Aupp ðXÞ ¼ fx 2 Uj½xR \ X – /g

ð17Þ

3. The proposed method The OWA operator is an important tool to cope with multi-attribute data, and it is different from the classical weighted average in that given weight method; further, OWA considers not only attributes ordering but also decision-makers’ preferences (situation). OWA provides a new method for aggregating multiple inputs that lie between the max and min operators (Ahn, 2006); it also provides a unified framework for decision-making under uncertainty, where different decision criteria, such as maximax (optimistic), maximin (pessimistic), equally likely (Laplace), and Hurwicz criteria, are characterized by different OWA operator weights (Wang, Luo, & Hua, 2007). Rough sets, proposed by Pawlak (2002), are an extension of the set theory for the study of information systems characterized by insufficient and imperfect data, and it has been successfully applied in AI, knowledge discovery in database, and data-mining (DM). There are at least two methods to study rough sets. One is the constructive method, and the other is the axiomatic approach (Shen & Loh, 2004). The axiomatic approach is different from the constructive approach; the axiomatic approach aims to investigate the mathematical characters of rough sets, which may help to develop methods for applications. Hence, the rough set has two advantages: (1) attributes reduction of a singledimension data set; and (2) attributes reduction of a hybrid-structural data set. In order to improve the accuracy of forecasting results, this study employs the rough sets method to generate rules from aggregated values by OWA. From the OWA and rough set advantages

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Fig. 1. The process of proposed model.

mentioned above, this paper proposes a hybrid model (see in Fig. 1), which combines OWA and rough set to enhance the classification method and can achieve three advantages, as follows: (1) Decrease the numbers of attributes by attribute selection. (2) Reduce data dimension via the OWA operator. (3) From advantages (1) and (2), use the rough set to extract classification rules, which have fewer rules. For easy understanding, the proposed algorithm is step-by-step, introduced in the following:

Step 1: Select attribute In this step, we use five attribute selection methods (ChiSquared (Anderson, 1996; Huang et al., 2008), Gain Ratio (Huang et al., 2008), Information Gain (Marko et al., 2003), ReliefF (Huang et al., 2008; Karnik et al., 1999), and Symmetrical Uncertainty (Kononenko et al., 1997; Robnik-Sikonja & Kononenko, 2003)) to evaluate the importance of attributes. Step 2: Calculate OWA weights From Eqs. (6)–(8), we can get the OWA weights, such as Table 1 (attribute numbers = 4, and a = [0.5, 1.0]). Step 3: Calculate the aggregated values by OWA operator When the attributes ordering and numbers of attributes are known, the OWA operator could fuse attribute weight and attribute value to obtain the aggregated values; i.e., we multiply the attribute as Eq. (9). Step 4: Classify OWA aggregated values by rough set This step takes the aggregated values as input variables and the revenue growth rate as output class. The dataset is partitioned into training data, 67%, and testing datasets 33%. The training dataset is utilized for training to generate classification rules by the LEM2 algorithm (set coverage = 0.9) (Grzymala-Busse & Stefanowski, 1997). The remainder 33% data are testing data to verify the performance of the proposed method. We utilize the OWA operator to calculate the aggregated values and use the rough set to product the classification rules. Then, compute the accuracy rate by the classification rules. Step 5: Build OWA rough set model In order to get the optimal OWA rough set model (i.e., adapting optimal a parameter), the computation is repeated from Step 2 to Step 4 for a = 0.5–1.0, Step = 0.1. Step 6: Verification and comparison In order to cross-verify, the experiment is repeated 10 times with different sampling data (67% training dataset and 33% testing dataset). In comparison, this step uses four different methods to compare with the proposed method. The four methods are: (a) rough set theory (Jackson et al., 1998), (b) decision tree C4.5 (Quinlan, 1993), (c) Bayesian networks (Pearl, 1988), and (d) multilayer perceptron (Zhao, Xu, Yue, Liebich, & Zhang, 1998).

