ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Fuzzy expert systems in civil engineering

Imperial Users onl

Modeling of dynamic systems with Petri nets and fuzzy logic

Aktuelle Methoden zur dynamischen Modellierung von biologischen Systemen sind für Benutzer ohne mathematische Ausbildung oft wenig verständlich. Des Weiteren fehlen sehr oft genaue Daten und detailliertes Wissen über Konzentrationen, Reaktionskinetiken oder regulatorische Effekte. Daher erfordert eine computergestützte Modellierung eines biologischen Systems, mit Unsicherheiten und grober Information umzugehen, die durch qualitatives Wissen und natürlichsprachliche Beschreibungen zur Verfügung gestellt wird. Der Autor schlägt einen neuen Ansatz vor, mit dem solche Beschränkungen überwunden werden können. Dazu wird eine Petri-Netz-basierte graphische Darstellung von Systemen mit einer leistungsstarken und dennoch intuitiven Fuzzy-Logik-basierten Modellierung verknüpft. Der Petri Netz und Fuzzy Logik (PNFL) Ansatz erlaubt eine natürlichsprachlich-basierte Beschreibung von biologischen Entitäten sowie eine Wenn-Dann-Regel-basierte Definition von Reaktionen. Beides kann einfach und direkt aus qualitativem Wissen abgeleitet werden. PNFL verbindet damit qualitatives Wissen und quantitative Modellierung.Current approaches in dynamic modeling of biological systems often lack comprehensibility,n especially for users without mathematical background. Additionally, exact data or detailed knowledge about concentrations, reaction kinetics or regulatory effects is missing. Thus, computational modeling of a biological system requires dealing with uncertainty and rough information provided by qualitative knowledge and linguistic descriptions. The author proposes a new approach to overcome such limitations by combining the graphical representation provided by Petri nets with the modeling of dynamics by powerful yet intuitive fuzzy logic based systems. The Petri net and fuzzy logic (PNFL) approach allows natural language based descriptions of biological entities as well as if-then rule based definitions of reactions, both of which can be easily and directly derived from qualitative knowledge. PNFL bridges the gap between qualitative knowledge and quantitative modeling

A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, which rigorously defines the infinitesimals

EXPLOITING HIGHER ORDER UNCERTAINTY IN IMAGE ANALYSIS

Soft computing is a group of methodologies that works synergistically to provide flexible information processing capability for handling real-life ambiguous situations. Its aim is to exploit the tolerance for imprecision, uncertainty, approximate reasoning, and partial truth in order to achieve tractability, robustness, and low-cost solutions. Soft computing methodologies (involving fuzzy sets, neural networks, genetic algorithms, and rough sets) have been successfully employed in various image processing tasks including image segmentation, enhancement and classification, both individually or in combination with other soft computing techniques. The reason of such success has its motivation in the fact that soft computing techniques provide a powerful tools to describe uncertainty, naturally embedded in images, which can be exploited in various image processing tasks. The main contribution of this thesis is to present tools for handling uncertainty by means of a rough-fuzzy framework for exploiting feature level uncertainty. The first contribution is the definition of a general framework based on the hybridization of rough and fuzzy sets, along with a new operator called RF-product, as an effective solution to some problems in image analysis. The second and third contributions are devoted to prove the effectiveness of the proposed framework, by presenting a compression method based on vector quantization and its compression capabilities and an HSV color image segmentation technique

Uncertainty and Interpretability Studies in Soft Computing with an Application to Complex Manufacturing Systems

