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Therefore is fuzzy order -contractive with.
If (A=B), then proximal fuzzy order reversing mapping will become fuzzy order reversing.
If (A=B), then a proximal fuzzy order preserving mapping will become fuzzy order preserving.
Now we can see that is fuzzy order -contractive with.
Thus F is a fuzzy order K-set-valued mapping.
First, two fixed point theorems are proved for fuzzy order -contractive type mappings.
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Subsequently, several authors have discussed various aspects of the theory and applications of fuzzy sets such as fuzzy topological spaces, similarity relations and fuzzy ordering, fuzzy measures of fuzzy events, and fuzzy mathematical programming.
Let (T Arightarrow B) be continuous, proximally monotone, and proximal fuzzy ordered ψ-contraction of type-I, (g Arightarrow A) surjective, fuzzy expansive and inverse monotone mapping.
A mapping (T Alongrightarrow B) is called a fuzzy ordered η-proximal contraction if, for any u, v, x, and y in A, the following condition holds: left.
Let (T Arightarrow B) is continuous, proximally monotone, and proximal fuzzy ordered ψ-contraction of type-I, (g Arightarrow A) surjective, a fuzzy isometry, and an inverse monotone mapping.
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).
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