Metrization theorems in L-topological spaces

Fuzzy Set Field and Fuzzy Metric

“…Hsu [14] introduced fuzzy metric space with metric defined between fuzzy points and examined the completion of fuzzy metric space. For different notions of fuzzy metric space and for further research work see for instance Shi [15], Shi and Zheng [16], Shi [17] and others.…”

On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric

“…As a natural generalization of the concept of set, fuzzy sets was introduced initially by Zadeh [39]. Since then, to use this concept in topology and analysis many authors have expansively developed the theory of fuzzy sets and application [3,6,16,17,18,19,23,24,28,32,37,38]. Various concepts of fuzzy metrics on ordinary set were considered in [7,9,13,20,26].…”

Conjugate Families of Mappings in Pointwise Metric Fuzzy Lattices

“…For the works of pointwise metrics on fuzzy lattices, some of them dealt with concept of neighborhood (for example, see Peng [12][13]), and others did that of the remote-neighborhood (for example, see Shi [18][19][20][21]). In [27] it is pointed out that there exists a kind of conjugacy between neighborhood and remoteneighborhood, and the topology induced by a pseudo-metric is determined by the conjugate families of mappings.…”

“…We appoint that Ø = 0, in the cases of a lattice and the set of nonnegative real numbers. Other unexplained terminologies and notations and further details can be found in [9,[12][13][18][19][20][21][22][23][24].…”