Sentence examples for fuzzy derivation from inspiring English sources

The remainder of this paper is organized as follows: In Section 2, which is reserved for some preliminaries, we collect some useful results on fuzzy derivation and integration.

A ℂ-linear mapping D : ( X, N ) → ( X, N ) is called a ternary fuzzy derivation if D ( [ x y z ] ) = [ D ( x ) y z ] + [ x D ( y ) z ] + [ x y D ( z ) ]. for all x, y, z ∈ X.

A ℂ-linear mapping H : ( X, N ) → ( Y, N ′ ) is called a ternary homomorphism if H ( [ x y z ] ) = [ H ( x ) H ( y ) H ( z ) ]. for all x, y, z ∈ X ; (2) A ℂ-linear mapping D : ( X, N ) → ( X, N ) is called a ternary fuzzy derivation if D ( [ x y z ] ) = [ D ( x ) y z ] + [ x D ( y ) z ] + [ x y D ( z ) ]  .

Fuzzy rule derivation is often difficult and time-consuming, and requires expert knowledge.

A ℂ-linear mapping D : ( X, N ) → ( X, N ) is called a fuzzy ∗-derivation if D ( x y ) = D ( x ) y + x D ( y ) and D ( x ∗ ) = D ( x ) ∗ for all x, y ∈ X. Definition 2.7 Let X be a nonempty set.

A C -linear mapping D : ( X, N x ) → ( X, N x ) is called a fuzzy ∗-derivation if D ( x y ) = D ( x ) y + x D ( y ) and D ( x ∗ ) = D ( x ) ∗ for all x, y ∈ X. Definition 2.7 Let X be a set.

for all x, y ∈ X and all t > 0. Then δ ( x ) : = N - lim n → ∞ 2 n f ( x 2 n ) exists for each x ∈ X and defines a fuzzy ∗-derivation δ : X → X such that N ( f ( x ) − δ ( x ), t ) ≥ ( 2 − 2 L ) t ( 2 − 2 L ) t + L φ ( x, 2 x, x ) (5.2). for all x ∈ X and all t > 0. Proof The proof is similar to the proof of Theorem 3.1.

for all x 1, …, x n − 1 ∈ X and all t > 0. Then D ( x ) : = N - lim p → ∞ f ( x ( n − m + 1 ) p ) ( n − m + 1 ) − p exists for all x ∈ X and defines a fuzzy ∗-derivation D : X → X such that N ( f ( x ) − D ( x ), t ) ≥ ( n − m + 1 ) ( n m ) ( 1 − L ) t ( n − m + 1 ) ( n m ) ( 1 − L ) t + L φ ( x, …, x ). for all x ∈ X and all t > 0. Proof The proof is similar to the proof of Theorem 3.1.

Using the fixed point method, we prove the Hyers-Ulam-Rassias stability of fuzzy ∗-derivations in fuzzy Banach ∗-algebras.

Neural networks can provide an alternative means for fuzzy rule-base derivation and tuning for ventilator control.

end{aligned} (21)In the following discussion, we will detail the derivation of fuzzy weight (w_i ).