Filter Specifications and Approximation Theory (The Mathematical Approach to the Approximation Problem)

2019 ◽  
pp. 49-64
Author(s):  
George S. Moschytz
Keyword(s):  
Approximation Theory ◽  
Approximation Problem ◽  
Mathematical Approach

scholarly journals Fuzzy Least Squares Approximation Using Fuzzy Polynomial

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Kun Liu ◽  
Xiaobin Guo
Keyword(s):  
Least Squares ◽  
Approximation Theory ◽  
Numerical Approximation ◽  
Original Problem ◽  
Fuzzy Numbers ◽  
Approximation Problem ◽  
Simple Approach ◽  
Least Squares Approximation ◽  
Numerical Examples ◽  
Function Relation

In this paper, the fuzzy polynomial is introduced and applied to investigate the least squares approximation problem based on LR fuzzy numbers. A new and simple approach to solve the original problem is constructed by using approximate fuzzy polynomial. Two numerical examples are given to illustrate the proposed method. Since a large number of data exist as an uncertain property and need a function relation to reflect the laws between different variables, our results enrich fuzzy numerical approximation theory.

Towards an Approximation Theory of Discrete Problems. Part I

1991 ◽  
Vol 15 (2) ◽  
pp. 187-208
Author(s):  
Andrzej Skowron ◽  
Jaroslaw Stepaniuk
Keyword(s):  
Approximation Theory ◽  
Uniform Approximation ◽  
Dynamic Logic ◽  
Approximation Problem ◽  
Completeness Theorem ◽  
Approximate Reasoning ◽  
Propositional Dynamic Logic ◽  
Atomic Properties ◽  
Discrete Problems ◽  
Approximate Formulas

The purpose of this paper is to make the first step towards an approximation theory of discrete problems in which one can express and prove properties of approximating algorithms as well as carry out an approximate reasoning. We introduce an approximation propositional dynamic logic (APDL) with approximations of programs and formulas. We discuss the expressibility of APDL. The main theorem is the completeness theorem for a fragment of APDL. We consider also the approximation problem of properties expressible in APDL by a distinguished set of so called simple approximate formulas and programs, generated only from approximations of atomic properties and approximations of atomic programs. The solution of the uniform approximation problem is presented and a result about an appoximation of decision algorithms is given.

A mathematical approach to data evaluation with focus on prediction of minimal residual disease in pediatric ALL

2012 ◽  
Vol 224 (03) ◽  
Author(s):  
A Torge ◽  
M Zimmermann ◽  
A Möricke ◽  
R Köhler ◽  
A Schrauder ◽  
...  
Keyword(s):  
Minimal Residual Disease ◽  
Residual Disease ◽  
Data Evaluation ◽  
Mathematical Approach ◽  
Pediatric All ◽  
Minimal Residual

269. Use of an Objective Mathematical Approach to Facilitate Assigning Skin Notations

2000 ◽  
Author(s):  
M. Boeniger ◽  
H. Ahlers ◽  
B. Lushniak ◽  
R. Mickelsen ◽  
A. Morton ◽  
...  
Keyword(s):  
Mathematical Approach
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