## Displaying similar documents to “L-guilds and binary L-merotopies.”

### N-Dimensional Binary Vector Spaces

Formalized Mathematics

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The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields...

### Morphology for Image Processing. Part I

Formalized Mathematics

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In this article we defined mathematical morphology image processing with set operations. First, we defined Minkowski set operations and proved their properties. Next, we defined basic image processing, dilation and erosion proving basic fact about them [5], [8].

### $\gamma$-Compactness in $L$-Topological Spaces

Kragujevac Journal of Mathematics

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### On the $L$-valued categories of $L$-$E$-ordered sets

Kybernetika

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The aim of this paper is to construct an $L$-valued category whose objects are $L$-$E$-ordered sets. To reach the goal, first, we construct a category whose objects are $L$-$E$-ordered sets and morphisms are order-preserving mappings (in a fuzzy sense). For the morphisms of the category we define the degree to which each morphism is an order-preserving mapping and as a result we obtain an $L$-valued category. Further we investigate the properties of this category, namely, we observe some special...

### Relational Formal Characterization of Rough Sets

Formalized Mathematics

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The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based...

### On the Order Type L-valued Relations on L-powersets.

Mathware and Soft Computing

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### On extension of the group operation over the Čech-Stone compactification

Colloquium Mathematicae

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The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto ${\left(\beta \right)}^{2}$ of the group operation. We find a subclass of ultrafilters for which this extension is well-defined and give some examples of pathologies. Next, for a given locally compact group and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to...

### Free Quillen factorization systems.

Georgian Mathematical Journal

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### Generated fuzzy implications and fuzzy preference structures

Kybernetika

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The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet $\left(p,i,j\right)$, which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated.