Fuzzy inference engine, as one of the most important components of fuzzy systems, can obtain some meaningful outputs from fuzzy sets on input space and fuzzy rule base using fuzzy logic inference methods. In order to enhance the computational efficiency of fuzzy inference engine in multi-input-single-output (MISO) fuzzy systems, this paper aims mainly to investigate three MISO fuzzy hierarchial inference engines based on fuzzy implications satisfying the law of importation with aggregation functions (LIA). We firstly find some aggregation functions for well-known fuzzy implications such that they satisfy (LIA) with them. For a given aggregation function, the fuzzy implication which satisfies (LIA) with this aggregation function is then characterized. Finally, we construct three fuzzy hierarchical inference engines in MISO fuzzy systems applying aforementioned theoretical developments.
Time-varying classifiers, namely, evolving classifiers, play an important role in a scenario in which information is available as a never-ending online data stream. We present a new unsupervised learning method for numerical data called evolving Internal-eXternal Fuzzy clustering method (Fuzzy eIX). We develop the notion of double-boundary fuzzy granules and elaborate on its implications. Type 1 and type 2 fuzzy inference systems can be obtained from the projection of Fuzzy eIX granules. We perform the principle of the balanced information granularity within Fuzzy eIX classifiers to achieve a higher level of model understandability. Internal and external granules are updated from a numerical data stream at the same time that the global granular structure of the classifier is autonomously evolved. A synthetic nonstationary problem called Rotation of Twin Gaussians shows the behavior of the classifier. The Fuzzy eIX classifier could keep up with its accuracy in a scenario in which offline-trained classifiers would clearly have their accuracy drastically dropped.
Since then, it has been of interest both for theoretical researcher and application scientists for applications varying from financial analysis, text summarization, image processing, information retrieval, stock prediction to keyword extraction, feature selection to mention a few. Fuzzy Rough Set (Pawlak, 1982, Jensen and Shen, 2004) was proposed for fuzzification of lower and upper approximation, which in applications to problems is very intuitive and useful, given the fact that each member of the universe bears a membership to the set under consideration. Since, there are two sets in a Rough Set based application namely lower approximation and upper approximation, hence, there are two Fuzzy Sets under study in the domains of Fuzzy Rough Set based analysis. In problems in which two Fuzzy Rough Sets have been computed and compared, how to determine the similarity and other relations between these pairs of Fuzzy Rough Sets? This can be illustrated with the example of application validated in this paper, viz.
Odor identification is an important area in a wide range of industries like cosmetics, food, beverages and medical diagnosis among others. Odor detection could be done through an array of gas sensors conformed as an electronic nose where a data acquisition module converts sensor signals to a standard output to be analyzed. To facilitate odors detection a system is required for the identification. This paper presents the results of an automated odor identification process implemented by a fuzzy system and an electronic nose. First, an electronic nose prototype is manufactured to detect organic compounds vapor using an array of five tin dioxide gas sensors, an arduino uno board is used as a data acquisition section. Second, an intelligent module with a fuzzy system is considered for the identification of the signals received by the electronic nose. This solution proposes a system to identify odors by using a personal computer. Results show an acceptable precision.
We revisit Zadeh's notion of "evidence of the second kind" and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and Possibility theory. In this perspective, Dempster-Shafer theory deals with belief functions generated by random sets, while Possibility theory deals with belief functions induced by fuzzy sets. The more general theory allows us to represent and combine evidence that is both uncertain and fuzzy. We demonstrate the application of this formalism to statistical inference, and show that it makes it possible to reconcile the possibilistic interpretation of likelihood with Bayesian inference.