Related papers: A countable set derived by fuzzy set
An $\omega_1$-compact space is a space in which every closed discrete subspace is countable. We give various general conditions under which a locally compact, $\omega_1$-compact space is $\sigma$-countably compact, i.e., the union of…
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan's theorem on a superstable theory.
The concept of weighted $\beta\gamma$ - summability of order $\theta$ in case of fuzzy functions is introduced and classified into ordinary and absolute sense. Several inclusion relations among the sets are investigated. Also we have found…
We give a partial solution to a question by Alas, Junqueria and Wilson by proving that under PFA the one-point compactification of a locally compact, discretely generated and countably tight space is also discretely generated. After this,…
The authors introduced in a previous paper the notion of fuzzy Gromov-Hausdorff distance between non-Archimedean compact fuzzy metric spaces, presenting a fuzzy version of the Gromov's completeness theorem. In this paper we present a fuzzy…
From the more than two hundred partial orders for fuzzy numbers proposed in the literature, only a few are total. In this paper, we introduce the notion of admissible order for fuzzy numbers equipped with a partial order, i.e. a total order…
Classical machine learning classifiers tend to be overconfident can be unreliable outside of the laboratory benchmarks. Properly assessing the reliability of the output of the model per sample is instrumental for real-life scenarios where…
We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be.…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
We show (in ZFC) that the cardinality of a compact homogeneous space of countable tightness is no more than the size of the continuum.
This note presents a presheaf theoretic approach to the construction of fuzzy sets, which builds on Barr's description of fuzzy sets as sheaves of monomorphisms on a locale. A presheaf-theoretic method is used to show that the category of…
We consider a complete metric space $(X,d)$ and a countable number of contractive mappings on $X$, $\mathcal{F}=\{F_i:i\in\mathbb N\}$. We show the existence of a {\em smallest} invariant set (with respect to inclusion) for $\mathcal{F}$.…
This report presents an expression for the number of a multiset's sub-multisets of a given cardinality as a function of the multiplicity of its elements. This is also the number of distinct samples of a given size that may be produced by…
In this paper we consider systems which consist of binary components with known reliabilities. We discuss their algebraic properties and define the corresponding algebraic structure, which we call the reliability algebra. We prove that the…
Reasoning with fuzzy sets can be achieved through measures such as similarity and distance. However, these measures can often give misleading results when considered independently, for example giving the same value for two different pairs…
Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a…
A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets.…
In this note, we present a characterization of sets definable in Skolem arithmetic, i.e., the first-order theory of natural numbers with multiplication. This characterization allows us to prove the decidability of the theory. The idea is…
We give a definition of compactness in L-fuzzy topological spaces and provide a characterization of compact L-fuzzy topological spaces, where L is a complete quasi-monoidal lattice with some additional structures, and we present a version…
In this paper, we present a proof of the consistency of the New Foundations set theory ($\mathit{NF}$). $\mathit{NF}$'s main idea is to permit very large sets (including the Universal Set) by restricting set formation to stratified…