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題名：構建多指標數列集灰關聯演算法及其在決策分析之應用
作者：詹家和
作者(外文)：Chia-Ho Chan
校院名稱：銘傳大學
系所名稱：管理研究所博士班
指導教授：林進財
黃旭男
學位類別：博士
出版日期：2009
主題關鍵詞：灰訊息包；多指標數列集；層級結構；購買決策；灰關聯分析法；multi-index model sequence；grey information package theory；purchase decision；hierarchy structure；grey relational analysis
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灰色理論是新興的決策分析法，其中又以灰關聯分析法是灰色理論中最常被使用的分析方法之一。灰關聯分析法在實際運用時，只能針對多指標數列集內，各數列其元素個數相等之數列進行分析。當各數列元素個數不同時，如何進行灰關聯分析，則是過往研究鮮少提及之地方。面對數列不等長之灰關聯分析問題，本研究運用灰色訊息包、整體在部分中，已知部分可組成最小整體等概念，構建一個新的多指標數列集灰關聯演算法。這個新的演算法共有三個步驟：步驟一，利用聯集的方式進行指標選取，以建構最小整體信息指標集；步驟二，使用最小整體信息指標集，重新建構新的等長數列之最小訊息數列集，以作為原始數列元素個數不同之數列集的替代數列集；步驟三，利用所建立之最小整體信息數列集，進行灰關聯分析。最後，本研究以兩個案例說明本演算法的操作過程與實證結果，其中，案例一是如何藉由演算法進行消費者電腦購買決策分析之應用；案例二則是應用本演算在層級分析法中，選擇最適的層級結構。研究結果顯示本研究所建構之演算法，可做為決策者進行決策分析時之分析工具。
Grey theory is an emerging decision analysis method. Within grey theory, grey relational analysis is one of the most commonly used analytical methods. In practical application of grey relational analysis, only sequences with equal numbers of elements within a multiple index sequence set can be analyzed using the method. How to perform grey relational analysis when the number of elements differs between sequences is an area that has not yet been thoroughly explored by previous studies. In facing grey relational analysis problems with sequences of different lengths, this study employs grey information package theory. In portions of the whole, it is already known that portions can form the least overall equivalence concept to establish a new multiple index sequence grey relational algorithm. This new algorithm is made up of three steps. Step 1: use a union method to perform index selection and establish a least overall message index set. Step 2: use the least overall message index to construct a least message sequence set for sequences of equivalent length to act as a substitute sequence set for the original sequence set consisting of sequences of differing lengths. Step 3: use the established least overall message sequence set to perform grey relational analysis. Finally, this study presents two examples to demonstrate the operational process of the algorithm. The first example applies the algorithm to analysis for purchase decision of a computer. The second example employs the algorithm to select a best-fitting hierarchy structure from analysis hierarchy process for application in decision analysis. Research results show that the algorithm established by this study can be used as an analytical tool for decision-makers in performing decision analysis.
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