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This article commences with a brief historical introduction to interval analysis and some applications in engineering. This is followed by a simple example motivating the use of interval analysis. A more detailed definition of interval analysis and some properties are then given followed by a discussion of the application of interval analysis to the problem of computing inclusions for the range of...
In this Chapter, we present results derived in the context of state estimation of a class of real-life systems that are driven by some poorly known factors. For these systems, the representation of uncertainty as confidence intervals or the ellipsoids offers significant advantages over the more traditional approaches with probabilistic representation of noise. While the filtered-white-Gaussian noise...
This paper deals with the estimation of the parameters of a model from experimental data. The aim of the method presented is to characterize the set S of all values of the parameter vector that are acceptable in the sense that all errors between the experimental data and the corresponding model outputs lie between known lower and upper bounds. This corresponds to what is known as bounded-error estimation...
The relevance, applicability and importance of fuzzy sets is generally linked to successful applications in the domain of engineering, especially when subjective notions are modelled and matched with data. For problems in which uncertainty has been modelled using probability theory in the past, discussions on what approach is right, frequently conclude that both should complement each other. In the...
In recent years we witness a rapid growth of interest in rough set theory and its applications, worldwide. The theory has been followed by the development of several software systems that implement rough set operations, in particular for solving knowledge discovery and data mining tasks. Rough sets are applied in domains, such as, for instance, medicine, finance, telecommunication, vibration analysis,...
“Nearest” neighborhoods are informally used in many areas of AI and database. Mathematically, a “nearest” neighborhood system that maps each object p a unique crisp/fuzzy subset of data, representing the “nearest” neighborhood, is a binary relation between the object and data spaces. “Nearest” neighborhood consists of data that are semantically related to p, and represents an elementary granule (atoms)...
Defuzzification is an important operation in the theory of fuzzy sets. It transforms a fuzzy set information into a numeric data information. This operation along with the operation of fuzzification is critical to the design of fuzzy systems as both of these operations provide nexus between the fuzzy set domain and the real valued scalar domain. We need the synergy of both of these domains to solve...
In this chapter, we propose two new algorithms to infer automatically a fuzzy partition for the universe of a set of values, when each of these values is associated with a class. These algorithms are based on the use of mathematical morphology operators that are used to filter the given set of values and highlight kernel for fuzzy subsets. Their purpose is to be used in an inductive learning algorithm...
We present a coding method for linguistic variables which we have named Incremental Discretization. It allows us to express any fuzzy subset of the universe of discourse of the linguistic variable in binary or bipolar terms. This will permit us to process fuzzy information expressed in linguistic terms using discrete models of Artificial Intelligence. In order to test the effectiveness, we apply this...
Fuzzy quantification is a linguistic granulation technique capable of expressing the global characteristics of a collection of individuals, or a relation between individuals, through meaningful linguistic summaries. However, existing approaches to fuzzy quantification fail to provide convincing results in the important case of two-place quantification (e.g. “many blondes are tall”). We develop an...
The structure of fuzzy models produced by a heursitic analysis of the problem domain is compared with that of models algorithmically generated from training data. The trade-offs between granularity, specificity, interpretability, and efficiency are examined for rule-bases produced in each of these manners. An algorithm that combines rule learning with region merging is introduced to incorporate beneficial...
The basic premise of granular computing is that, by reducing precision in our model of a system, we can suppress minor details and focus on the most significant relationships in the system. In this chapter, we will test this premise by defining a granular neural network and testing it on the Iris data set. Our hypothesis is that the granular neural network will be able to learn the Iris data set,...
A review of fuzzy clustering and its use in the data-driven construction of nonlinear models and controllers is given. The focus is on algorithms of the fuzzy c-means type. Two application examples are presented: automated design of operating points for gain scheduling in flight control systems and nonlinear black-box identification. In the latter case, a comparison with an alternative technique is...
The goal of input-output modeling is to apply a test input to a system, analyze the results, and learn something useful from the cause-effect pair. Any automated modeling tool that takes this approach must be able to reason effectively about sensors and actuators and their interactions with the target system. The granulation level of the information involved in this process ranges from low-level data...
The paper deals with optical music recognition (OMR) as a process of structured data processing applied to music notation. Granularity of OMR in both its aspects: data representation and data processing is especially emphasised in the paper. OMR is a challenge in intelligent computing technologies, especially in such fields as pattern recognition and knowledge representation and processing. Music...
In this chapter, we present a new approach for MPEG variable bit rate (VBR) video modeling using a type-2 fuzzy logic system (FLS). We demonstrate that a type-2 fuzzy membership function, i.e., a Gaussian MF with uncertain variance, is most appropriate to model the log-value of I/P/B frame sizes in MPEG VBR video. We treat the video traffic as a dynamic system, and use a type-2 FLS to model this system...
One of the most important problems on rule induction methods is that they cannot extract the rules that plausibly represent experts’ decision processes: the induced rules are too short to represent the reasoning of domain experts. In this paper, the characteristics of experts’ rules are closely examined and a new approach to extract plausible rules is introduced, which consists of the following three...
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