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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 ⊕ and ⊗ , respectively). The eigenproblem is the search for a vector x (an eigenvector) and a constant λ (an eigenvalue) such that A ⊗ x = λ ⊗ x , where A is a given matrix. This paper investigates a generalization of the eigenproblem in fuzzy algebra. We solve the equation A ⊗ x = λ ⊗ B ⊗ x with given matrices A , B and unknown constant λ and vector x . Generalized eigenvectors have interesting...

Tolerances on poset algebras

Bohdan Zelinka (1992)

Mathematica Bohemica

To everz partiallz ordered set a certain groupoid is assigned. A tolerance on it is defined similarlz as a congruence, onlz the requirement of transitivitz is omitted. Some theorems concerning these tolerances are proved.

Tolerances on powers of a finite algebra

Jaromír Duda (1992)

Mathematica Bohemica

It is shown that any power A n , n ≥ 2 , of a finite k -element algebra A , k ≥ 2 , has factorable tolerances whenever the power A 4 k 2 - 3 k has the same property.

Currently displaying 81 – 100 of 125