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Satellite images increasingly become a major data source for monitoring changes in the natural environment. A main task in the analysis of satellite images is concerned with the modelling of land use classes by reducing uncertainty during a classification process. In the approach presented in this paper uncertainty is perceived to be due to the vagueness of geographical categories caused by either the complexity of the category (like 'urban area') or by the use of the category in several application contexts. Two circumstances of use of an extended set theoretical concept (fuzzy sets) are discussed. First, two algorithms from the ISODATA class are used to determine the grades of membership to three a priori defined classes (woodland, suburban area, urban area) of a LANDSAT TM satellite image of Vienna, Austria. The results are visualized by a RGB image of the grades of membership to each category. Second, a measure of fuzziness is employed on the results. The measure relies on the concept of distance between a seUcategory and its complement. The so determined vagueness provide more information on the uncertainty of the different categories and may improve further information processing tasks. (authors' abstract) / Series: Discussion Papers of the Institute for Economic Geography and GIScience

In this thesis, a framework for generic uncertainty analysis is developed. The two basic uncertainty characteristics aleatoric and epistemic uncertainty are differentiated. Polymorphic uncertainty as the combination of these two characteristics is discussed. The main focus is on epistemic uncertainty, with fuzziness as an uncertainty model. Properties and classes of fuzzy quantities are discussed. Some information reduction measures to reduce a fuzzy quantity to a characteristic value, are briefly debated. Analysis approaches for aleatoric, epistemic and polymorphic uncertainty are discussed. For fuzzy analysis α-level-based and α-level-free methods are described. As a hybridization of both methods, non-flat α-level-optimization is proposed. For numerical uncertainty analysis, the framework PUQpy, which stands for “Polymorphic Uncertainty Quantification in Python” is introduced. The conception, structure, data structure, modules and design principles of PUQpy are documented. Sequential Weighted Sampling (SWS) is presented as an optimization algorithm for general purpose optimization, as well as for fuzzy analysis. Slice Sampling as a component of SWS is shown. Routines to update Pareto-fronts, which are required for optimization are benchmarked. Finally, PUQpy is used to analyze example problems as a proof of concept. In those problems analytical functions with uncertain parameters, characterized by fuzzy and polymorphic uncertainty, are examined.

傳統消費者選擇理論通常假設經濟主體為理性且對自身偏好的感受明確，但基於決策者對事物組合間的偏好具有模糊性的現象，使得以明確偏的衡量方式會因分析方法的限制，讓收集而得的資訊被相當程度的扭曲或漏失，因而造成決策的不適當。經濟學家已開始討論有關模糊性的決策行為，而在模糊決策問題中常遭遇需由模糊效用認定事物組合間順序以作選擇的情形，這可經由模糊效用間的直接比較來解決。Ponsard(1986)證明了模糊效用的存在事實；Billot(1992)運用最大轉換算子的處理，將模糊偏好關係以效用來表示。本文利用兩者的概念為基礎，嘗試建立一修正的模糊效用函數，希望對傳統模式的缺失進行改善。而本模式為Billot的轉換算子的延伸，能對無異類集合內的元素進一步地作排序，使合理的偏好幾乎都能被此模式所代表的效用函數刻劃。

We propose a running example for heterogeneous approach based on new type of fuzzification that diversifies fuzziness of every object, fuzziness of every attribute and fuzziness of every table value in a formal context. Moreover we suggest another working examples on heterogeneous environment and provide additional utilization and illustration of this new model that allows to use Formal Concept Analysis also for heterogenenous data. An interpretation of heterogeneous formal concepts and the resulting concept lattice is included.

