Fuzzy topology generated by fuzzy norm

On I-topology generated by fuzzy norm

“…By (2.1) and (2.2), it is easy to verify [2]). A fuzzy set on (X, · , L, R) is said to be · -open if for every x ∈ supp = {x ∈ X | (x) > 0}, there exist ε > 0 and ∈ (0, 1] such that (x, ε) ⊂ .…”

“…A fuzzy set on (X, · , L, R) is said to be · -open if for every x ∈ supp = {x ∈ X | (x) > 0}, there exist ε > 0 and ∈ (0, 1] such that (x, ε) ⊂ . [2]). Let (X, · , L, R) be a FNS.…”

“…[2]). In the FNS (X, · , min, max), every -sphere (x, ε) is an I-open fuzzy set for T · , i.e., (x, ε) ∈ T · .…”

“…Xiao and Zhu [14] studied the linear topological structure of FNSs. Das and Das [2] constructed a fuzzy topology T · on the FNS (X, · , min, max) and studied some basic properties of this fuzzy topology. According to the standardized terminology in [8], the fuzzy topology related in [2] should be called I-topology, where I = [0, 1].…”

Analyzing the solution of a system of fuzzy linear equations by a fuzzy distance

“…In some works, the authors try to present a view of a fuzzy norm (Bag and Samanta 2008; Bertoluzza et al 1995;Das and Pankaja Das 1999;Heilper 1997).…”