The notion of an ordered fuzzy (quasi- metric space is defined in the obvious manner.
A 4-tuple ((X,M,ast,preceq)) is called a partially ordered fuzzy metric space if ((X,preceq)) is a partially ordered set and ((X,M,ast)) is a non-Archimedean fuzzy metric space.
If ((X,M,star)) is a fuzzy metric space and ((X,preceq)) is partially ordered, then ((X,M,star)) is called a partially ordered fuzzy metric space.
Let (RM) be an ordering method, (S) the set of fuzzy numbers for which the method (RM) can be applied, and (mathcal {A}) and (mathcal {A'}) finite subsets of (S).
Corollary 3.15 is valid for partially ordered fuzzy metric spaces in the sense of Kramosil and Michálek, so it is also valid for fuzzy metric spaces in the sense of George and Veeramani.
(ii) Corollary 3.15 is valid for partially ordered fuzzy metric spaces in the sense of Kramosil and Michálek, so it is also valid for fuzzy metric spaces in the sense of George and Veeramani. .
Let A, B be nonempty subsets of partially ordered fuzzy metric space ((X,M,ast,preceq)) and (psi :[0,1]longrightarrow[0,1]) be a continuous mapping.
Under some weaker conditions, some coincidence point and common fixed point theorems are established in partially ordered fuzzy metric spaces using weakly compatible mappings.
A mapping (T Alongrightarrow B) is said to be a fuzzy ordered ψ-contraction if, for any (x,yin A) with (xpreceq y), we have (M(Tx,Ty,t geqpsi [M x,y,t)]) for all (t>0).
