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An ILP model for a monotone graded classification problem

Peter Vojtáš, Tomáš Horváth, Stanislav Krajči, Rastislav Lencses (2004)

Kybernetika

Motivation for this paper are classification problems in which data can not be clearly divided into positive and negative examples, especially data in which there is a monotone hierarchy (degree, preference) of more or less positive (negative) examples. We present a new formulation of a fuzzy inductive logic programming task in the framework of fuzzy logic in narrow sense. Our construction is based on a syntactical equivalence of fuzzy logic programs FLP and a restricted class of generalised annotated...

An inquiry-based method for Choquet integral-based aggregation of interface usability parameters

Miguel-Ángel Sicilia, Elena García Barriocanal, Tomasa Calvo (2003)

Kybernetika

The concept of usability of man-machine interfaces is usually judged in terms of a number of aspects or attributes that are known to be subject to some rough correlations, and that are in many cases given different importance, depending on the context of use of the application. In consequence, the automation of judgment processes regarding the overall usability of concrete interfaces requires the design of aggregation operators that are capable of modeling approximate or ill-defined interactions...

An orthogonality-based classification of conjectures in ortholattices.

Enric Trillas, Ana Pradera (2006)

Mathware and Soft Computing

A mathematical model for conjectures (including hypotheses, consequences and speculations), was recently introduced, in the context of ortholattices, by Trillas, Cubillo and Castiñeira (Artificial Intelligence 117, 2000, 255-257). The aim of the present paper is to further clarify the structure of this model by studying its relationships with one of the most important ortholattices' relation, the orthogonality relation. The particular case of orthomodular lattices -the framework for both Boolean...

Analogie - užitečná heuristická strategie

Petr Eisenmann, Jiří Přibyl (2016)

Učitel matematiky

This article describes a heuristic strategy of analogy and illustrates it by five school mathematics examples. These examples are efficiently solved while using such a strategy.

Analysis of correlation based dimension reduction methods

Yong Joon Shin, Cheong Hee Park (2011)

International Journal of Applied Mathematics and Computer Science

Dimension reduction is an important topic in data mining and machine learning. Especially dimension reduction combined with feature fusion is an effective preprocessing step when the data are described by multiple feature sets. Canonical Correlation Analysis (CCA) and Discriminative Canonical Correlation Analysis (DCCA) are feature fusion methods based on correlation. However, they are different in that DCCA is a supervised method utilizing class label information, while CCA is an unsupervised method....

Analyzing the reasoning mechanisms in fuzzy rule based classification systems.

Oscar Cordón, María José del Jesús, Francisco Herrera (1998)

Mathware and Soft Computing

Fuzzy Rule-Based Systems have been succesfully applied to pattern classification problems. In this type of classification systems, the classical Fuzzy Reasoning Method classifies a new example with the consequent of the rule with the greatest degree of association. By using this reasoning method, we do not consider the information provided by the other rules that are also compatible (have also been fired) with this example.In this paper we analyze this problem and propose to use FRMs that combine...

Ant-based extraction of rules in simple decision systems over ontological graphs

Krzysztof Pancerz, Arkadiusz Lewicki, Ryszard Tadeusiewicz (2015)

International Journal of Applied Mathematics and Computer Science

In the paper, the problem of extraction of complex decision rules in simple decision systems over ontological graphs is considered. The extracted rules are consistent with the dominance principle similar to that applied in the dominancebased rough set approach (DRSA). In our study, we propose to use a heuristic algorithm, utilizing the ant-based clustering approach, searching the semantic spaces of concepts presented by means of ontological graphs. Concepts included in the semantic spaces are values...

Antiassociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2017)

Mathematica Bohemica

Given a groupoid G , , and k 3 , we say that G is antiassociative if an only if for all x 1 , x 2 , x 3 G , ( x 1 x 2 ) x 3 and x 1 ( x 2 x 3 ) are never equal. Generalizing this, G , is k -antiassociative if and only if for all x 1 , x 2 , ... , x k G , any two distinct expressions made by putting parentheses in x 1 x 2 x 3 x k are never equal. We prove that for every k 3 , there exist finite groupoids that are k -antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal.

Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential.

Charles L. Fefferman, Luis A. Seco (1993)

Revista Matemática Iberoamericana

In [FS1] we announced a precise asymptotic formula for the ground-state energy of a non-relativistic atom. The purpose of this paper is to establish an elementary inequality that plays a crucial role in our proof of that formula. The inequality concerns the Thomas-Fermi potentialVTF = -y(ar) / r, a > 0, where y(r) is defined as the solution of⎧   y''(x) = x-1/2y3/2(x),⎨   y(0) = 1,⎩   y(∞) = 0.

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