Rough set theory is relativly new to area of soft computing to handle the uncertain big data efficiently. It also provides a powerful way to calculate the importance degree of vague and uncertain big data to help in decision making. Risk assessment is very important for safe and reliable investment. Risk management involves assessing the risk sources and designing strategies and procedures to mitigate those risks to an acceptable level. In this paper, we emphasize on classification of different types of risk factors and find a simple and effective way to calculate the risk exposure.. The study uses rough set method to classify and judge the safety attributes related to investment policy. The method which based on intelligent knowledge accusation provides an innovative way for risk analysis. From this approach, we are able to calculate the significance of each factor and relative risk exposure based on the original data without assigning the weight subjectively.
Rough Set Theory Big Data Risk Analysis Data Mining Variable Weight Significance of Attribute Core Attribute Attribute Reduction1. Introduction
Rough Set Theory, proposed in 1982 by Zdzislaw Pawlak, this theory is now in a state of constant development. Its methodology is concerned with the classification and analysis of imprecise, uncertain or incomplete information and knowledge, and of is considered one of the first non-statistical approaches in data analysis (Pawlak, 1982) [1] . The theory has found applications in many domains, such as decision support engineering, environment, banking, medicine and others [2] .
Over the years, rough set theory has become a valuable tool in the resolution of various problems, such as: representation of uncertain or imprecise knowledge; knowledge analysis; evaluation of quality and availability of information; identification and evaluation of data dependency; reasoning based an uncertain and reduct of information data.
In this paper, we describe the different risk factors of investment risk and find a big data approach to emphasize the significance risk factors to more smother way to invest. The key point of this paper is we can calculate the importance degree of different level risk factor from the inconsistent and incomplete data by rough set theory.
2. Data Preprocessing2.1. Understanding Data
There are mainly three types of investment risk. In Figure 1, we show the main risks. There are
1) Strategic Risk
2) Operational Risk
3) Financial Risk
We can also divide the micro level risks in macro level risk. Here we show the financial risks hierarchy.
Financial risk is an umbrella term for multiple types of risk associated with financing [3] , including financial transactions that include company loans in risk of default. Risk is a term often used to imply downside risk, meaning the uncertainty of a return and the potential for financial loss [4] . Figure 2 shows the risk hierarchy of the financial risk as an example of parent level risk.
Types of Financial Risk:
1) Prices
Types of business organizational risk
Risk hierarchy of financial risk [<xref ref-type="bibr" rid="scirp.69365-ref5">5</xref>]
Interest rates
Currencies
Stock market
Energy market risk
Non energy market risk
2) Complex financial products
3) Liquidity risk
4) Customer credit
In the same way we can divide the other high level risks (Strategic & Operational Risk) in a hierarchy way [6] .
2.2. Data Collection & Representation
We process the collected data on such a fashion that it fit on our context. First phase of the data processing is encode it in simple and recognition able way. Here, in Table 1, we encode the financial risk as FR and its child as FR-n. Example: Prices as FR1. The Prices is immediate child of financial risk. There are also 5 Childs of Parent Prices. We encode the Childs as FR1n, example: Interest rates as FR11, Currencies as FR12.
The second phase is arranging the data in matrix format. We already encoded the risk factors as attributes. Now we arrange the each attribute scores by each managerial rank people as a row of matrix. Figure 3 repre- sents the risk matrix of financial risks.
3. USACE & Hierarchical Holographic Model Based Investment Risk Analysis3.1. Basic Concepts3.1.1. USACE Model
USACE has been managing risk for a long time, beginning well before risk analysis grew into prominence.
Risk management components can be found in a number of USACE programs. In the 1980s, USACE grappled with the problem of modernizing its approach to the major rehabilitation of existing projects [7] [8] . Efforts to objectively assess the reliability of the existing structures gave rise to the use of risk-based analytical techniques and analyses that supported decision-making.
