本研究在探討一個模糊投資組合，以上市公司股票投資收益與月報酬率風險參數。利用上市公司的股票，我們以投資組合測試的案例，使用風險中立模式進行投資組合分析，並以不同的結果進行敏感性分析。
  該數據被分成五個類股有建築，紡織，電子，化工，金融。其中探討企業績效的方法由盈利能力，成長率，償付能力，股息收益率等作為變數計算權重。。
  我們想知道最好的選擇類型的股票，並利用TOPSIS法來考慮風險模型的線性規劃問題藉此得到的投資報酬率的模糊投資組合模型。本研究是以計算公開的公司信息為起承，股票的最佳選擇和最佳效益為賺取為核心，給予投資人客觀的投資組合建議。

This paper considers a fuzzy portfolio selection problem with a constrained set of stock investment returns and satisfaction levels in terms of the total return and risk parameter. Using the stock of the listed companies, we find portfolios we tested the illustrated experiments with a sensitivity analysis that employed different investment risks cause have different results. 
  The data are divided into five sectors that are construction, textile, electronic, chemical, and financial. The results indicate that firm performance, which is measured by profitability, growth rate, solvency, dividend yield rate. 
  We want talk about the fuzzy model portfolioby using TOPSIS method and linear program model to choice the best type of stock. This paper consider how to know the best selection of stocks and best benefit for earning after calculating the companies reveal’s information in public.

Table of Contents
Table of Contents	I
List of Tables	III
List of Figures	VI
1	Introduction	1
1.1.	Research Background	1
1.2.	Purpose of Research	1
1.3.	Method of Research	1
2	Literature Review	2
2.1	Profitability	2
2.2	Portfolios	2
2.3	Markowitz Theory	3
3	The portfolio model and estimated method	4
3.1	A fuzzy value with lower and upper possibility means	4
3.2	Portfolio model	4
3.3	TOPSIS method	8
4	Selection process of security samples	11
4.1	Numerical example	35
4.2	Sensitivity analysis	36
4.2.1	Unconstrained investment of fuzzy portfolio model in 10 companies	36
4.2.2	Unconstrained investment of fuzzy portfolio model in 5 companies	37
4.2.3	Ratio of constrained investment of 10 companies.	38
4.2.4	Constrained models of 10 companies.	40
4.2.5	Constrained models of 5 companies.	44
4.2.6	10 companies of portfolio model with constrained by RC*	48
4.2.7	5 companies of portfolio model with constrained by RC*	49
4.2.8	When the textile sector ratio cut 10%.	49
4.2.9	When the chemical sector ratio cut 10%.	51
4.2.10	When the construction sector ratio cut 10%	51
4.2.11	When the financial sector ratio cut 10%.	53
4.2.12	When the electronic sector ratio cut 10%.	54
4.2.13	Flexible portfolio model (5 companies adjust by textile)	56
4.2.14	Flexible portfolio model (5 companies adjust by chemical)	56
4.2.15	Flexible portfolio model (5 companies adjust by construction)	57
4.2.16	Flexible portfolio model (5 companies adjust by financial)	58
4.2.17	Flexible portfolio model (5 companies adjust by electronic)	58
5	Conclusions	61
References:	63
 
List of Tables

Table 4- 1 10 individual listed companies of textile sector.	11
Table 4- 2 The normalized matrix G	12
Table 4- 3 The weighted normalized matrix G*	12
Table 4- 4 Ideal solution	13
Table 4- 5 Degree of separation S*	13
Table 4- 6 Degree of separation S-	14
Table 4- 7 Relative proximity	15
Table 4- 8 10 individual listed companies of electronic sector.	16
Table 4- 9 The normalized matrix G	16
Table 4- 10 The weighted normalized matrix G*	17
Table 4- 11 Ideal solution	18
Table 4- 12 Degree of separation S*	18
Table 4- 13 Degree of separation S-	19
Table 4- 14 Relative proximity	20
Table 4- 15 10 individual listed companies of chemical sector.	21
Table 4- 16 The normalized matrix G	21
Table 4- 17 The weighted normalized matrix G*	22
Table 4- 18 Ideal solution	23
Table 4- 19 Degree of separation S*	23
Table 4- 20 Degree of separation S-	24
Table 4- 21 Relative proximity	25
Table 4- 2210 individual listed companies of construction sector.	26
Table 4- 23 The normalized matrix G	26
Table 4- 24 The weighted normalized matrix G*	27
Table 4- 25 Ideal solution	28
Table 4- 26 Degree of separation S*	29
Table 4- 27 Degree of separation S-	29
Table 4- 28 Relative proximity	30
Table 4- 29 10 individual listed companies of financial sector.	31
Table 4- 30 The normalized matrix G	31
Table 4- 31 The weighted normalized matrix G*	32
Table 4- 32 Ideal solution	32
Table 4- 33 Degree of separation S*	33
Table 4- 34 Degree of separation S-	33
Table 4- 35 Relative proximity	34
Table 4- 36 The ranking results for stocks analysis, and use RC*to choice 50 stocks to 10 stocks.	35
Table 4- 37 Unconstrained investment of fuzzy portfolio model in 10 companies	36
Table 4- 38 Unconstrained investment of fuzzy portfolio model in 5 companies	37
Table 4- 39  By TOPSIS method and Table36 ranking, we own RC* value in fuzzy portfolio model.	38
Table 4- 40 We find out the RC* value rate in fuzzy portfolio model by Table39.	39
Table 4- 41 We find out the RC* value rate in fuzzy portfolio model by Table39.	39
Table 4- 42 10 companies of portfolio model with constrained investment proportion by RC*.	48
Table 4- 43 5 companies of portfolio model with constrained investment proportion	49
Table 4- 44 Textile percentage decrease about 10%	50
Table 4- 45 Chemical percentage decrease about 10%	51
Table 4- 46 Construction percentage decrease about 10%	52
Table 4- 47 Financial percentage decrease about 10%	53
Table 4- 48 Electronic percentage decrease about 10%	54
Table 4- 49 Textile percentage decrease about 10%	56
Table 4- 50 Chemical percentage decrease about 10%	57
Table 4- 51 Construction percentage decrease about 10%	57
Table 4- 52 Financial percentage decrease about 10%	58
Table 4- 53 Electronic percentage decrease about 10%	59

 
List of Figures
Figure 1 10 companies of ROI charts.	55
Figure 2 5 companies of ROI chart.	60

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