Sentence examples for using the extension principle from inspiring English sources

A particular emphasis is placed upon the treatment of information within a probabilistic-fuzzy mathematical model using the extension principle.

By using the extension principle, we can easily prove the result.

Meanwhile Lakshmikantham et al. [13] investigated the solution of two-point boundary value problems associated with nonlinear fuzzy differential equations by using the extension principle.

Differentiability of fuzzy-valued functions was first introduced by Chang and Zadeh [3], and followed by Dubois and Prade [4], who defined and used the extension principle [5].

The concept of the fuzzy derivative was first introduced by Chang and Zadeh [14]; it was followed up by Dubois and Prade [15] who used the extension principle in their approach.

The concept of a fuzzy derivative was first introduced by Chang and Zadeh [1], followed up by Dubois and Prade [2] who used the extension principle in their approach.

In this paper, we design tight-frame symmetric wavelet filters by using the unitary extension principle of [A. Ron, Z. Shen, J. Funct. Anal. 148 (1997) 408 447].

By using the unitary extension principle, we constructed tight framelets with desired approximation order from a given smoothed pseudo spline.

Moreover, by using the unitary extension principle, we get the construction of tight framelets with desired approximation order based on smoothed pseudo splines.

In this section, we give a construction of tight framelets and discuss the approximation order of tight framelets from smoothed pseudo splines by using the unitary extension principle of [4].

Practical results are obtained which overcome those based on the extension principle or α-cuts.