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

Fuzzy preorder and fuzzy topology

“…However, as shown in Theorem 4.15, the assumption that * is a nonstrict continuous Archimedean t-norm is not necessary. And it should be noted that Theorem 4.16 was also proved in [30] when R is a classical preorder. Generally, Theorem 4.16 is not true for fuzzy preorders, even if * is a nonstrict continuous Archimedean t-norm and n is the corresponding negation operator ¬ : [0, 1] − → [0, 1] which is an involution in this case.…”

IF-topologies and IF-automata

“…Motivated by Das (1999) and Srivastava and Tiwari (2003), we introduce in this section, notions of IF-subsystems and strong IFsubsystems of an IF-automaton. We then introduce an IFtopology on the state-set of an IF-automaton and show that the IF-subsystems are precisely the IF-closed sets with respect to this IF-topology.…”

“…In Das (1999), a fuzzy topology on the state-set of a ffsm was introduced, and it was shown that fuzzy subsystems were precisely the closed fuzzy sets with respect to this fuzzy topology. In Srivastava and Tiwari (2003), we introduced another fuzzy topology on the state-set of a fuzzy automaton and showed that strong fuzzy subsystems were precisely the closed fuzzy sets with respect to this fuzzy topology. Also, it was shown that all the 'level topologies' of this fuzzy topology coincide with a (crisp) topology on the state-set of a fuzzy automaton, introduced in Srivastava and Tiwari (2002).…”

On Links between Rough Sets and Digital Topology

“…Lashin et al [21] introduced the topology generated by a subbase, also defined a topological rough membership function by the subbase of the topology. In addition, connections between fuzzy rough set theory and fuzzy topology were also investigated (see [22]- [24]). …”