In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

In the application of fuzzy reasoning, researchers usually choose the membership function optionally in some degree. Even though the membership functions may be different for the same concept, they can generally get the same or approximate results. The robustness of the membership function optionally chosen has brought many researchers’ attention. At present, many researchers pay attention to t...

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...

The aim of this paper is to develop an individual neural network generation and ensemble algorithm based on quotient space granularity clustering. Firstly, we give the characteristics of the quotient space granularity and affinity propagation(AP) clustering. Secondly, we introduce the quotient space concept to the AP clustering analysis, which can find an optimal granularity from all possible g...

The paradigmatic result in symplectic toric geometry is the paper of Delzant that classifies compact connected symplectic manifolds with effective completely integrable torus actions, the so called (compact) symplectic toric manifolds. The moment map induces an embedding of the quotient of the manifold by the torus action into the dual of the Lie algebra of the torus; its image is a simple unim...

OBJECTIVE To investigate the characteristics of attention in school-age children with mild autism spectrum disorder (ASD), and to provide a basis for clinical treatment. METHODS A total of 20 school-age children with mild ASD were enrolled, and the intermediate visual and auditory continuous performance test (IVA-CPT) was used to assess their attention. A total of 20 children with attention d...

A complete two-dimensional local field K of mixed characteristic with finite second residue field is considered. It is shown that the rank of the quotient U(1)K 2 K/TK , where TK is the closure of the torsion subgroup, is equal to the degree of the constant subfield of K over Qp. Also, a basis of this quotient is constructed in the case where there exists a standard field L containing K such th...

Abstract We study subfields of quotient division algebras of domains of finite GK dimension and introduce a combinatorial property we call the straightening property. We show that many classes of algebras have this straightening property and show that if A is a domain of GK dimension d with this property that is not PI, then the maximal subfields of the quotient division algebra of A have trans...

In this article we show that the quotient M∞/B(Qp) of the Lubin–Tate space at infinite level M∞ by the Borel subgroup of upper triangular matrices B(Qp) ⊂ GL2(Qp) exists as a perfectoid space. As an application we show that Scholze’s functor H i ét(PCp ,Fπ ) is concentrated in degree one whenever π is an irreducible principal series representation or a twist of the Steinberg representation of G...