The Extension of Dominance-Based Rough Set Approach for Solving MCDM Problems Kao-Yi Shen1 and Gwo-Hshiung Tzeng2 1Department 2
of Banking and Finance, Chinese Culture University (SCE), Taipei, Taiwan Graduate Institute of Urban Planning, College of Public Affairs, National Taipei University, New Taipei City, Taiwan
RST&A Workshop, 2014 Joint Rough Set Symposium, July 9, Granada, Spain
• Research Background • What and Why • Extend DRSA to solve certain MCDM problems
• Findings in two studies (as examples) • Conclusion
Outlines
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• RSA • Indiscernibility
• DRSA • Preferential characteristic of attributes • Dominance relationship
• What DRSA supports for solving MCDM problems • Reduce attributes to discern patterns (REDUCT, CORE) • “If….., then….” decision rules=>Output as a pre-defined DC
• General situations in MCDM problems (such as ranking or selection)=>Output in the form of an aggregated score
Research Background
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• Normally, ONE decision attribute • Pre-defined decision classes with preferential characteristic
• However, in practical applications, several issues remain exist….
Classification in DRSA
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• Selection or Ranking while facing undefined DC for certain alternatives • For alternatives that all fall in the same DC
st The 1 issue in MCDM
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Undefined?
DC 1
Type 1 rules
DC 2
Type 2 rules
Undefined? Type 3 rules
New Alternative 1
DC 3
New Alternative 2
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Type 1 rules
New Alternative 1
New Alternative 2
DC 1
New Alternative 3
How to make ranking?
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• Use decision rules considering “discretization” of attributes • “natural language” for DM to assign an alternative to discretized attributes
• Increase classification accuracy • “discretization” might effect classification accuracy • machine learning technique • Fuzzy-ANN(ANFIS)
• Fuzzy intervals
nd The 2 issue in MCDM
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Inducted DRSA decision rules
If “attribute 1 is high” & “attribute 2 is low”
DC 1
What does it mean by “low” for attribute 2? Debt ratio=33.45% ?
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Limited budget…
A set of decision rules =>how to set up priority for improvements?
The 3rd issue =>Guiding improvements
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• Diagnosing FP of commercial banks • DRSA+ANFIS (iFuzzy2013 and S.I. of IJFS2014)
1.
2.
3.
Classification and Prediction FP by DRSA decision rules Increase classification & identify fuzzy intervals for strong rules for DMs DEMATEL for exploring directional influences among core attributes
• Ranking and guiding improvements for semiconductor companies • RPDA+VIKOR (JRS2014)
1.
2.
Transfer DRSA rules into RPDA model for ranking undefined alternatives or alternatives categorized in the same DC Infuse VIKOR aggregation method for guiding improvements
What & Why=>in two studies
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• To meet decision maker’s requirements in a real business environment • • • •
Predict future financial performance effectively Easy-to-understand (understandable) decision rules Applicable guidance while adopting the rules Use the obtained rules to rank alternatives precisely
• Examine the prediction capability of the combined computational intelligence for financial applications • • • •
DRSA=>obtain granule of knowledge for FP prediction: CORE & Rules Neuro-fuzzy technique (ANFIS)=>increase accuracy=>fuzzy intervals DEMATEL=>directional influences of criteria/dimensions=>implications VIKOR=>aggregate performance gaps and rank alternatives accordingly =>identify improvement priority for DMs
Obstacles faced by DMs
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• A combined soft computing model for the financial performance prediction problem • A real case from the Taiwan’s banking industry • • • • •
Data: a group of commercial banks in Taiwan (data in 2008~2012) Data source: http://www.cbc.gov.tw/np.asp?ctNode=721 Four strong decision rules and retrieved eight criteria (CORE) Five sample banks were examined with affirmative result Implications for commercial banks are also obtained (directional influences+INRM=>Directional Flow Graph)
In the first case…….
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• Transformed DRSA rules into Rule-based Probabilistic Decision Approach (RPDA) model • An infused model for enhancing ranking & improvement for semiconductor companies • Data: 2007~2012 (a group of public-listed stocks from Taiwan) • 4(positive)+4(negative) strong rules to position (rank) new alternatives • The potential of using VIKOR to guide for improvements
In the second case….
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Measure its performance scores on two groups of rules
PLUS
R1
Alternative
MINUS
R4 Positive Rules(desired DC) R5
R8 Negative Rules(unwanted DC)
RPDA model
Calculate the Prob. weight of each rule
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• R1 (Prob. weight=32.63%) (LongCapital≻M) & (Speed≻M) & (AR_turnover≻M) & (AR_days≻H)
& (ROE≻M) & (CashFlow_adq≻M) =>Good
decision class
• If Company A •
LongCapital=M, Speed=H, AR_turnover=L, AR_days=M, ROE=M, CashFlow_adq=M
• Performance score on R1=4/6=66.67%
One example of RPDA
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Research Methods for Problems-Solving Data Processing / Statistical and Multivariate Analysis
Planning / Designing
Evaluating / Choosing
External Environment- ex. Business Governance
MODM
Explorative Model
Personal / Social Attribute
Future Prospecting/ Forcasting Data Processing/ Analysis Data Investigating / Collecting Data Sets: Crisp Sets Fuzzy Sets
Regression/Fuzzy Regression ARIMA Grey Forecasting Baysian Regression
MODM (GP, MOP, Compromise solution, etc.) + Single level + Fuzzy + Multi-level + Multi-stage + Dynamics + Habitual Domain
Statistical/Multivariate Analysis Fuzzy Statistical/Multivariate Analysis Data Mining
Goal
Dimensions
Perception/ feeling
variables
MADM
Normative Models
Response/ Kansei
Objects (Internal Real Situations): features/attributes/ criteria/objectives/
- ISM, Fuzzy ISM - DEMATEL, Fuzzy DEMATEL - Fuzzy Cognitive Map (FCM) - Formal Concept Analysis - Linear Structure Equation Model (LISEM, or called “SEM”) - Systems Dynamics - Input-Output Analysis
MCDM
De Novo Programming (Including Fuzzy)
Genetic Algorithms
Criteria
Policy Strategic alternatives
C1 . . .Cj w1 . . .wj
. . . . . .