Σκοπός της παρούσας εργασίας ήταν η δημιουργία ενός ευφυούς συστήματος για τη διάγνωση νοσημάτων του προστάτη αδένα με βάση σημεία και συμπτώματα που διαπιστώνονται σε έναν ασθενή όπως καταγράφονται κατά την κλινική του εξέταση. Τα βασικά σημεία της εργασίας είναι τα εξής: αρχικά παράγεται το μοντέλο της διαγνωστικής στρατηγικής που ακολουθείται για τη διάγνωση των συγκεκριμένων παθήσεων και στη συνέχεια γίνεται εκμαίευση της διαγνωστικής γνώσης από ειδικούς ή/και από εμπειρικά δεδομένα. Η διαδικασία και η γνώση αναπαρίστανται με χρήση υβριδικών μεθόδων αναπαράστασης και με τη χρήση ασάφειας ή/και αβεβαιότητας, η οποία είναι εγγενής σε τέτοια διαγνωστικά συστήματα. Το σύστημα αναπτύχθηκε με τέτοια εργαλεία που δίνουν την δυνατότητα στέγασής του σε ιστότοπο ώστε να χρησιμοποιηθεί ως ειδικός συμβουλευτικός οδηγός από ενδιαφερομένους μη ειδικούς ιατρούς & από ασθενείς καθώς και από φοιτητές υγειονομικών σχολών για εκπαιδευτική χρήση. Το σύστημα περιέχει γνώση εμπειρογνωμόνων σε συνδυασμό με στοιχεία πλούσιας βιβλιογραφικής αναζήτησης και μελέτης. Τέλος πραγματοποιήθηκε επικύρωση των αποτελεσμάτων μέσα από μια τυχαιοποιημένη κλινική έρευνα. Η υλοποίηση του συστήματος μας στηρίζεται σε ένα ειδικό κέλυφος δημιουργίας ευφυών συστημάτων και σε εργαλεία μεθόδων μηχανικής μάθησης. Επίσης, υλοποιούνται δύο εκδοχές (Hirofilos Ι & ΙΙ) και γίνεται σύγκριση των απο-τελεσμάτων. Αναγνωρίστηκε η σαφής υπεροχή του Hirofilos ΙΙ που αναπτυχθηκε με σύστημα μηχανικής εκμάθησης και με δυνατότητα διαχρονικής αναβάθμισης. / During making this project our concern was the creation of a new expert system for diagnosis prostate disease depending on the clinical status of a patient as these are identified during medical examination. The main points were as follows: First has been constructed a diagnosis process model which was followed by the diagnosis for the most common prostate diseases. Secondly was implemented extracting of the medical knowledge based on specialists or/and experimental data. The whole process and the medical Knowledge will be developed using hybrid methods of representation and having the partcipation of such saying fuzziness or inaccuracy, that is innate in that kind of intelligent decision-support. The new intelligent system is already accommodated on a hospital server and is used as a decision-support system, as well as an e-learning platform for medical students. For the implementation of the new system have been used an expert system shell and knowledge engineering tools.

We propose a running example for heterogeneous approach based on new type of fuzzification that diversifies fuzziness of every object, fuzziness of every attribute and fuzziness of every table value in a formal context. Moreover we suggest another working examples on heterogeneous environment and provide additional utilization and illustration of this new model that allows to use Formal Concept Analysis also for heterogenenous data. An interpretation of heterogeneous formal concepts and the resulting concept lattice is included.

Video database applications call for flexible and powerful modeling and querying facilities, which require an integration or interaction between database and knowledge base technologies. It is also necessary for many real life video database applications to incorporate uncertainty, which naturally occurs due to the complex and subjective semantic content of video data. In this thesis study, firstly, a fuzzy conceptual data model is introduced to represent the semantic content of video data. UML (Unified Modeling Language) is utilized and extended to represent uncertain information along with video specific properties at the conceptual level. Secondly, an intelligent fuzzy object-oriented database framework is presented for video database applications. The introduced fuzzy conceptual model is mapped to the presented framework, which is an adaptation of the previously proposed IFOOD architecture. The framework provides modeling and querying of complex and rich semantic content and knowledge of video data including uncertainty. Moreover, it allows (fuzzy) semantic, temporal, (fuzzy) spatial, hierarchical, regional and trajectory queries, based on the video data model. We think that the presented conceptual data model and framework can be adapted to any application domain related to video databases.

In some classification problems where human judgments, qualitative and imprecise data exist, uncertainty comes from fuzziness rather than randomness. Limited number of fuzzy classification approaches is available for use for these classification problems to capture the effect of fuzzy uncertainty imbedded in data. The scope of this study mainly comprises two parts: new fuzzy classification approaches based on Tanaka&rsquo / s Fuzzy Linear Regression (FLR) approach, and an improvement of an existing one, Improved Fuzzy Classifier Functions (IFCF). Tanaka&rsquo / s FLR approach is a well known fuzzy regression technique used for the prediction problems including fuzzy type of uncertainty. In the first part of the study, three alternative approaches are presented, which utilize the FLR approach for a particular customer satisfaction classification problem. A comparison of their performances and their applicability in other cases are discussed. In the second part of the study, the improved IFCF method, Nonparametric Improved Fuzzy Classifier Functions (NIFCF), is presented, which proposes to use a nonparametric method, Multivariate Adaptive Regression Splines (MARS), in clustering phase of the IFCF method. NIFCF method is applied on three data sets, and compared with Fuzzy Classifier Function (FCF) and Logistic Regression (LR) methods.

In the paper at hand we apply it to Bayesian statistics to obtain "Fuzzy Bayesian Inference". In the subsequent sections we will discuss a fuzzy valued likelihood function, Bayes' theorem for both fuzzy data and fuzzy priors, a fuzzy Bayes' estimator, fuzzy predictive densities and distributions, and fuzzy H.P.D .-Regions. (author's abstract) / Series: Forschungsberichte / Institut für Statistik