Related papers: Fuzzy Categories
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…
Cofibration categories are a formalization of homotopy theory useful for dealing with homotopy colimits that exist on the level of models as colimits of cofibrant diagrams. In this paper, we deal with their enriched version. Our main result…
In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics…
For a set-endofunctor $F$, we extend the notion of universal $F$-coalgebras to $F$-graphs. These generalized coalgebras are models for various types of graphs, such as (un)directed (hyper)graphs, relational structures or fuzzy graphs. The…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
Description Logics (DLs) are appropriate, widely used, logics for managing structured knowledge. They allow reasoning about individuals and concepts, i.e. set of individuals with common properties. Typically, DLs are limited to dealing with…
This paper examines attribute dependencies in data that involve grades, such as a grade to which an object is red or a grade to which two objects are similar. We thus extend the classical agenda by allowing graded, or fuzzy, attributes…
We introduce continuous Frobenius categories. These are topological categories which are constructed using representations of the circle over a discrete valuation ring. We show that they are Krull-Schmidt with one indecomposable object for…
We construct an explicit combinatorial model of the functor which adds right adjoints to the morphisms of an $\infty$-category, and we speculate on possible extensions to higher dimensions.
Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical…
A groupoid is a small category in which all morphisms are isomorphisms. An inductive groupoid is a specialised groupoid whose object set is a regular biordered set and the morphisms admit a partial order. A normal category is a specialised…
fc-multicategories are a very general kind of two-dimensional structure, encompassing bicategories, monoidal categories, double categories and ordinary multicategories. We define them and explain how they provide a natural setting for two…
To each colored graph, one can associate its closure in the universal space of isomorphism classes of pointed colored graphs, and this subspace can be regarded as a generalized subshift. Based on this correspondence, we extend the notion of…
Cographs--defined most simply as complete graphs with colored lines--both dualize and generalize ordinary graphs, and promise a comparably wide range of applications. This article introduces them by examples, catalogues, and elementary…
There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely…
In the standard Category of Graphs, the graphs allow only one edge to be incident to any two vertices, not necessarily distinct, and the graph morphisms must map edges to edges and vertices to vertices while preserving incidence. We refer…
The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
Fuzzy measures, also referred to as nonadditive measures, emerge from the foundational concept of additive measures by transforming additivity into monotonicity. In comparison to the expansive $2^n$ coefficients of fuzzy measures, additive…