Related papers: A countable set derived by fuzzy set
Every mathematical structure has an elementary extension to a pseudo-countable structure, one that is seen as countable inside a suitable class model of set theory, even though it may actually be uncountable. This observation, proved easily…
The paper deals with special types of $L$-ordered set, $L$-fuzzy complete lattices, and fuzzy directed complete posets (fuzzy $dcpo$s). First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an…
A fractional fuzzy Potts measure is a probability distribution on spin configurations of a finite graph $G$ obtained in two steps: first a subgraph of $G$ is chosen according to a random cluster measure $\phi_{p,q}$, and then a spin…
This paper deals with the resolutions of fuzzy relation equations with addition-min composition. When the fuzzy relation equations have a solution, we first propose an algorithm to find all minimal solutions of the fuzzy relation equations…
In a series of papers, M.Talagrand, the second author and others investigated at length the properties and structure of pointwise compact sets of measurable functions. A number of problems, interesting in themselves and important for the…
It is shown that CH implies the existence of a compact Hausdorff space that is countable dense homogeneous, crowded and does not contain topological copies of the Cantor set. This contrasts with a previous result by the author which says…
We show that the consistency of $\mathrm{ZF} + \mathrm{AD}_{\mathbb{R}} + ``\Theta$ is measurable$"$ implies the consistency of $\mathrm{ZF} +``\Theta$ is the least strongly regular cardinal and the least measurable cardinal$"$ + $``$all…
For a set of distances D={d_1,...,d_k} a set A is called D-avoiding if no pair of points of A is at distance d_i for some i. We show that the density of A is exponentially small in k provided the ratios d_1/d_2, d_2/d_3, ..., d_{k-1}/d_k…
We consider capacity (fuzzy measure, non-additive probability) on a compactum as a monotone cooperative normed game. Then it is naturally to consider probability measures as elements of core of such game. We prove an analogue of…
Given any compact manifold M, we construct a non-empty open subset O of the space of C^1-diffeomorphisms of M and a dense subset D of O such that the centralizer of every diffeomorphism in D is uncountable, hence non-trivial.
Evaluating argument strength in quantitative argumentation systems has received increasing attention in the field of abstract argumentation. The concept of acceptability degree is widely adopted in gradual semantics, however, it may not be…
We prove a compactness criterion in $L^p({\mu},X)$: a subset of $L^p({\mu},X)$ is relatively norm compact iff the set of integrals of its functions over any measurable set is relatively norm compact, it satisfies the Fr\'echet oscillation…
In this paper we define fuzzy sequential topology on a non empty set X which is a collection of fuzzy sequential sets satisfying certain conditions given in its definition and many pleasant properties of a countable number of fuzzy…
A set of graphs is said to be independent if there is no homomorphism between distinct graphs from the set. We consider the existence problems related to the independent sets of countable graphs. While the maximal size of an independent set…
Given a subset of $X\subseteq \mathbb{R}^{n}$ we can associate with every point $x\in \mathbb{R}^{n}$ a vector space $V$ of maximal dimension with the property that for some ball centered at $x$, the subset $X$ coincides inside the ball…
Under $\mathrm{ZF}$, we show that the statement that every subset of every $\mathbb{R}$-vector space has a maximal convex subset is equivalent to the Axiom of Choice. We also study the strength of the same statement restricted to some…
In the first part we construct some Buck measurable sets. In the second part we apply the Niven theorem for Buck's measure density to certain sets.
Higher order set theory has been a topic of interest for some time, with recent efforts focused on the strength of second order set theories [KW16]. In this paper we strive to present one 'theory of collections' that allows for a formal…
We describe in this paper additively left stable sets, i.e. sets satisfying $\left((A+A)-\inf(A)\right)\cap[\inf(A),\sup(A)]=A$ (meaning that $A-\inf(A)$ is stable by addition with itself on its convex hull), when $A$ is a finite subset of…
We consider approximately greater than relations on fuzzy sets and discuss their properties.