Wyniki wyszukiwania - BazTech

Ograniczanie wyników

4 Fundamenta Informaticae

Znaleziono wyników: 4

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Pawlak information system

Sortuj według:

Ogranicz wyniki do:

An Incidence Algebra Approach to Knowledge Granulation in Pawlak Information Systems

Wolski M., Gomolińska A.

Fundamenta Informaticae

2013

Vol. 128, nr 1-2

223--238

Representation theory is a branch of mathematics whose original purpose was to represent information about abstract algebraic structures by means of methods of linear algebra (usually, by linear transformations and matrices). G.-C. Rota in his famous Foundations defined a representation of a locally finite partially ordered set (locally finite poset) P in terms of a module over a ring \mathbbA, which can further be extended by the addition of a convolution operation to an associative \mathbbA-algebra called an incidence algebra of P. He applied this construction to solve a number of important problems in combinatorics. Our goal in this paper is to discuss the concept of an incidence algebra as a representation of a Pawlak information system. We shall analyse both incidence algebras and information systems in the context of granular computing, a paradigm which has recently received a lot of attention in computer science. We discuss therefore the concept of an incidence algebra on two levels: the level of objects which form a preordered set and the level of information granules which form a poset. Since incidence algebras induced on these two levels are Morita equivalent, we may focus our attention on the incidence algebra of information granules. We take the lattice of closed ideals of this algebra, where the maximal elements serve as a representation of information granules. The poset of maximal closed ideals obtained in this way is isomorphic to the set of information granules of the Pawlak information system equipped with a natural information order.

Satisfiability of Formulas from the Standpoint of Object Classification: The RST Approach

Gomolińska A.

Fundamenta Informaticae

2008

Vol. 85, nr 1-4

139-153

In this article we discuss judgment of satisfiability of formulas of a knowledge representation language as an object classification task. Our viewpoint is that of the rough set theory (RST), and the descriptor language for Pawlak's information systems of a basic kind is taken as the study case. We show how certain analogy-based methods can be employed to judge satisfiability of formulas of that language.

Satisfiability and Meaning of Formulas and Sets of Formulas in Approximation Spaces

Gomolińska A.

Fundamenta Informaticae

2005

Vol. 67, nr 1-3

77--92

In this paper, we study general notions of satisfiability and meaning of formulas and sets of formulas in approximation spaces. Rather than proposing one particular form of rough satisfiability and meaning, we present a number of alternative approaches. Approximate satisfiability and meaning are important, among others, for modelling of complex systems like systems of adaptive social agents. Finally, we also touch upon derivative concepts of meaning and applicability of rules.

A Graded Meaning of Formulas in Approximation Spaces

Gomolińska A.

Fundamenta Informaticae

2004

Vol. 60, nr 1-4

159--172

The aim of the paper is to introduce degrees of satisfiability as well as a graded form of the meaning of formulas and their sets in the approximation space framework.