Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variable-basis fuzzy interior operators   For a topological space it is well-known that the associated closure and
interior operators provide equivalent descriptions of set-theoretic topology;
but it is not generally true in other categories, consequently it makes sense
to define and study the notion of interior operators I in the context of fuzzy
set theory, where we can find categories in a lattice-theoretical context.
Fuzzy interior operators have been studied by U. Hohle, A. Sostak and others,
(1999), these works were used to describe L-topologies on a set X. More
recently, M. Diker, S. Dost and A. Ugur (2009) present interior and closure
operators on texture spaces in the sense of Cech, and F. G. Shi(2009) studies
interior operators via L-fuzzy neighborhood systems. The aim of this paper is
to propose a more general theory of variable basis fuzzy interior operators,
employing both categorical tools and the lattice theoretical foundations
investigated by S. E. Rodabaugh (1999), where tha lattices are usually
non-complemented. furthermore, we construct some topological categories.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys