Piecewise-linear approximation of nonlinear models based on interval numbers (INs)

Linear models are ususally preferable due to their simplicity. However, nonlinear models often emerge in practice. A popular approach for dealing with nonlinearities is using a piecewise-linear approximation. In such context, inspired from both Fuzzy Inference Systems (FISs) of TSK type and Self-Organizing Maps (SOMs), this work introduces enhancements based on Interval Numbers and, ultimately, on lattice theory. Advantages include a capacity to deal with granular inputs, introduction of tunable nonlinearities, representation of all-order statistics, and induction of descriptive decision-making knowledge (rules) from the training data. Preliminary computational experiments here demonstrate a good capacity for generalization; furthermore, only a few rules are induced

Fuzzy Interval Numbers (FINs): Lattice theoretic tools for improving prediction of sugar production from populations of measurements

Abstract – This work presents novel mathematical tools developed during a study of an industrial-yield prediction problem. The set F of Fuzzy Interval Numbers, or FINs for short, is studied in the framework of lattice theory. A FIN is defined as a mapping to a metric lattice of generalized intervals, moreover it is shown analytically that the set F of FINs is a metric lattice. A FIN can be interpreted as a convex fuzzy set, moreover a statistical interpretation is proposed here. Algorithm CALFIN is presented for constructing a FIN from a population of samples. An underlying positive valuation function implies both a metric distance and an inclusion measure function in the set F of FINs. Substantial advantages, both theoretical and practical, are shown. Several examples illustrate geometrically on the plane both the utility and the effectiveness of novel tools. It is outlined comparatively how some of the proposed tools have been employed for improving prediction of sugar production from populations of measurements for Hellenic Sugar Industry, Greece

Lattice Computing: A Mathematical Modelling Paradigm for Cyber-Physical System Applications

By “model”, we mean a mathematical description of a world aspect [...

A Comparison Of Word- and Sense-Based . . .

Most of the text categorization algorithms in the literature represent documents as collections of words. An alternative which has not been sufficiently explored is the use of word meanings, also known as senses. In this paper, using several algorithms, we compare the categorization accuracy of classifiers based on words to that of classifiers based on senses. The document collection on which this comparison takes place is a subset of the annotated Brown Corpus semantic concordance. A series of experiments indicates that the use of senses does not result in any significant categorization improvement