3.1.2. Hierarchical Holographic Modeling (HHM)
Haimes (1981) started the research in the field of HHM. HHM addresses the issues related to hierarchical institutional, managerial, organizational or functional decision-making structures [9] . Kaplan et al. (2001) suggested that HHM has been regarded as a general method for identifying the set of risk scenarios [10] . HHM is parti-
cularly useful in modeling large-scale, complex, and hierarchical systems. The HHM methodology recognizes that most organizational as well as technology-based systems are hierarchical in structure, and thus the risk ma- nagement of such systems must be driven by and responsive to this hierarchical structure.
Himes, et al. (2002) suggested that the nature and capability of HHM is to identify a comprehensive and large set of risk scenarios [12] . To deal with this large set we need a systematic process that filters and ranks these identified scenarios is needed so that risk mitigation activities can be prioritized. In addition, Kaplan et al. (2001) [10] suggested that HHM could be viewed as one of the methods of Theory of Scenario Structuring (TSS), which is the part of QRA that is useful in identifying the set of risk scenario.
3.2. Technical Approach
Figure 4 shows the risk assessment model we use to assess the risks. This model consists of 6 sub elements. There are communicate and consult, establish decision context, identify risk, analyze risk, evaluate risk and risk management decision.
Every investment involves some degree of risk. Risk is quantifiable both in absolute and in relative terms. A solid understanding of risk in its different forms can help investors to better understand the opportunities, trade-offs and costs involved with different investment approaches.
We can implement USACE model to analysis investment risk [10] [13] [14] .
3.2.1. Establish Decision Context
All but the simplest investments expose investors to multiple financial risks that can result from a range of events and scenarios. Risk can involve the collapse of a specific company, industry sector or currency.
In this decision context the future investor can analyze the risk of investment and improve their decision making ability. To mitigate the risks of investment next phases are also very important.
3.3.2. Identify Risks
There are mainly three types of investment risk. There are
Strategic Risk
Operational Risk
Financial Risk.
Here we will only discuss about Financial Risk as an example.
1) Prices
Interest rates
Currencies
Proposed model for risk assessment
Stock market
Energy market risk
Non energy market risk
2) Complex financial products
3) Liquidity risk
4) Customer credit
3.3.3. Analyze Risk
To calculate the importance degree and ordered list of each risk attributes we follow some steps. Those steps shortly describe in Table 2. In bellow we will describe the steps.
U= {1, 2, 3, 4, 5, 6…..} represents the study objects, i.e. a set of company managers evaluation value about investment risk factor, represents the all risks evaluation indicators as explained in section understanding data. Based on interview data from the evaluation value by the company, a score of 1 to 5 is given to each indicator, with 5 being the highest risk exposure level.
In above Table 3 shows the likertscale for scoring the risk attributes. The scoring means that in one case, if certain factor is very important, such as country risk, then 5 is given to represent very high risk level. On the contrary, if an indicator is relatively reliable and safe, for instance non energy source, then 1 can be given to represent very low risk exposure in this aspect. In addition, the outcome on investment is represented by D = {outcome}. Y stands for loss, and N means no loss.
SIM (A) denotes binary similarity relation between objects that are indiscernible with regards to indicator’s value. The similarity relation can be defined as
stands for pair of study objects. This means, two study objects (x, y) has binary similarity relation if the value of each attribute for object x, i.e. a(x), is the same as the value of the corresponding attribute for object y, i.e. a(y). For any value of attribute which is missing, i.e. a(x) = * or a(y) = *, a(x) and a(y) are considered the same since * can represent any number.
For any value of attribute which is missing, i.e. a(x) = * or a(y) = *, a(x) and a(y) are considered the same since * can represent any number.
Basics steps of risk analysis
Input: Risk Matrix
1. From the simple assessment value generates the dataset.
2. By using rough set theory create the discernibility matrix using equation.
3. From the importance degree function calculate each risk factor or attribute’s importance degree of
4. Normalize the importance degree of risk by the distribution function.
5. After calculating the distribution of Risk factor, Integrate risk factor with the attribute weight. Assessment value of risk
6. Summarize the child level risk and calculate the parent level risk
Output: Importance Degree & Ordered List
Description of exposure of the risk [<xref ref-type="bibr" rid="scirp.69365-ref15">15</xref>]
Exposure Level
Description
5
Very High
4
High
3
Medium
2
Low
1
Very Low
SA(x) represents the maximal set of objects which are possibly indiscernible by A with x.
