The approximation of piecewise linear membership functions and Łukasiewicz operators

Dombi, József; Gera, Zsolt

doi:10.1016/j.fss.2005.02.016

Cited by 57 publications

(41 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We see that the logistic model admits all three formulation types: the E-type (13), the D-type (11) or (12) and the R-type (10).…”

Section: B Case Study 2: Verhulst Logistic Growthmentioning

confidence: 93%

See 1 more Smart Citation

Building reaction kinetic models for amiloid fibril growth

Markov

2016

BIOMATH

View full text Add to dashboard Cite

Abstract-In this work we discuss some methodological aspects of the creation and formulation of mathematical models describing the growth of species from the point of view of reaction kinetics. Our discussion is based on familiar examples of growth models such as logistic growth and enzyme kinetics. We propose several reaction network models for the amiloid fibrillation processes in the citoplasm. The solutions of the models are sigmoidal functions graphically visualized using the computer algebra system Mathematica.

show abstract

“…We see that the logistic model admits all three formulation types: the E-type (13), the D-type (11) or (12) and the R-type (10).…”

Section: B Case Study 2: Verhulst Logistic Growthmentioning

confidence: 93%

“…Let x 0 (−γ) = x * < 1/2, γ > 0, then x * is the initial value for the D-type model (12) having as solution the shifted function x γ , that is x γ (0) = x * . Using the E-type presentation (13), the latter gives (1 + e kγ ) −1 = x * , hence…”

Section: Lag Timementioning

confidence: 99%

Building reaction kinetic models for amiloid fibril growth

Markov

2016

BIOMATH

View full text Add to dashboard Cite

show abstract

“…The equation was rediscovered in 1911 by A. G. McKendrick [35] for the bacterial growth in broth and was tested using nonlinear parameter estimation. The logistic function finds applications in an wide range of fields, including biology, ecology, population dynamics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, financial mathematics, statistics, fuzzy set theory, to name a few [12], [13], [11], [14], [18].…”

Section: Preliminariesmentioning

confidence: 99%

“…In Section 3 we study the uniform and Hausdorff approximation of the cut functions by logistic functions. Curiously, the uniform distance between a cut function and the logistic function of best uniform approximation is an absolute constant not depending on the slope of the functions, a result observed in [18]. By contrast, it turns out that the Hausdorff distance (H-distance) depends on the slope and tends to zero when increasing the slope.…”

Section: Introductionmentioning

confidence: 96%

“…In Section 4 we discuss the approximation of the cut function by a family of squashing functions induced by the logistic function. It has been shown in [18] that the latter family approximates uniformly the cut function arbitrary well. We propose a new estimate for the H-distance between the cut function and its best approximating squashing function.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

Илиев

Kyurkchiev²,

Markov³

2015

BIOMATH

View full text Add to dashboard Cite

Abstract-We study the uniform approximation of the sigmoid cut function by smooth sigmoid functions such as the logistic and the Gompertz functions. The limiting case of the interval-valued step function is discussed using Hausdorff metric. Various expressions for the error estimates of the corresponding uniform and Hausdorff approximations are obtained. Numerical examples are presented using CAS MATHEMATICA.

show abstract

Data‐enabled cognitive modeling: Validating student engineers’ fuzzy design‐based decision‐making in a virtual design problem

Irgens

Chesler

Linderoth

et al. 2017

Comp Applic In Engineering

View full text Add to dashboard Cite

The ability of future engineering professionals to solve complex real-world problems depends on their design education and training. Because engineers engage with open-ended problems in which there are unknown parameters and multiple competing objectives, they engage in fuzzy decision-making, a method of making decisions that takes into account inherent imprecisions and uncertainties in the real world. In the design-based decision-making field, few studies have applied fuzzy decision-making models to actual decision-making process data. Thus, in this study, we use datasets on student decision-making processes to validate approximate fuzzy models of student decision-making, which we call data-enabled cognitive modeling. The results of this study (1) show that simulated design problems provide rich datasets that enable analysis of student design decision-making and (2) validate models of student design cognition that can inform future design curricula and help educators understand how students think about design problems.

show abstract

The approximation of piecewise linear membership functions and Łukasiewicz operators

Cited by 57 publications

References 12 publications

Building reaction kinetic models for amiloid fibril growth

Building reaction kinetic models for amiloid fibril growth

On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

Data‐enabled cognitive modeling: Validating student engineers’ fuzzy design‐based decision‐making in a virtual design problem

Contact Info

Product

Resources

About