Two categories $\mathrm{𝕊𝕖𝕥}\left(\Omega \right)$ and $\mathrm{𝕊𝕖𝕥𝔽}\left(\Omega \right)$ of fuzzy sets over an $MV$-algebra $\Omega$ are investigated. Full subcategories of these categories are introduced consisting of objects $\left(\mathrm{s}ub\right(A,\delta )$, $\sigma )$, where $\mathrm{s}ub(A,\delta )$ is a subset of all extensional subobjects of an object $(A,\delta )$. It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.

The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications...

If an extension V ⊆ V̅ satisfies the δ approximation and cover properties for classes and V is a class in V̅, then every suitably closed embedding j: V̅ → N̅ in V̅ with critical point above δ restricts to an embedding j ↾ V amenable to the ground model V. In such extensions, therefore, there are no new large cardinals above δ. This result extends work in [Ham01].

The extraction of logical rules from data has been, for nearly fifteen years, a key application of artificial neural networks in data mining. Although Boolean rules have been extracted in the majority of cases, also methods for the extraction of fuzzy logic rules have been studied increasingly often. In the paper, those methods are discussed within a five-dimensional classification scheme for neural-networks based rule extraction, and it is pointed out that all of them share the feature of being...

Following Malykhin, we say that a space $X$ is extraresolvable if $X$ contains a family $𝒟$ of dense subsets such that $\left|𝒟\right|>\Delta \left(X\right)$ and the intersection of every two elements of $𝒟$ is nowhere dense, where $\Delta \left(X\right)=min\left\{\right|U|:U$ is a nonempty open subset of $X\}$ is the dispersion character of $X$. We show that, for every cardinal $\kappa$, there is a compact extraresolvable space of size and dispersion character $2^{\kappa }$. In connection with some cardinal inequalities, we prove the equivalence of the following statements: 1) $2^{\kappa }<2^{{\kappa }^{+}}$, 2) ${\left({\kappa }^{+}\right)}^{\kappa }$ is extraresolvable and...