| 摘要: | 對軟體發展中各個階段的風險問題，若無適當的方法予以評判及管控，將有延誤時程、成本增加、效能不足、與維護不佳等困擾。有鑑於此，我們曾於 〔Fuzzy Sets and Systems, Vol. 79 (1996), 323-336; Vol. 80 (1996), 261-271、Information Sciences, Vol.113,(1999),301-311; Vol. 153 (2003), 177-197 、 International Journal of Reliability, Quality and Safety Engineering, Vol. 11 No. 2, (2004), 17-33、ICIC Express Letters, Vol. 4, No.2 (2010) 319-323〕提出各種不同評估模式及各提出不同演算法以計算出整體風險率。在上述諸研究之評估表中，如果我們能夠把統計信賴區間的觀念引進來，取代先前使用單一值i M ，更能符合實際上之應用，因此本研究以統計信賴區間為評價之模糊評估軟體發展整體風險率，其可靠度更具說服力。對於每一個評估項目中假設統計資料為, 1,2,..., ; 1,2,.., ij i M j = n i = m ， 則平均數 M i m n M ni j ij i i [0,1], 1,2,..., 1 1 = Σ ∈ = = 當作i M 的點推定值，然而由於我們無法得知i i M − M 的機率， 而且i M 值在不同的時間點都會有變動而不是固定不變， 因此用點推定並不是很適合，更好的方法就是利用統計信賴區間來取代點推定。i M 的(1 −α) ×100% 信賴區間為 i m n s M t n s M t i i i n i i i ni i [ 1( ) , 1( ) ], 1,2,..., − + = − − α α ， 其中信賴度0 < α < 1 ， 變異數 M M i m n s i n j ij i i i ( ) , 1,2,..., 1 1 1 2 − 2 = − = Σ = ，利用自由度−1 i n 的 t 分配1( ) α − i tn 滿足機率≥ α = α ( −1( )) i P T tn ，決策者可依實際需求選擇適當之α 值及樣本數以做出最佳之評估。於本研究中，我們也將證明存在一三角形模糊數( ( ) , , ( ) ) 1 1 i i i i n i i i n n s M M t n s M t i i α α − − − + 與此信賴區間 [ ( ) , ( ) ] 1 1 i i i n i i i n n s M t n s M t i i α α − − − + 成一對一的對應(one to one corresponding)，因此信賴區間 [ ( ) , ( ) ] 1 1 i i i n i i i n n s M t n s M t i i α α − − − + 可以三角形模糊數( ( ) , , ( ) ) 1 1 i i i i n i i i n n s M M t n s M t i i α α − − − + 表示；我們也將利用Fuzzy compositional rule of inference 及用Signed distance的分析，並據此一評價模式再提出二種的新演算法並將就各個演算法提出一個定理，不僅可分別就最大隸屬度原則、機率分布原則、模糊語言評價準則進行評判，亦可可評判各個Attribute的風險率、及整體風險率。 經由演算的結果，將可證得本研究所提的方法是很符合人類思想的模糊語言系列而也在實際應用上具有更高的可靠度。
During the past decades, computer technologies have changed so fast that the need of large software system becomes much more intensive. There will be many problems occur in the software system development life cycle, such as postponed schedule, increased cost, inefficiency and abandonment. The risk evaluation and management is an important issue. We presented a hierarchical structure model of aggregative risk in software development and proposed algorithms to tackle the rate of aggregative risk in Fuzzy Sets and Systems, Vol. 79, No. 3 (1996) 323-336; Vol. 80, No.3 (1996) 261-271, Information Sciences 113 (1999) 301-311; Vol. 153 (2003), 177-197, International Journal of Reliability, Quality and Safety Engineering, Vol. 11 No. 2, (2004), 17-33, ICIC Express Letters, Vol. 4, No.2 (2010) 319-323. If we use the average value i M as the point estimate i M from past statistical data, we will not know the probability of the error i i M − M . Moreover, the may fluctuate around the point estimate i M during a time interval. It follows that to use the point estimate i M to estimate the i M is not suitable for real cases. Therefore, it is more desirable to use the statistical confidence interval. We use the statistical confidence interval instead of the point estimate. Let the statistical data be , 1,2,..., ; 1,2,.., ij i M j = n i = m . Then, the average value is M i m n M ni j ij i i [0, 1], 1,2,..., 1 1 = Σ ∈ = = . Due to the unknown probability of error in point estimation i M and i M is unknown, we use the confidence interval of i M instead. The (1−α)×100% confidence interval of i M is i m n s M t n s M t i i i n i i i n i i [ ( ) , ( ) ], 1,2,..., 1 1 − + = − − α α , where 0 <α < 1 variance M M i m n s ni j ij i i i ( ) , 1,2,..., 1 1 1 2 − 2 = − = Σ = Let T be the random variable of t distribution with −1 i n degrees of freedom ( ) 1 α − ni t then satisfies ≥ α = α ( − ( )) ni 1 P T t , the decision makers can consider a suitableα and sample size choose a point within the interval to estimate i M . Also, in this study, we’ll show that there exists a triangular fuzzy number ( ( ) , , ( ) ) 1 1 i i i i n i i i n n s M M t n s M t i i α α − − − + one to one corresponding to [ ( ) , ( ) ] 1 1 i i i n i i i n n s M t n s M t i i α α − − − + . Also, we’ll propose two algorithms to evaluate the rate of aggregative risk in a fuzzy environment by fuzzy sets theory during any phase of the life cycle. Via the proposed two algorithms, we’ll propose two propositions which not only can tackle the maximal membership grade principle, probability distribution principle and fuzzy linguistics criteria to do the evaluation, but also can evaluate the grade of linguistic for the attribute, the grade of linguistic for the aggregative model, overall appraisal of each attribute, and overall appraisal of the aggregative risk. |
