多向度評量法改良及應用之研究__臺灣人文及社會科學引文索引資料庫

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題名：	多向度評量法改良及應用之研究
作者：	陳奕廣
作者(外文)：	Yi-Kuang Chen
校院名稱：	國立臺灣科技大學
系所名稱：	工業管理系
指導教授：	周碩彥
學位類別：	博士
出版日期：	2000
主題關鍵詞：	多向度評量法；設施佈置；模糊理論；模糊群聚；模擬退火法；Multidimensional Scaling (MDS)；Facilities Layout；ALSCAL；Fuzzy Theory；Fuzzy Clustering；Simulated Annealing
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多向度評量法或稱為多元尺度法是種簡單而有用的數學工具，讓我們猶如在地圖上，在空間中將受試體之相似性呈現出來，多向度評量法可在概念與基本向度未完全掌握的領域中使其資料系統化。多向度評量法最早是在心理學領域發展出來的﹐引用在行銷上，經常用以探討產品認知空間來瞭解消費者對所調查產品的認知情形、發現消費者的需求及定位新產品的走向等。本論文旨在探討多向度評量法之改良與應用，在改良方面，主要利用模糊理論改善多向度評量法分析資料之人為主觀描逑能力，在應用方面是以設施佈置為例，探討多向度評量法在工業管理應用之可行性。
在實務上，設施佈置問題由於考慮因素眾多，往往很難找到最佳解，故文獻上大都採用數學規劃、圖解法和啟發式法則等方法以求得近似解。我們應用多向度評量法和模擬退火法發展一同時考慮定性與定量因素之設施佈置整合系統，作為企業界建立設施佈置之輔助工具。我們使用多向度評量法處理部門間相關性之定性因素，將設施佈置之多項因素(多維空間)降低為最大相關性之二維佈置圖，以便作為產生實際佈置空間之依據。且考慮空間大小限制、搬運成本等量化因素，利用模擬退火法解決在bay structure中為了找最佳佈置之旋轉角度，以期得到最小搬運成本和部門區域變異之最佳佈置圖，如此將使結果更具整體及合理性，以符合產業界之實務需要。
多向度評量法從輸入資料之相似性(或偏好性)至輸出資訊之向度決定均受到人為因素之影響，充滿高度之不確定性。多向度評量法所收集之相似性(或偏好性)資料一般不是點資料，而是區間資料，傳統多向度評量法程式之輸入將其簡化為點資料，如此將降低其資料描逑之正確性。模糊理論是目前處理不確定性的重要方法，不僅學術界廣為使用，且已大量應用在工業產品上。為了有效解決多向度評量法之主觀資料描逑的需求，我們導入模糊數之觀念並證明其適用性，且以常用之多向度評量法程式ALSCAL為例，將其改成可處理模糊數之FALSCAL(Fuzzy-ALSCAL)程式，處理模糊多向度評量法系統所收集之模糊輸入值，使多向度評量法所處理之資料更能反應實際狀況。
另外，分析多向度評量法之輸出，一般均由分析者根據其專業及主觀之判斷，僅在二維空間直接分群並分析之，如此極為依賴分析者之整体分辨力，且資料由多維降為二維時已流失部份資訊。模糊群聚演算法是模糊理論在群聚分析之常用工具，是一種根據相似性或相異性，利用一定的演算法，客觀地將相似者歸集在同一群組的分析技術，故我們建立以模糊群聚演算法協助分析之工具，並以視覺化之方式呈現其結果以利分析者判斷工作之進行。

以文找文

MDS is a useful mathematical tool that enables the spatial representation of the similarities of objects as in a map and the systematization of data in areas where organized concepts and underlying attributes are not well developed. In this thesis, the improvement and application of the Multidimensional Scaling (MDS)} methodology is studied. The fuzzy set theory is used to improve the subjectivity characterization of MDS. A procedure for generating facility layout is established to illustrate the applicability of MDS in the domain of industrial management.
The facility layout problems are very difficult from a practical as well as a methodological point of view. Thus, mathematical programming, graphical, and heuristic techniques have been applied to layout problems for identifying satisfactory, rather than optimal, solutions. In this thesis, MDS algorithms are used as dimension reduction tools, arranging facilities in a two-dimensional space while preserving the adjacency relationship between facilities. The output of MDS is a scatter diagram, and is in turn used as the input or location reference for developing into the final block layout. The bay structures of the layout are considered where the given floor space is first partitioned horizontally or vertically into bays, which are subsequently partitioned into the blocks. The simulated annealing approach is adopted to rotate the scatter diagram so that a layout with the minimum total cost of traveling between facilities and the least shape violation is found.
The input data of MDS is usually obtained through questionnaire administration. It has been established that the decision or judgement made by a respondent is usually inexact, and therefore should be represented by a range rather than an exact value. Fuzzy set theory is an important tool in uncertain environment, and has many applications in various fields. Fuzzy numbers from fuzzy set theory are used to characterize such ranges in order to enhance the subjectivity characterization of MDS input. Fuzzy data collected from fuzzy questionnaires is used as the input of the MDS so that the uncertainty of input data can be incorporated in the analysis. By employing the notion of fuzzy distances for representing the similarity between fuzzy data, the popular ALSCAL procedure is modified to deal with fuzzy input data.
In addition, in traditional MDS analysis the clustering is done visually with the two dimensional arrangement of stimuli. As the MDS approach may distort the relation among the stimuli during the dimension reduction process, the clustering should therefore be performed in a higher dimensional space to include as much original information as possible. The interpretation of the two-dimensional arrangement of stimulus points output from MDS systems is essential to the effectiveness of the analysis. To enhance such a process, a fuzzy clustering tool, which provides various sets of clusters based on the requirement on the degree of similarity, is developed and integrated with an MDS system.

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