Sentence examples for be a soft set from inspiring English sources

Let ( F, A ) be a soft set in a soft topological space X.

Definition 6.1 Let F ∈ S ( U ) be a soft set and let T : F → ˜ F be a soft mapping.

Example 6.2 Let U = R, E = Z and let F ∈ S ( U ) be a soft set of the form F = { ( p, ( p, p + 1 ] ) : p ∈ E }.

Let X be the universal set and R be the set of parameters or attributes with (Asubseteq R), the pair ((F,A)) is said to be a soft set over X, where F is a mathematical function given by (F Arightarrow P X)).

It follows from V 2 ) in Theorem 1 that every τ ∼ -soft neighbourhood of e F belongs to N ( e F ). Conversely, let ( G B ) 1 be a soft set belonging to N ( e F ), and let ( G B ) 2 be the soft set of soft points e M ∈ ∼ X ∼ such that ( G B ) 1 ∈ N ( e M ).

Next, we prove the following theorem which relates the concepts of soft interior and soft closure:  Theorem 5. Let F B be a soft set of soft topological space ( F A, τ ~ ) Open image in new window.Then, (1) ( ¯ F B c ~ ) = ( F B ° ) c ~ Open image in new window.

Clearly, (K,A) is a soft set over G1 and is called soft kernel corresponding to {α x ;x ∈ A}.

If ( F, E ) is a soft set over the universe U, then ( F, E ) is a Boolean-valued information system.

A soft complement of F, denoted by F c ˜, is a soft set of the form F c ˜ = { ( p, U ∖ Λ F ( p ) ) : p ∈ E }.

If ( F, A ) is a soft set of soft topological space X, then sbcl ( ( F, A ) ) is the smallest sb-closed set containing ( F, A ). Thus, sbcl ( F, A ) = ( F, A ) ∪ ~ [ int ( cl ( ( F, A ) ) ) ∩ ~ cl ( int ( ( F, A ) ) ) ].

If ( F, A ) is a soft set of soft topological space X then sbint ( ( F, A ) ) is the largest sb-open set contained in ( F, A ). Thus, sbint ( F, A ) = ( F, A ) ∩ ~ [ int ( cl ( ( F, A ) ) ) ∪ ~ cl ( int ( ( F, A ) ) ) ].