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Orthocomplemented difference lattices with few generators

Milan Matoušek, Pavel Pták (2011)

Kybernetika

The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result...

Orthomodular lattices with almost orthogonal sets of atoms

Sylvia Pulmannová, Vladimír Rogalewicz (1991)

Commentationes Mathematicae Universitatis Carolinae

The set A of all atoms of an atomic orthomodular lattice is said to be almost orthogonal if the set { b ∈ A : b ≰ a ' } is finite for every a ∈ A . It is said to be strongly almost orthogonal if, for every a ∈ A , any sequence b 1 , b 2 , ⋯ of atoms such that a ≰ b 1 ' , b 1 ≰ b 2 ' , ⋯ contains at most finitely many distinct elements. We study the relation and consequences of these notions. We show among others that a complete atomic orthomodular lattice is a compact topological one if and only if the set of all its atoms is almost orthogonal.

Ovchinnikov's automorphisms revisited.

Enric Trillas, Adolfo Rodríguez de Soto, Susana Cubillo (1994)

Mathware and Soft Computing

In [6] an approach to the representation of synonyms and antonyms via the automorphisms of the De Morgan Algebra [0,1]X was suggested. In [3], Ovchinnikov established a representation theorem for automorphisms of the function's complete and completely distributive lattice [0,1]X with the pointwise extension of Min and Max operations in [0,1]. Ovchinnikov results are now inmediately generalized by using a positive t-norm T and its dual eta-dual t-conorm T*. These results are applied to study the...

OWA operators for discrete gradual intervals: implications to fuzzy intervals and multi-expert decision making

Zdenko Takáč (2016)

Kybernetika

A new concept in fuzzy sets theory, namely that of gradual element, was introduced recently. It is known that the set of gradual real numbers is not ordered linearly. We restrict our attention to a discrete case and propose a class of linear orders for discrete gradual real numbers. Then, using idea of the so-called admissible order of intervals, we present a class of linear orders for discrete gradual intervals. Once we have the linear orders it is possible to define OWA operator for discrete gradual...

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