1) Determine all reducts
A reduct is a minimal set of indicators from A that preserves the original classification defined by A. This can be determined by establishing Boolean Discernibility Matrix [1] [2] [16] with for any pair (x, y) of the objects.
Δ is a discernibility function for information table.
Δ(x) is a discernibility function for object x in information table.
Table 4 shows the discernibility matrix which we already showed mathematically.
2) Calculate the importance degree of each risk indicator
Then the importance degree of each indicator can be calculated by using [1] [2] [17] [18] the following equation:
Discernibility matrix of financial risks
11
12
13
14
15
16
17
18
19
20
21
1
R1R3R6 R8R10R 11R13
R1R2R3 R6R8R 10R11R13
R1R4R5R 8R9R11 R12R13
R1R2R3 R6R8R11 R13
R1R3R4 R5R6R8 R9R10R 11R12
R3R5R9 R10R11R 12R13
R1R2R3 R4R5R8 R10R11
R1R4R6 R8R10R11R12R13
R3R4R6 R8R9R10 R11R12 R13
R1R3R4 R5R8R11 R12R13
R1R2R3 R9R10 R11
2
R1R2R4 R5R6R 8R10R13
R4R5R6 R8R10
R1R2R4 R5R8R9 R11R12
R4R5R6 R8
R1R2R3 R4R5R6 R7R8R9 R10R12 R13
R1R2R5 R7R9R10 R11R12 R13
R3R4R5 R7R8R10 R13
R2R4R5 R6R7R8 R10R11 R12R13
R1R2R6 R7R8R9 R10R11 R12R13
R2R3R5 R8R11 R12
R3R4R5 R7R9R10 R13
3
R1R2R4 R5R6R8R 10R11R13
R1R4R5 R6R8R10 R11
R1R2R8 R9R11 R12
R1R4R5 R6R8R11
R1R2R3 R6R7R9R 10R11R12 R13
R2R5R7 R8R9R10 R11R12 R13
R1R3R5 R7R10R 11R13
R1R2R5 R6R7R8 R10R11 R12R13
R2R4R6 R7R9R10 R11R12 R13
R1R2R3 R4R12
R1R3R4 R5R7R8 R9R10R 11R13
4
R1R5R 6R8R10
R1R2R5 R6R8R10 R13
R1R4R8 R9R11 R12R13
R1R2R5 R6R8R13
R1R3R4 R6R7R8 R9R10 R12R13
R5R7R9 R10R11 R12R13
R1R2R3 R4R5R7 R8R10 R13
R1R4R5 R6R7R8 R10R11 R12
R4R6R7 R8R9R10 R11R12
R1R3R4 R8R11 R12R13
R1R2R3 R5R7R9 R10R13
5
R1R3R4 R6R8R10
R2R3R4 R6R8R10 R13
R1R4R5 R6R8R9 R11R12 R13
R2R3R4 R6R8R13
R1R4R5 R6R7R8 R9R10 R12R13
R1R3R5 R7R9R10 R11R12 R13
2RR4R5 R6R7R8 R10R13
R4R6R7 R8R10 R11R12
R1R3R4 R7R8R9R 10R11R12
R4R5R6 R8R11R 12R13
R2R4R7 R9R10 R13
6
R1R4R5 R7R8R10 R13
R1R2R4 R5R7R10
R1R4R5 R7R8R9 R11R12
R1R2R4 R5R7
R1R4R5R 7R8R9R1 0R12R13
R1R5R7 R8R9R10 R11R12 R13
R1R2R4 R5R7R8 R10R13
R1R4R5 R7R8R10 R11R12 R13
R1R7R8 R9R10R 11R12R13
R1R5R7 R8R11 R12
R1R2R4 R5R7R8 R9R10 R13
7
R1R4R6 R8R9
R2R4R6 R8R9 R13
R1R5R8 R10R11 R12R13
R2R4R6 R8R9R10 R13
R1R3R5 R6R7R9 R12R13
R1R5R7 R8R9R10 R11R12 R13
R2R3R5 R7R9R13
R6R7R8 R9R10 R11R12
R1R4R6 R7R11 R12
R3R4R5 R9R11R 12R13
R2R3R4 R7R8R9 R13
8
R1R2R5 R6R8R10
R5R6R8 R10R13
R1R2R4 R5R8R9 R11R12 R13
R5R6R8 R13
R1R2R3 R4R5R6 R7R9R10 R12R13
R1R2R5 R7R8R9 R10R11 12R13R
R3R4R5 R7R10 R13
R2R4R5 R6R7R8 R10R11 12R
R1R2R4 R6R7R9 R10R11 12R
R2R3R4 R5R11R 12R13
R3R5R7R 8R9R10 R13
9
R1R4R6 R8
R2R4R6 R8R13
R1R5R8 R9R10R 11R12R13
R2R4R6 R8R10 R13
R1R3R5 R6R7R9 R12R13
R1R5R7 R8R9R10 R11R12 R13
R2R3R5 R7R13
R6R7R8 R10R11 R12
R1R4R6 R7R9R11 R12
R3R4R5 R11R12 R13
R2R3R4R 7R8R9 R13
10
R1R2R3 R4R8R10
R3R4R8 R10R13
R1R2R5 R6R8R9 R11R12 R13
R3R4R8 R13
R1R2R5 R7R9R10 R12R13
R1R2R3 R5R7R8 R9R10R11 R12R13
R5R6R7 R10R13R
R2R7R8 R10R11 R12
R1R2R3 R4R6R7 R9R10 R11R12
R2R4R5 R6R11 R12R13
R4R7R8 R9R10 R13
Here Card (Eij) number of items in one index where a is present.
Example:.
Importance degrees of financial risks
Thereafter, the importance degree can be normalized for easier comparison, showed in Figure 5, which can
by the following equation:
3) Integration with Attribute Weight and Expert Opinion