Cn wn
a1 Performance
ai
Matrix (crisp/fuzzy)
ami Normalizing
Additive Types SAW TOPSIS, VIKOR PROMETHEE ELECTRE Grey Relation
Weightings AHP / Fuzzy AHP ANP / Fuzzy ANP DANP /Fuzzy DANP Entropy Measure Fuzzy Integral Dynamic Weighting Neural Networks Weighting
Non-Additive Types Fuzzy Integral Neural Network + Fuzzy
Neural Networks Logic Reasoning
Grey Hazy Sets Rough Sets
Descriptive Model
Changeable Spaces Programming (Decision Space and Objective Space)
- DEA - Fuzzy DEA - Network DEA - MOP DEA - Fuzzy MOP DEA - MOP Network DEA
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and Service
19 Data Mining Concepts of Intelligent Computation in Knowledge Economy
Big Data
Core Indicators
Data Mining
Reasons for the Proposed Model 20
Core indicators with decision rules
Granulized information Big data set
ANFIS Fine-tune for better discretization Dominance relationship Explore implicit knowledge Obtain objective inductions
Human beings encounter difficulties in handling big data
Dominance-based Rough Set Approach 21 ~DRSA & ANFIS~
CORE indicators
The strength and limitations of human Bounded rationality (H.A. Simon, 1972)
DEMATEL Experience and knowledge Fuzzy intervals for better usage
DFG Explore directional influences among the CORE
From Decision Rules to Implications
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Neuro-Fuzzy Refined Decision Rules 23
• Original Top 1/3 (by ranking)
• Equal width max
min
• Normal distribution based
Table 10 Comparison of the three discretization methods Bank Rule C4 E3 E4 L1 L2 G1 G3 G4 Class Original A R1 2 3 1 3 3 3 3 2 Good three level B R1 3 3 2 2 2 1 3 1 Good ranking C R2 3 3 2 2 2 1 3 3 Good D R3 3 1 2 1 3 1 1 1 Bad1 E R3 1 2 3 1 3 1 3 1 Bad Equal A -1 2 2 1 2 3 1 2 N.A. -width B 1 2 2 1 2 1 1 2 N.A. -C 3 2 2 1 2 1 1 2 N.A. D R3 1 1 2 1 3 1 1 1 Bad1. E R3 1 1 3 1 3 1 2 1 Bad. Normal A -2 2 1 2 2 3 2 2 N.A. distribution B -2 2 2 2 2 1 2 2 N.A. based C R2 3 3 2 2 2 1 2 3 Good D R3 2 1 2 1 3 1 2 1 Bad1 E -1 2 3 1 3 2 3 1 N.A. 1 Bank D’s performance in 2012 should not be classified as Bad. Decision Rule 3
Bank D
L1 M L:[-11.81,13.35,35.95] M:[12.65,41.61,61.55] H:[37.01,53.86,86.03] L1=15.41
G1 L L:[-46.40,-15.49,13.54] M:[-15.79,15.93,45.53] H:[5.98,44.56,76.04] G1=-9.06
G4 L L:[-95.49,-51.85,-8.62] M:[-51.97,-9.02,34.31] H:[-11.27,34.02,77.87] G4=-10.10
𝑥 ± (0.5 × 𝑆𝐷
Comparison of Discretization Methods
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Bad
N.A.
0%
Table 8 Relative importance and cause-effect analysis of criteria C4 E3 E4 L1 L2 G1 G3 G4
ri 3.36 4.30 4.24 2.99 3.61 4.06 2.68 2.06
di 3.31 3.44 3.33 3.59 3.44 3.46 3.51 3.20
ri +di 6.68 7.74 7.57 6.59 7.05 7.52 6.19 5.26
ri -di 0.05 0.86 0.91 -0.60 0.17 0.59 -0.84 -1.14
Table 9 Relative importance and cause-effect analysis of dimensions D1 (Capital Sufficiency) D2 (Asset Quality) D3 (Liquidity) D4 (Growth)
Ri 1.63 2.12 1.65 1.48
Di 1.64 1.71 1.79 1.74
Ri +Di 3.27 3.84 3.44 3.22
Ri -Di -0.01 0.41 -0.14 -0.26
DEMATEL Analysis From 25 (ratios) to 8 criteria (CORE)
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• Implications • DRSA Decision Rules • DEMATEL Analysis • Find improvement priority • Explore plausible relationship among criteria • Design/select improvement plans
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• Solve FP problem in a real business environment • Meet decision maker’s requirements • Understandable decision rules (R1, R2, R3, and R4) • Easier to apply the rules (fine-tuned fuzzy intervals) • Guidance for future planning and improvements (DFG)
• Improved classification=>discretization enhancement
Findings in the 1st study
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The 2nd study (RPDA) will be reported later in this conference
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• DRSA is a suitable decision aid for solving MCDM problems • Certain issues remain • Aforementioned issues • Limitation of DM while adopting those rules
• Integration with the other soft computing techniques or decision method=>enhancement • More empirical cases will be explored in the future
Conclusion
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~Thank you~ Presenter: Kao-Yi Shen Ph.D. Email:
[email protected] 31
