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A categorical view at generalized concept lattices

Stanislav Krajči (2007)


We continue in the direction of the ideas from the Zhang’s paper [Z] about a relationship between Chu spaces and Formal Concept Analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of Krajči [K1]): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image / inverse image operator and show their commutativity...

A discussion on aggregation operators

Daniel Gómez, Montero, Javier (2004)


It has been lately made very clear that aggregation processes can not be based upon a unique binary operator. Global aggregation operators have been therefore introduced as families of aggregation operators { T n } n , being each one of these T n the n -ary operator actually amalgamating information whenever the number of items to be aggregated is n . Of course, some mathematical restrictions can be introduced, in order to assure an appropriate meaning, consistency and key mathematical capabilities. In this...

A Distance-Based Method for Attribute Reduction in Incomplete Decision Systems

Demetrovics, Janos, Thi, Vu Duc, Giang, Nguyen Long (2013)

Serdica Journal of Computing

There are limitations in recent research undertaken on attribute reduction in incomplete decision systems. In this paper, we propose a distance-based method for attribute reduction in an incomplete decision system. In addition, we prove theoretically that our method is more effective than some other methods.

A method for knowledge integration

Martin Janžura, Pavel Boček (1998)


With the aid of Markov Chain Monte Carlo methods we can sample even from complex multi-dimensional distributions which cannot be exactly calculated. Thus, an application to the problem of knowledge integration (e. g. in expert systems) is straightforward.

A rough set-based knowledge discovery process

Ning Zhong, Andrzej Skowron (2001)

International Journal of Applied Mathematics and Computer Science

The knowledge discovery from real-life databases is a multi-phase process consisting of numerous steps, including attribute selection, discretization of real-valued attributes, and rule induction. In the paper, we discuss a rule discovery process that is based on rough set theory. The core of the process is a soft hybrid induction system called the Generalized Distribution Table and Rough Set System (GDT-RS) for discovering classification rules from databases with uncertain and incomplete data....

A short note on Perez’s approximation by dependence structure simplification

Radim Jiroušek (2007)


Perez’s approximations of probability distributions by dependence structure simplification were introduced in 1970s, much earlier than graphical Markov models. In this paper we will recall these Perez’s models, formalize the notion of a compatible system of elementary simplifications and show the necessary and sufficient conditions a system must fulfill to be compatible. For this we will utilize the apparatus of compositional models.

Alternative definitions of conditional possibilistic measures

Ivan Kramosil (1998)


The aim of this paper is to survey and discuss, very briefly, some ways how to introduce, within the framework of possibilistic measures, a notion analogous to that of conditional probability measure in probability theory. The adjective “analogous” in the last sentence is to mean that the conditional possibilistic measures should play the role of a mathematical tool to actualize one’s degrees of beliefs expressed by an a priori possibilistic measure, having obtained some further information concerning...

An Algorithmic Approach to Inferring Cross-Ontology Links while Mapping Anatomical Ontologies

Petrov, Peter, Krachounov, Milko, van Ophuizen, Ernest, Vassilev, Dimitar (2012)

Serdica Journal of Computing

ACM Computing Classification System (1998): J.3.Automated and semi-automated mapping and the subsequently merging of two (or more) anatomical ontologies can be achieved by (at least) two direct procedures. The first concerns syntactic matching between the terms of the two ontologies; in this paper, we call this direct matching (DM). It relies on identities between the terms of the two input ontologies in order to establish cross-ontology links between them. The second involves consulting one or...

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...

Building adaptive tests using Bayesian networks

Jiří Vomlel (2004)


We propose a framework for building decision strategies using Bayesian network models and discuss its application to adaptive testing. Dynamic programming and A O algorithm are used to find optimal adaptive tests. The proposed A O algorithm is based on a new admissible heuristic function.

Can interestingness measures be usefully visualized?

Robert Susmaga, Izabela Szczech (2015)

International Journal of Applied Mathematics and Computer Science

The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These originally four-dimensional...

Concept approximations based on rough sets and similarity measures

Jamil Saquer, Jitender Deogun (2001)

International Journal of Applied Mathematics and Computer Science

The formal concept analysis gives a mathematical definition of a formal concept. However, in many real-life applications, the problem under investigation cannot be described by formal concepts. Such concepts are called the non-definable concepts (Saquer and Deogun, 2000a). The process of finding formal concepts that best describe non-definable concepts is called the concept approximation. In this paper, we present two different approaches to the concept approximation. The first approach is based...

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