“…Note that different t-norms were used in Ref. 35 to model AND operator in fuzzy classiÞcation rules with triangular antecedent membership functions. However, our aim is not to generate fuzzy classiÞcation rules, but by clustering we want to generate a fuzzy model from any given data.…”
The tuning of a fuzzy model is discussed in the context of choices made between different t-norms. The effects of the choice is illustrated by looking at two fuzzy models initially generated, respectively, by grid partition and a novel variant of subtractive clustering. The new variant of subtractive clustering introduced in the paper is based on the standard method of subtractive clustering, where in this new method, the measure of similarity and thus also cluster shapes depend on a choice of t-norm T . C
“…Note that different t-norms were used in Ref. 35 to model AND operator in fuzzy classiÞcation rules with triangular antecedent membership functions. However, our aim is not to generate fuzzy classiÞcation rules, but by clustering we want to generate a fuzzy model from any given data.…”
The tuning of a fuzzy model is discussed in the context of choices made between different t-norms. The effects of the choice is illustrated by looking at two fuzzy models initially generated, respectively, by grid partition and a novel variant of subtractive clustering. The new variant of subtractive clustering introduced in the paper is based on the standard method of subtractive clustering, where in this new method, the measure of similarity and thus also cluster shapes depend on a choice of t-norm T . C
“…The fuzzy classification system. We decided to use Gaussian (bell-shaped) functions, as they result in smooth decision boundaries when prod-max inference is used [35]. Additionally, we allow the linguistic term don't care in the antecedents, associated with a fuzzy set l dc , 8x 2 X : l dc ðxÞ ¼ 1.…”
The interpretability and flexibility of fuzzy ifthen rules make them a popular basis for classifiers. It is common to extract them from a database of examples. However, the data available in many practical applications are often unlabeled, and must be labeled manually by the user or by expensive analyses. The idea of semi-supervised learning is to use as much labeled data as available and try to additionally exploit the information in the unlabeled data. In this paper we describe an approach to learn fuzzy classification rules from partially labeled datasets.
“…A few current approaches have some limitations due to either their ad hoc nature, or their ability to deal with only a specific aspect of the problem of visualisation of fuzzy systems [2,4,5,12,11,15,16]. In addition, visualisation methods are often focused on data sets and only loosely coupled with the analytical process.…”
Abstract.Complex fuzzy systems exist in many applications and effective visualisation is required to gain insights in the nature and working of these systems, especially in the implication of impreciseness, its propagation and impacts on the quality and reliability of the outcomes. This paper presents a design of a visualisation system based on multi-agent approach with the aim to facilitate the organisation and flow of complex tasks, their inter-relationships and their interactions with users. This design extends our previous work on the analysis of the fundamental ontologies which underpin the structure and requirements of fuzzy systems.
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