Arun K. Srivastava

Fuzzy Hausdorff topological spaces

Abstract We introduce the notion of a fuzzy Hausdorff topological space and make a few observations to establish the appropriateness of this notion.

Fuzzy rough sets, fuzzy preorders and fuzzy topologies

This paper shows that observations made by different authors at different times regarding one-to-one correspondence between the family of fuzzy preorders on a nonempty set and the family of all fuzzy topologies on this set satisfying certain extra conditions are essentially equivalent.

The epireflective hull of the Sierpinski object in FTS

Abstract In the category TOP of topological spaces, the epireflective hull of the standard two-point Sierpinski space is known to coincide with the subcategory of T0 topological spaces. In this note, we determine the epireflective hulls of the recently found ‘Sierpinski objects’ in the categories FTS, FNS and ω(TOP) of, respectively, fuzzy topological spaces, fuzzy neighborhood spaces and topologically generated fuzzy topological spaces. We thereby identify the corresponding ‘T0-objects’ in these categories and note that the categories FTS, FNS and ω(TOP) are ‘universal’.

On relationships among fuzzy approximation operators, fuzzy topology, and fuzzy automata

The fuzzy approximation operator associated with an approximation space (X, R) turns out to be a (saturated) Kuratowski fuzzy closure operator on X precisely when the relation R on X is reflexive and transitive. It is shown that all the level topologies of the fuzzy topology so obtained on X coincide. These observations are then applied to fuzzy automata.

On fuzzy connectedness

Abstract In this note, we discuss some of the properties of various fuzzy connectedness concepts.

A Topology for Fuzzy Automata

This work is an introductory investigation, on the lines of [9] and [10], into some topological aspects of fuzzy machines (studied in [4-8]), wherein we introduce a topology on the state-set of a fuzzy automaton and use it, together with some standard topological results, to deduce some fuzzy automata theoretic results given in [4-8].

Fuzzy Sierpinski space

Abstract Recently, Kerre [1] introduced the concept of a fuzzy Sierpinski space. We give here an alternative definition and establish its appropriateness.

A topology for automata: A note

Let A = ( Q, X, δ ) be an X -automaton, with Q its state set. For a subset B ⊆ Q , the source of B is defined as σB = { q Ȩ Q | δ ( q, x ) Ȩ B for some x Ȩ X }. The source turns out to be a closure operator for Q and defines a topology on Q , vis. B ⊆ Q is closed iff B = σB . It is shown that many automata-theoretic concepts, e.g., separation, connectivity, retrievability, strong connectivity, etc., have standard topological analogs under this topology and many results concerning these concepts are direct consequences of this observation.

On fuzzy sobriety

Abstract This paper mainly shows that sober fuzzy topological spaces form the epireflective hull of the fuzzy Sierpinski space in the category of T 0 -fuzzy topological spaces.

On fuzzy hausdorffness concepts

We continue our earlier work on fuzzy Hausdorffness [11] by relating our fuzzy Hausdorffness notion with those due to other authors.