近年來，由於人類對自然現象、社會現象或經濟現象的認知意識逐漸產生多元化的研判與詮釋，也因此致使人類思維數據化的概念已逐漸廣泛的被應用，對數據分析已從傳統以單一數值或平均值的分析作法，演變為考量多元化數值的分析作為。有鑑於此，在數據資料具備「模糊性」特質的現今，藉由模糊區間的演算方法，進一步探討之間的關係。 傳統的統計分析，對於兩變數間線性關係的強度判斷，一般是藉由皮爾森相關係數（Pearson’s Correlation Coefficient）的方法予以衡量，同時也可以經由係數的正、負符號判斷變數間的關係方向。然而，在現實生活中無論是環境資料或社會經濟資料等，均可能以模糊的資料型態被蒐集，如果當資料型態係屬於模糊性質時，將無法透過皮爾森相關係數的方法計算。 因此，本研究欲研擬一個較簡而易懂的方法，計算模糊區間資料的相關係數，據以呈現兩組模糊區間資料的相互影響程度。此外，若時間性之模糊區間資料被蒐集之際，我們亦提出利用中心點與長度之模糊自相關係數（ACF with the Fuzzy Data of Center and Length；簡稱CLACF）及模糊區間資料之自相關函數(ACF with Fuzzy Interval Data；簡稱FIACF)的方法，探討時間性模糊資料的自相關係數予以衡量。 / The classical Pearson’s correlation coefficient has been widely adopted in various fields of application. However, when the data are composed of fuzzy interval values, it is not feasible to use such a traditional approach to evaluate the correlation coefficient. In this study, we propose the specific calculation of fuzzy interval correlation coefficient with fuzzy interval data to measure the relationship between various stocks. In addition, in time series analysis, the auto-correlation function (ACF) can evaluate the effect of stationary for time series data. However, as the fuzzy interval data could be occurred, then the classical time series analysis will be not applied. In this paper, we proposed two approaches, ACF with the fuzzy data of center and length (CLACF) and ACF with fuzzy interval data (FIACF), to calculate the auto-correlation coefficient for fuzzy interval data, and use the scheme of Mote Carlo simulation to illustrate the effect of evaluation methods. Finally, we offer empirical study to indentify the performance of CLACF and FIACF which may measure the effect of lagged period of fuzzy interval data for daily price (low, high) of the Centralized Securities Trading Market and the result show that the effect of evaluation lagged period via CLACF and FIACF may response the effect more easily than classical evaluation of ACF for the close price of Centralized Securities Trading Market.

資料分類的應用在時間數列的分析與預測過程相當重要。而模糊資料近年來更受到重視，其應用的範圍包含：財金、社會、生醫、電機等各個領域。本研究欲運用模糊資料分類法，對區間時間數列的轉折偵測與模式建構做一個深入探討。主要應用平均累加模糊熵(average of the sum of fuzzy entropies)， 找出其結構性改變的區間。並針對區間型時間數列進行模式建構診斷與預測。最後我們以單身人口數與失業率為實列做一個詳細的探討。結果顯示，失業率對單身人口數有顯著的影響而孤鸞年的效應並不顯著。 / The application of data classifications in time series analysis and forecasting is rather important. The fuzzy data classification has received much attention recently. It can be applied on various fields such as finance, sociology, biomedicine, electrical engineering and so on. This study is to use the fuzzy data classification to perform an intensive research on the change periods detection and model construction of the interval time series. We use average of the sum of fuzzy entropies to find out interval of the structural changes. Focusing on the time series of intervals, we build a model and make prediction about it. At the end, based on the case study on the population of singles versus, we thoroughly discuss this topic. The result shows that the unemployment rate does significantly correlate with the population of singles, but the "widow's year" does not .

Aujourd’hui, les recherches autour du stockage et de l’intégration des données spatiales constituent un maillon important qui redynamise les recherches sur la qualité des données. La prise en compte de l’imperfection des données géographiques, particulièrement l’imprécision, ajoute une réelle complexification. Parallèlement à l’augmentation des exigences de qualité centrées sur les données (précision, exhaustivité, actualité), les besoins en information intelligible ne cessent d’augmenter. Sous cet angle, nous sommes intéressés aux bases de données géographiques imprécises (BDGI) et leur cohérence. Ce travail de thèse présente des solutions pour la modélisation et la construction des BDGI et cohérentes pour les SGBD SQL et NoSQL.Les méthodes de modélisation conceptuelle de données géographiques imprécises proposées ne permettent pas de répondre de façon satisfaisante aux besoins de modélisation du monde réel. Nous présentons une version étendue de l’approche F-Perceptory pour la conception de BDGI. Afin de construire la BDGI dans un système relationnel, nous présentons un ensemble de règles de transformation automatique de modèles pour générer à partir du modèle conceptuel flou le modèle physique. Nous implémentons ces solutions sous forme d’un prototype baptisé FPMDSG.Pour les systèmes NoSQL type document. Nous présentons un modèle logique baptisé Fuzzy GeoJSON afin de mieux cerner la structure des données géographiques imprécises. En plus, ces systèmes manquent de pertinence pour la cohérence des données ; nous présentons une méthodologie de validation pour un stockage cohérent. Les solutions proposées sont implémentées sous forme d'un processus de validation. / Today, research on the storage and the integration of spatial data is an important element that revitalizes the research on data quality. Taking into account the imperfection of geographic data particularly the imprecision adds a real complexity. Along with the increase in the quality requirements centered on data (accuracy, completeness, topicality), the need for intelligible information (logically consistent) is constantly increasing. From this point of view, we are interested in Imprecise Geographic Databases (IGDBs) and their logical coherence. This work proposes solutions to build consistent IGDBs for SQL and NoSQL database systems.The design methods proposed to imprecise geographic data modeling do not satisfactorily meet the modeling needs of the real world. We present an extension to the F-Perceptory approach for IGDBs design. To generate a coherent definition of the imprecise geographic objects and built the IGDB into relational system, we present a set of rules for automatic models transformation. Based on these rules, we develop a process to generate the physical model from the fuzzy conceptual model. We implement these solutions as a prototype called FPMDSG.For NoSQL document oriented databases, we present a logical model called Fuzzy GeoJSON to better express the structure of imprecise geographic data. In addition, these systems lack relevance for data consistency; therefore, we present a validation methodology for consistent storage. The proposed solutions are implemented as a schema driven pipeline based on Fuzzy GeoJSON schema and semantic constraints.