Elsevier

Fuzzy Sets and Systems

Volume 161, Issue 7, 1 April 2010, Pages 935-953
Fuzzy Sets and Systems

Interior and closure operators on texture spaces—I: Basic concepts and C˘ech closure operators

https://doi.org/10.1016/j.fss.2009.09.023Get rights and content

Abstract

This paper is the first of a series of three papers on the theory of interior and closure operators. Here, the theory is discussed from the textural point of view. First, the interior and closure operators on texture spaces are defined and some basic properties are given in terms of neighbourhoods and coneigbourhoods. Then the category dfIC whose objects are interior–closure spaces and the morphisms are bicontinuous difunctions is shown to be topological over the ground category dfTex of textures and difunctions. Further, considering the closure operator on Hutton algebras (known as fuzzy lattices) in the sense of C˘ech, the category HutCl of Hutton closure spaces and continuous mappings is defined. Finally, the category cdfIC of complemented bicontinuous difunctions and complemented interior-closure texture spaces and the opposite category of HutCl are shown to be equivalent.

References (19)

There are more references available in the full text version of this article.

Cited by (14)

  • Textural dependency and concept lattices

    2021, International Journal of Approximate Reasoning
  • On the reflective and coreflective subcategory of stratified L-Čech closure spaces

    2020, Fuzzy Sets and Systems
    Citation Excerpt :

    Write L-STop for the category of stratified L-co-topological spaces and continuous maps. Readers can refer to [3,4,18] for more on L-Čech closure operators and to [2,7,11,37] for more on Čech closure operators. Write L-CC for the category of L-Čech closure spaces and continuous maps; and write L-SCC for the full subcategory of L-CC consisting of stratified L-Čech closure spaces.

  • Textures and Rough Sets

    2017, Handbook of Neural Computation
  • Dual closure operators and their applications

    2015, Journal of Algebra
    Citation Excerpt :

    Starting with [51], in recent years several authors have investigated categorical interior operators, with the formation of the interior of a subspace of a topological space providing the role model; see [9,10,31,19,37].

  • Interior and neighbourhood

    2014, Topology and its Applications
    Citation Excerpt :

    Categorical interior operators were introduced by Vorster in [17] and subsequently studied in [1,2] and [12]. They have recently been applied to the study of fuzzy spaces [11] and texture spaces [4]. On the other hand, neighbourhoods with respect to closure operators were introduced in [8] to study convergence on categories.

  • Textures and covering based rough sets

    2012, Information Sciences
View all citing articles on Scopus

This work has been supported by (TÜBİTAK) (The Turkish Scientific and Technological Research Organization) under the project TBAG 107T310.

View full text