Attribute values are collected from the old investor. All values are distributed in liker scale 1 to 5. This attribute value is a qualitative value, so it’s important to integrate with the distribution of importance degree. The basic rule of integration is multiply with the average of attribute value, shown in Figure 6.
3.3.4. Evaluate Risks
Using HHM We can divide the risks in hierarchical way. In the top level the organizational risk, then macro level risk and then micro level risk.
Described in Figure 7, the hierarchical separation of risks we can calculate the significance of micro level risk, macro level risk and investment risk for an organization and also can put more clear gesture on risk management decision.
1) Calculation of Parents Risk Assessment
After calculating all micro level risk, we can combine using HHM model. The basic rule of HHM model is the summation of child level risk represents the parent level risk.
So if we want to calculate the Assessment value of operation risk the below equation can serve our purpose.
After this phase we can generate all risk assessment value. Now we can arrange the list ascending order or descending order to evaluate the risk priority.
3.3.5. Risk Management Decision
Risk management provides the mechanism to make intelligent decisions with risk reduction as a key input driver. Risk management provides a disciplined environment for proactive decision making in order to:
Proactively identify risks
Prioritize risks
Implement strategies for dealing with risks
Assure and measure effectiveness of implemented strategies
Risk assessments of financial risks
Risk assessment hierarchies of financial risks
4. Result Analysis
Traditional risk assessments that include asset valuation do not always capture the essence and uncertainty of the underlying risks. Based on those attributes, we analysis the risk attributes. But because of the sensitive informative and conduct the questionnaire surveys, it is not the elaborative or deep analysis, It is justified with other literature and shows the risk importance of risk attributes.
4.1. Calculate the Importance Degree of the Risk Indicators
To calculate the risk degree importance, we have taken the same methodology shown to calculate risk attributes using RST theory in a process of factors decisional matrix and weighted average to calculate the risk values. Figure 6 shows the importance degree of risk indicators values (ω) for financial risk analysis. The normalized risk (ω) values are for the easier comparison and relate with other risk justification. Also from Figure 5, we may conclude the risk indicators values. In the financial policy (FR1), the energy risk (FR14 = 0.088) is the highest importance of degree in risk indicators because of the lack sufficient energy supply shortage. In the row of risk indicators, the monetary system (FR = 15) may affect the overseas companies in financial risk uncertainties. In the rest of the financial attributes, researches find as per the weighted average, liquidity risk (FR31 = 0.013) is the significant risk values in the company solvency and financial regulation (FR21 = 0.071) in the segment of internal policy of that industry. Overall, financial global uncertainties (FR51 = 0.068) has also the degree of importance in risk analysis.
Figure 8 represents the risk indicator value f based graph, where FR31, FR52 got highest exposure then followed by FR14, FR41, and FR15.
4.2. Risk Analysis and Comparative Risk Ranking Analysis
After calculating the normalized risk values (ω), we have calculated the final risk analysis value based on the experts knowledge. It makes the justification for risk analysis and to assume the reliable risk attributes degree of importance results where financial risk is sensible to any company’s performance.
Importance degrees of the risk indicators
From Figure 9, we can describe the highest degree of risk attributes; (FR31 = 0.39) liquidity risk has the highest value which indicates the most degree of importance in terms of experts’ knowledge (Q). Then, the interest risk uncertainties (FR11 = 0.324) indicates the degree of importance in the Financial policy risk types segment. Among the other risk uncertainties, FR14 = 0.25 and FR41 = 0.22 has the significant degree of importance in the financial risk uncertainties.
Table 5 shows the comparative analysis between the risks attributes results which contains the risk values of normalized value (ω) and the average of expert’s opinions (Q).
Most of the risk attributes are having same rank between the two types the risk values. Here, an interest rates uncertainty (FR11) has the highest rank in the experts’ knowledge but it importance as the less significant for companies under the financial policy segment. Similarly, energy risk has the top degree of significance in company manager’s view but its second type degree of risk in case of expert’s eyes. It is normal that experts’ calculation may differ with company managers because the knowledge and practical gap between the two views have shown in Figure 10.
4.3. Risk Analysis Using HMM Method of Financial Risk
The major advantage of the HHM framework for risk assessment and management is its ability to identify risk scenarios that result from and propagate through the multiple overlapping hierarchies in real-life systems. In the planning, design, or operational modes, the ability to model and quantify the risks contributed by each subsystem facilitates understanding, quantifying, and evaluation the risks of the whole system. In particular, the ability to model the intricate relations among the various subsystems and the ability to account for all relevant and important elements of risk and uncertainty renders the modeling process more representative and encompassing.
Using this equation we can calculate the parent risk.
4.3.1. Importance Degree
Using the above equation we calculate the micro level risk of the financial risk.
In Figure 11, result shows business environment risk got the highest risk exposure. Then regulatory environment, brand and communication and strategic information got almost same level risk exposure. The lowest risk exposure is organization behavior design on the basis of importance degree of micro level risk.
Comparative images between the risk indicators and risk analysis ranking
Distribution of importance degree
Company solvency 0.14 + 0.19 = 0.33
FR4 0.25 + 0.07 = 0.32
FR5 0.23 + 0.32 = 0.55
In Figure 12, results show business environment risk got the highest risk exposure. Then regulatory environ- ment, brand and communication and strategic information got almost same level risk exposure. The lowest risk exposure is organization behavior design on the basis of distribution of micro level risk.
4.4. Comparative Risk Analysis
From the SAP Risk Management we know that the risk score calculation method differs if the probability is enabled in the Maintain Analysis Profile Customizing activity [19] .
If the probability is enabled, the risk score = probability X impact.
If the probability is disabled, the risk score = sum of all impact values.
By solving the deferring characteristic of risk in engineering project using variable weight theory [20] to improve the accuracy of risk evaluation. And result produce from our Rough Set Theory Approach, if we compare all three methods we can find the similarity between them.
From the graphs shown in Figure 13, we can realize on all three approaches the certain risks get highest exposure.
5. Conclusions
We have identified a set of key internal and external uncertainties, which are eventually highlighted as “risk de terminants” based on their occurrence and consequential effects on the business performance. This paper pres- ents the identified risk determinants and describes a methodology to identify them.
The merits of RST to handle incomplete and uncertain information, and its capability of minimizing subjective analysis have been exploited in this study. After identifying the uncertainties and categorizing in major risk types, we set the data table and put in RST software coding to Initialized Information. Then, to find out the
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