Table 1 The results of selecting attributes (the same orderings in first 4 attributes) in 2004 year. Chi-Squared

Gain Ratio

Information Gain

ReliefF

Symmetrical Uncertainty

Operating profit 488.2104 Gross profit 230.6929 Net operating revenue 145.2658 Gross sales 136.8393 Cost of goods sold 120.2838 Employee numbers 112.1195 Fixed asset 97.8788 Total depreciation 41.641 Total non-operating income 34.0894 Total labor 33.1478 Total non-operating expenses 0 Operating expense 0

Operating profit 0.071 Net operating revenue 0.0354 Gross profit 0.0351 Gross sales 0.0311 Cost of goods sold 0.0284 Total labor 0.0264 Employee numbers 0.0239 Fixed asset 0.0222 Total depreciation 0.0214 Total non-operating income 0.0107 Total non-operating expenses 0 Operating expense 0

Operating profit 0.1354 Gross profit 0.0624 Net operating revenue 0.0385 Gross sales 0.0368 Employee numbers 0.0343 Cost of goods sold 0.0329 Fixed asset 0.0289 Total depreciation 0.0127 Total labor 0.0112 Total non-operating income 0.0104 Total non-operating expenses 0 Operating expense 0

Employee numbers 0.00504 Net operating revenue 0.003151 Gross sales 0.003144 Cost of goods sold 0.002839 Fixed asset 0.002702 Operating expense 0.002166 Gross profit 0.001972 Total depreciation 0.00191 Operating profit 0.001898 Total labor 0.001816 Total non-operating income 0.001132 Total non-operating expenses 0.000949

Operating profit 0.0915 Gross profit 0.0441 Net operating revenue 0.036 Gross sales 0.0329 Cost of goods sold 0.0298 Employee numbers 0.0275 Fixed asset 0.0245 Total depreciation 0.0154 Total labor 0.0151 Total non-operating income 0.0103 Total non-operating expenses 0 Operating expense 0

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4. A case study

Table 3 The OWA operator weights in 2004 year.

To further demonstrate the performance of the proposed model, we practically collected a dataset from the Taiwan Economic Journal (TEJ) database (TEJ, 1990). Furthermore, both the out-of-sample forecasting and in-sample estimation are conducted to compare with other methods.

a

Operating profit

Gross profit

Net operating revenue

Gross sales

a = 0.0 a = 0.1 a = 0.2 a = 0.3 a = 0.4 a = 0.5 a = 0.6 a = 0.7 a = 0.8 a = 0.9 a = 1.0

0 0.0104 0.045 0.0987 0.1671 0.25 0.3475 0.4609 0.5965 0.7641 1

0 0.0434 0.1065 0.1646 0.2133 0.25 0.2722 0.2754 0.2521 0.1822 0

0 0.1822 0.2521 0.2754 0.2722 0.25 0.2133 0.1646 0.1065 0.0434 0

1 0.7641 0.5965 0.4609 0.3475 0.25 0.1671 0.0987 0.045 0.0104 0

4.1. TEJ dataset The dataset of this research was sourced from the Taiwan Economic Journal database, which includes macroeconomics, finance, industries, and business datasets. All of the datasets provide the basic data, finance data, and share price data of listed companies and publicly held companies. For verification, this research collects the financial data of the 629 public companies listed in the TSE (Taiwan Stock Exchange) and OTC (Over-the-Counter) market electronic firms in 2004 and 2005, which includes 12 attributes with 2413 and 2490 records (in four seasons). The dataset is partitioned into 67% training data (1616 records) and 33% testing data (797 records) in 2004, and training data (1668 records) and 33% testing data (822 records) in 2005. 4.2. Analysis and results In this section, we forecast the industrial growth rate by the proposed algorithm in Section 3; the detailed processes are listed in the following: (1) Select attributes In this step, we distinguish the dataset with three classes (A, B, C) by operating grow-up rate. We set A, B, and C class, respectively, by the operating grow-up rate P100%, 0– 100%, and <0%. We use five attribute evaluation methods (Chi-Squared, Gain Ratio, Information Gain, ReliefF, and Symmetrical Uncertainty) to order the attributes of the dataset. From Tables 1 and 2, we can see that Chi-Squared, Information Gain, and Symmetrical Uncertainty have the same orderings in the first 4 attributes (1. Operating Inco-

Table 4 The OWA operator weights in 2005 year.

a

Operating profit

Gross profit

Net operating revenue

Gross sales

a = 0.0 a = 0.1 a = 0.2 a = 0.3 a = 0.4 a = 0.5 a = 0.6 a = 0.7 a = 0.8 a = 0.9 a = 1.0

0 0.0104 0.045 0.0987 0.1671 0.25 0.3475 0.4609 0.5965 0.7641 1

0 0.0434 0.1065 0.1646 0.2133 0.25 0.2722 0.2754 0.2521 0.1822 0

0 0.1822 0.2521 0.2754 0.2722 0.25 0.2133 0.1646 0.1065 0.0434 0

1 0.7641 0.5965 0.4609 0.3475 0.25 0.1671 0.0987 0.045 0.0104 0

me = OI; 2. Gross Sales = GS; 3. Operating Cost = OC; 4. Employees numbers = GN). Therefore, this paper uses the first 4 attributes to forecast the industrial growth rate. (2) Compute the OWA weights From Step 1, the attribute number is four. Then, OWA weights could be gotten by Eqs. (6)–(8). The OWA weights are listed in Tables 3 and 4 under attribute numbers = 4 and a = [0, 1.0].