In systems modelling and control theory, the benefits of applying neural networks have been extensively studied. Particularly in manufacturing processes, such as the prediction of mechanical properties of heat treated steels. However, modern industrial processes usually involve large amounts of data and a range of non-linear effects and interactions that might hinder their model interpretation. For example, in steel manufacturing the understanding of complex mechanisms that lead to the mechanical properties which are generated by the heat treatment process is vital. This knowledge is not available via numerical models, therefore an experienced metallurgist estimates the model parameters to obtain the required properties. This human knowledge and perception sometimes can be imprecise leading to a kind of cognitive uncertainty such as vagueness and ambiguity when making decisions. In system classification, this may be translated into a system deficiency - for example, small input changes in system attributes may result in a sudden and inappropriate change for class assignation. In order to address this issue, practitioners and researches have developed systems that are functional equivalent to fuzzy systems and neural networks. Such systems provide a morphology that mimics the human ability of reasoning via the qualitative aspects of fuzzy information rather by its quantitative analysis. Furthermore, these models are able to learn from data sets and to describe the associated interactions and non-linearities in the data. However, in a like-manner to neural networks, a neural fuzzy system may suffer from a lost of interpretability and transparency when making decisions. This is mainly due to the application of adaptive approaches for its parameter identification. Since the RBF-NN can be treated as a fuzzy inference engine, this thesis presents several methodologies that quantify different types of uncertainty and its influence on the model interpretability and transparency of the RBF-NN during its parameter identification. Particularly, three kind of uncertainty sources in relation to the RBF-NN are studied, namely: entropy, fuzziness and ambiguity. First, a methodology based on Granular Computing (GrC), neutrosophic sets and the RBF-NN is presented. The objective of this methodology is to quantify the hesitation produced during the granular compression at the low level of interpretability of the RBF-NN via the use of neutrosophic sets. This study also aims to enhance the disitnguishability and hence the transparency of the initial fuzzy partition. The effectiveness of the proposed methodology is tested against a real case study for the prediction of the properties of heat-treated steels. Secondly, a new Interval Type-2 Radial Basis Function Neural Network (IT2-RBF-NN) is introduced as a new modelling framework. The IT2-RBF-NN takes advantage of the functional equivalence between FLSs of type-1 and the RBF-NN so as to construct an Interval Type-2 Fuzzy Logic System (IT2-FLS) that is able to deal with linguistic uncertainty and perceptions in the RBF-NN rule base. This gave raise to different combinations when optimising the IT2-RBF-NN parameters. Finally, a twofold study for uncertainty assessment at the high-level of interpretability of the RBF-NN is provided. On the one hand, the first study proposes a new methodology to quantify the a) fuzziness and the b) ambiguity at each RU, and during the formation of the rule base via the use of neutrosophic sets theory. The aim of this methodology is to calculate the associated fuzziness of each rule and then the ambiguity related to each normalised consequence of the fuzzy rules that result from the overlapping and to the choice with one-to-many decisions respectively. On the other hand, a second study proposes a new methodology to quantify the entropy and the fuzziness that come out from the redundancy phenomenon during the parameter identification. To conclude this work, the experimental results obtained through the application of the proposed methodologies for modelling two well-known benchmark data sets and for the prediction of mechanical properties of heat-treated steels conducted to publication of three articles in two peer-reviewed journals and one international conference

Development of a hierarchical fuzzy model for the evaluation of inherent safety

Inherent safety has been recognized as a design approach useful to remove or reduce hazards at the source instead of controlling them with add-on protective barriers. However, inherent safety is based on qualitative principles that cannot easily be evaluated and analyzed, and this is one of the major difficulties for the systematic application and quantification of inherent safety in plant design. The present research introduces the use of fuzzy logic for the measurement of inherent safety by proposing a hierarchical fuzzy model. This dissertation establishes a novel conceptual framework for the analysis of inherent safety and proposes a methodology that addresses several of the limitations of the methodologies available for current inherent safety analysis. This research proposes a methodology based on a hierarchical fuzzy model that analyzes the interaction of variables relevant for inherent safety and process safety in general. The use of fuzzy logic is helpful for modeling uncertainty and subjectivities implied in evaluation of certain variables and it is helpful for combining quantitative data with qualitative information. Fuzzy logic offers the advantage of being able to model numerical and heuristic expert knowledge by using fuzzy IF-THEN rules. Safety is traditionally considered a subjective issue because of the high uncertainty associated with its significant descriptors and parameters; however, this research recognizes that rather than subjective, "safety" is a vague problem. Vagueness derives from the fact that it is not possible to define sharp boundaries between safe and unsafe states; therefore the problem is a "matter of degree". The proposed method is computer-based and process simulator-oriented in order to reduce the time and expertise required for the analysis. It is expected that in the future, by linking the present approach to a process simulator, process engineers can develop safety analysis during the early stages of the design in a rapid and systematic way. Another important aspect of inherent safety, rarely addressed, is transportation of chemical substances; this dissertation includes the analysis of transportation hazard by truck using a fuzzy logic-based approach

A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS - 6th ed.

It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dialectics; b) and its derivative “neutrosophic”, such as “neutrosophic logic”, “neutrosophic set”, “neutrosophic probability”, and “neutrosophic statistics” and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in 1980’s of a new literary and artistic avant-garde movement that he called “paradoxism”, because I received some books and papers dealing with it in order to review them for the German journal “Zentralblatt fur Mathematik”. It was an inspired connection he made between literature/arts and science, philosophy. We started a long correspondence with questions and answers. Because paradoxism supposes multiple value sentences and procedures in creation, antisense and non-sense, paradoxes and contradictions, and it’s tight with neutrosophic logic, I would like to make a small presentation