A representation theorem for fuzzy pseudometrics

A Representation Theorem for L-fuzzy Pseudo-metrics

“…is nondecreasing from the conditions (LF2) and (LF4). Hence left-continuity is the same as the property of preserving existing sups, that is to say, (LF5 * ) ( , , ) ( , , ) for each ( ) a J L  is called lower-semicontinuity [5] ( or named nests of pseudo-metrics). Remark 3.4 From Definition 3.3, it is not difficult to see that a d is increasing with respect to a , that is,…”

“…In 2012, Mardones-Pérez and De Prada Vicente [5] indicated that a fuzzy pseudo-metrics and [0,1)indexed families of pseudo-metrics that satisfy a property of lower-semicontinuity are connected one by one. However, he only thinks the situation where L =[0,1], and not consider the situation where L is a completely distributive De Morgan algebra.…”

Generalized fuzzy k-pseudo metric and its representation theorem

“…In 2012, there is a big step forward in the development of KM-fuzzy metric. Mardones-Pé rez and De Prada Vicente 5 pointed out that there is a close relation between a fuzzy pseudo metric and pseudo metrics in the interval [0,1) which satisfies a property of lower-semicontinuity (abbreviated as lsc.). In 2018, Sostak 6 generalized the definition of the fuzzy metric to the condition where…”

Pointwise k-Pseudo Metric Space

“…Metric spaces play an important role in the research and applications of mathematics. Since Zadeh introduced fuzzy set theory, there have been many interesting and creative works in which different approaches to the concept of a fuzzy metric were introduced and corresponding theories were developed and used for various applications [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”