Table 2 The results of selecting attributes (the same orderings in first 4 attributes) in 2005 year. Chi-Squared

Gain Ratio

Information Gain

ReliefF

Symmetrical Uncertainty

Operating profit 449.461 Gross profit 309.928 Employee numbers 200.732 Net operating revenue 157.457 Gross sales 155.963 Total labor 152.995 Cost of goods sold 72.155 Total non-operating income 45.693 Operating expense 38.871 Fixed asset 0 Total non-operating expenses 0 Total depreciation 0

Operating profit 0.0889 Employee numbers 0.0533 Gross profit 0.0505 Net operating revenue 0.0291 Gross sales 0.0288 Total labor 0.0235 Cost of goods sold 0.0223 Total non-operating income 0.0133 Operating expense 0.0128 Fixed asset 0 Total non-operating expenses 0 Total depreciation 0

Operating profit 0.137 Gross profit 0.096 Net operating revenue 0.0452 Gross sales 0.0446 Employee numbers 0.0302 Cost of goods sold 0.021 Total labor 0.0199 Total non-operating income 0.0133 Operating expense 0.0133 Fixed asset 0 Total non-operating expenses 0 Total depreciation 0

Net operating revenue 0.00142 Gross sales 0.0014178 Cost of goods sold 0.0013796 Total non-operating expenses 0.0013468 Employee numbers 0.0009295 Total non-operating income 0.0006504 Operating profit 0.0006418 Gross profit 0.0005293 Operating expense 0.0005023 Fixed asset 0.0003031 Total depreciation 0.0001037 Total labor 0.0000946

Operating profit 0.1025 Gross profit 0.0633 Employee numbers 0.0355 Net operating revenue 0.0336 Gross sales 0.0333 Cost of goods sold 0.0203 Total labor 0.0201 Total non-operating income 0.0125 Operating expense 0.0112 Fixed asset 0 Total non-operating expenses 0 Total depreciation 0

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(3) Calculate aggregated values by OWA operator When n = 4 and a = 0.5, from Eq. (9) and the results of Step 1–Step 2, the OWA aggregated value can be calculated. The result is shown in Tables 5 and 6. (4) Classify OWA aggregated values by rough set From above (3), the aggregated values are partitioned into 67% training data and 33% testing data. Using rough set to run the 67% training data, we set the coverage as 0.9; then, the decision table and classification rules could be

gotten. Therefore, in 67% training data (attribute = 4 and

a = 0.5), we can get 485 and 634 classification rules in years 2004 and 2005; the partial rules are shown in Figs. 2 and 3. (5) Build OWA rough set model Based on Step 4, the experiment is repeated 10 times and computes the mean 10 times as the accuracy rate. The results (mean of 10 times) under a different a are shown in Table 7.

Table 5 The aggregated values of a = 0.5 in 2004 year. No.

Operating profit

Gross profit

Employee numbers

Net operating revenue

Aggregate values

Pullulating rate level

1 2 3 4 5 .. . 2409 2410 2411 2412 2413

14,751,591 * 0.25 28,804 * 0.25 72,260 * 0.25 110,982 * 0.25 156,202 * 0.25 .. . 173,380 * 0.25 375,454 * 0.25 116,805 * 0.25 190,688 * 0.25 254,518 * 0.25

19,615,448 * 0.25 22,022 * 0.25 41,067 * 0.25 58,678 * 0.25 65,920 * 0.25 .. . 226,467 * 0.25 565,337 * 0.25 147,850 * 0.25 238,262 * 0.25 318,901 * 0.25

40,054,302 * 0.25 111,481 * 0.25 251,714 * 0.25 381,282 * 0.25 475,290 * 0.25 .. . 1,687,492 * 0.25 3,991,332 * 0.25 445,995 * 0.25 669,420 * 0.25 976,108 * 0.25

41,885,020 * 0.25 111,826 * 0.25 252,609 * 0.25 383,572 * 0.25 481,171 * 0.25 .. . 1,700,449 * 0.25 4,018,085 * 0.25 445,995 * 0.25 669,420 * 0.25 976,108 * 0.25

29,076,590 54,131 118,283 178,138 216,545 .. . 946,947 2,237,552 289,161 441,948 631,409

C B B B B .. . B C B B B

Table 6 The aggregated values of a = 0.5 in 2005 year. No.

