Abstract: Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric（p. q. metric） p: Lx xLx -[0,∞] where L is acompletely distributive lattice, and the associated family of neighborhood mappings {Dr |r>O}. Thefuzzy metric space in Erceg's sense is denoted by （Lx, p, Dr） since there exists a one to one correspondence between fuzzy p. q. metrics and associatcd families of neighborhood mapping, a family{Dr|r>0}satisfying certain conditions is also callcd a （standard） fuzzy p. q metric. In [2] Liang defimed apointwise fuzzy p. q. metric d: P（Lx）×P（Lx）-[0, ∞) and applicd it to the construction of theproduct fuzzy metric. In this paper, we give axiomatic definitions of molcculewise and fuzzy .

Key words:  , mokecukewise fuzzy p.q.metric,Setwise fuzzy p.q.metric.