COMMENTS ON SOME NEW CLASSES OF SIGMOIDAL AND ACTIVATION FUNCTIONS. APPLICATIONS

被引：7

作者：

Kyurkchiev, Nikolay ^{[1
]}

Nikolov, Geno ^{[2
]}

机构：

[1] Univ Plovdiv Paisii Hilendarski, Fac Math & Informat, 24 Tzar Asen Str, Plovdiv 4000, Bulgaria

[2] Univ Sofia St Kliment Ohridski, Fac Math & Informat, 5 James Bourchier Blvd, Sofia 1164, Bulgaria

来源：

DYNAMIC SYSTEMS AND APPLICATIONS | 2019年 / 28卷 / 04期

关键词：

new family of sigmoidal functions; Interval function; kappa-; function; Prototype filter; Hausdorff distance; NEURAL-NETWORK OPERATORS; APPROXIMATION;

D O I：

10.12732/dsa.v28i4.1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a new class of sigmoidal functions. We will consider the possibility of approximating the function kappa(t) = {0, 0 <= t < 1 [0, 1], t = 1 by new family with respect to Hausdorff distance. Some applications in the theory of impulse technics, filter synthesis and debugging theory are given. We analyze also the "real wealth data" and "actual data to estimate the number of software residual faults" by the new sigmoid. Some visualizations of the typical emitting charts are also given. We will consider also the possibility of approximating the function v(t) = {0, -1 <= t <= -2 beta/m 1/2, -2 beta/m < t < 2 beta/m 1, 2 beta/m <= t <= 1 by the new generalized Yun's activation function. Approximating of this function is related to the analysis of electric steps and chains. Numerical examples using GAS Mathematica, illustrating our results are presented.

引用

页码：789 / 808

页数：20

共 50 条

[1] On some applications of hypergeometric functions.
Devisme, J
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1932, 195 : 936 - 938
[2] Some new theorems on entire functions.
Lindelof, E
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1901, 133 : 1279 - 1281
[3] SUBCLASSES AND CLASSES OF BOOLEAN FUNCTIONS.
Yakubaitis, E.A.
Automatic Control and Computer Sciences, 1974, 8 (01): : 1 - 6
[4] Lower Bounds for Approximation of Some Classes of Lebesgue Measurable Functions by Sigmoidal Neural Networks
Montana, Jose L.
Borges, Cruz E.
BIO-INSPIRED SYSTEMS: COMPUTATIONAL AND AMBIENT INTELLIGENCE, PT 1, 2009, 5517 : 1 - 8
[5] EQUIVALENCE CLASSES OF BOOLEAN SYMMETRIC FUNCTIONS.
Miyakawa, Masahiro
Stojmenovic, Ivan
Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E, 1986, E69 (04): : 513 - 514
[6] On the convergence of certain classes of series of functions.
Carmichael, RD
AMERICAN JOURNAL OF MATHEMATICS, 1920, 42 : 77 - 90
[7] Comments on my work on Bayesetical functions.
Hartogs, F
MATHEMATISCHE ZEITSCHRIFT, 1937, 42 : 744 - 744
[8] Applications of some classes concerning with univalent functions
Owa, Shigeyoshi
14TH INTERNATIONAL SYMPOSIUM ON GEOMETRIC FUNCTION THEORY AND APPLICATIONS, 2019, 1212
[9] SOME SYSTEM THEORY APPLICATIONS OF BLOCK-PULSE FUNCTIONS.
Sinha, N.K.
Zhou Qi-Jie
Canadian electrical engineering journal, 1985, 10 (01): : 3 - 8
[10] ON SOME NEW CLASSES OF FUNCTIONS + DISTRIBUTIONS
ALBRYCHT, J
MUSIELAK, J
BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1964, 12 (07): : 391 - &

← 1 2 3 4 5 →