Operating profit

Gross profit

Employee numbers

Net operating revenue

Aggregate values

Pullulating rate level

1 2 3 4 5 6 .. . 2485 2486 2487 2488 2489 2490

87,254 * 0.25 2364 * 0.25 1646 * 0.25 7961 * 0.25 26,748 * 0.25 9812 * 0.25 .. . 343,093 * 0.25 609,487 * 0.25 55,682 * 0.25 90,892 * 0.25 122,134 * 0.25 188,878 * 0.25

247,252 * 0.25 15,526 * 0.25 27,148 * 0.25 44,397 * 0.25 77,655 * 0.25 28,991 * 0.25 .. . 559,380 * 0.25 989,227 * 0.25 71,415 * 0.25 125,534 * 0.25 176,262 * 0.25 263,390 * 0.25

166 * 0.25 134 * 0.25 152 * 0.25 152 * 0.25 160 * 0.25 64 * 0.25 .. . 175 * 0.25 210 * 0.25 193 * 0.25 185 * 0.25 190 * 0.25 182 * 0.25

874,969 * 0.25 231,504 * 0.25 483,205 * 0.25 688,509 * 0.25 1,149,570 * 0.25 167,528 * 0.25 .. . 4,096,020 * 0.25 6,308,289 * 0.25 258,965 * 0.25 435,175 * 0.25 612,074 * 0.25 1,028,197 * 0.25

302,410 62,382 128,038 185,255 313,533 51,599 .. . 1,249,667 1,976,803 96,564 162,947 227,665 370,162

C A C B B C .. . B C C B C C

Fig. 2. The partial rules under n = 4 and a = 0.5 in 2004 year.

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Fig. 3. The partial rules under n = 4 and a = 0.5 in 2005 year.

Table 7 The accuracy rate under different a (2004 year).

a

[Min, Max]

Average accuracy rate (%)

a = 0.5 a = 0.6 a = 0.7 a = 0.8 a = 0.9 a = 1.0

[0.93, 0.957] [0.939, 0.962] [0.944, 0.968] [0.947, 0.97] [0.948, 0.975] [0.958, 0.98]

94.44 95.22 95.77 96.12 96.28 96.82

5. Conclusions

Table 8 The accuracy rate under different a (2005 year).

a

[Min, Max]

Average accuracy rate (%)

a = 0.5 a = 0.6 a = 0.7 a = 0.8 a = 0.9 a = 1.0

[0.908, 0.941] [0.913, 0.957] [0.916, 0.953] [0.926, 0.959] [0.93, 0.964] [0.936, 0.968]

92.03 93.08 93.09 94.04 94.45 95.01

The proposed method Rough set theory (Jackson et al., 1998) Decision tree C4.5(Quinlan, 1993) Bayesian networks (Pearl, 1988) Multilayer perceptron (Zhao et al., 1998)

In this paper, a hybrid method, which combines OWA and rough set, has been proposed to enhance conventional classification methods. According to the experiments, we have two findings: (1) from Table 9, it is apparent that the proposed method outperforms the listing methods; and (2) from Tables 7 and 8, there is the optimal accuracy while the situation variable a is 1. It means apparently that investors will get a rather accurate RGR forecast as long as they employ the first input attribute, operation profit. In future work, we will build a prototype system based on the proposed method and use more open datasets to verify the performance of the proposed method. References

Table 9 Comparison results with other methods for TEJ dataset. Method

ing to the experiment’s result, we have the best accuracy; 96.82% and 95.01% in years 2004 and 2005. The result of the accuracy rate is shown in Table 9.

Average accuracy rate (%) 2004 year

2005 year

96.82 74.89 74.47 71.01 73.28

95.01 68.64 65.91 63.92 52.17

(6) Verification and comparison For comparison, this paper uses four data-mining methods to compare with the proposed model. The four methods are (a) rough set theory, (b) decision tree C4.5, (c) Bayesian networks, and (d) multilayer perceptron. We use the 67% dataset as training data and the 33% as testing data. Accord-

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