EUDML

A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.

Eigenspace of a circulant max–min matrix

Martin Gavalec; Hana Tomášková — 2010

Kybernetika

The eigenproblem of a circulant matrix in max-min algebra is investigated. Complete characterization of the eigenspace structure of a circulant matrix is given by describing all possible types of eigenvectors in detail.

Monotone interval eigenproblem in max–min algebra

Martin Gavalec; Ján Plavka — 2010

Kybernetika

The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented.

Products of ideals of Borel sets

Gavalec, Martin — 1981

Abstracta. 9th Winter School on Abstract Analysis

О ширине категории моноунарных алгебр

Martin Gavalec; Danica Jakubíková-Studenovská — 1978

Mathematica Slovaca

Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix

Imran Rashid; Martin Gavalec; Sergeĭ Sergeev — 2012

Kybernetika

Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Łukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to...

Tolerance problems for generalized eigenvectors of interval fuzzy matrices

Martin Gavalec; Helena Myšková; Ján Plavka; Daniela Ponce — 2022

Kybernetika

Fuzzy algebra is a special type of algebraic structure in which classical addition and multiplication are replaced by maximum and minimum (denoted $\oplus$ and $\otimes$ , respectively). The eigenproblem is the search for a vector $x$ (an eigenvector) and a constant $λ$ (an eigenvalue) such that $A \otimes x = λ \otimes x$ , where $A$ is a given matrix. This paper investigates a generalization of the eigenproblem in fuzzy algebra. We solve the equation $A \otimes x = λ \otimes B \otimes x$ with given matrices $A, B$ and unknown constant $λ$ and vector $x$ . Generalized eigenvectors have interesting...