=Paper=
{{Paper
|id=Vol-3156/paper8
|storemode=property
|title=Fuzzy Model of Raster Transformation of Square Elements
|pdfUrl=https://ceur-ws.org/Vol-3156/paper8.pdf
|volume=Vol-3156
|authors=Bohdan Durnyak,Mikola Lutskiv,Petro Shepita
|dblpUrl=https://dblp.org/rec/conf/intelitsis/DurnyakLS22
}}
==Fuzzy Model of Raster Transformation of Square Elements==
https://ceur-ws.org/Vol-3156/paper8.pdf
Fuzzy Model of Raster Transformation of Square Elements
Bohdan Durnyak, Mikola Lutskiv, Petro Shepita,
Ukrainian Academy of Printing, Pid Goloskom str., 19, Lviv, 79020, Ukraine
Abstract
Mamdani fuzzy model of the image raster transformation for square elements has been
developed on the basis of a fuzzy set of rules that reproduce the input geometric size and its
area, which is an information carrier, its fuzzification and inference have been carried out
using the input and output membership function, which more fully and quantitatively
describe the fuzzy ranges of light, gray and mid tones reproduction in the tone interval.
A simulator of a fuzzy model of raster transformation in Matlab: Simulink package has been
developed with the help of Fuzzy Logic Toolbox, which has simplified its implementation.
The simulator calculates three membership functions of fuzzy sets and visualizes them. The
results of the simulation modelling in the form of graphs of membership functions of input
and output variables are presented and their properties are analysed. Fuzzy models quantify
and objectively evaluate fuzzy ranges of light, gray, and dark tones during the rasterization
process, which is the advantage of fuzzy models over traditional ones.
Keywords 1
Raster transformation, fuzzy model, square, tone, fuzzification, inference, interval, simulation
1. Introduction
Rasterization is practically the most important basis for reproducing images in the printing
industry, which allows one to control the tone transfer. The term "rasterization" means the
decomposition of the image into small elements, which consist of printed and blank elements.
Depending on the ratio of the areas of sub-elements covered with paint and white paper for the human
eye, the impression of a gray tone is created [1, 2, 3]. This definition of the term rasterization is quite
narrow and mainly characterizes its technological and physical essence. At the same time,
rasterization is the main controlling, corrective and compensatory effect for other stages, namely the
production of printing plates and printing. Physically raster element first appears on the printing plate
as a printing element. The stage of making a printing plate and printing have limited control
capabilities. In the process of printing, the printing elements are covered with ink, a color image is
created, which is transmitted to the printed material through the offset cylinder. This is a physical
increase in color dots, which causes distortion of the raster image, which is called compression [4, 5,
6, 7, 8]. The compression itself is due to the increase in the area of raster dots at the stages of
manufacturing the printing plate and printing is the main reason for the deterioration of the quality of
the raster image. These and other effects must be corrected and compensated at the stage of
rasterization.
The latest CtP technologies provide high-quality production of raster printing plates, but do not
significantly improve the quality of printed products. Today, most traditional classical rasterization
methods are used in CtP systems, where you can select the desired form of the raster element and
specify the desired literature. The developers of these systems develop and, at the request of
customers, install alternative programs of frequency, hybrid, stochastic rasterization, which provide
higher quality color publications [7, 9, 10].
IntelITSIS’2022: 3rd International Workshop on Intelligent Information Technologies and Systems of Information Security, March 23–25,
2022, Khmelnytskyi, Ukraine
EMAIL: durnyak@uad.lviv.ua (Bohdan Durnyak); lutolen@i.ua (Mikola Lutskiv); pshepita@gmail.com (Petro Shepita);
ORCID: 0000-0003-1526-9005 (Bohdan Durnyak); 0000-0002-2921-3662 (Mikola Lutskiv); 0000-0001-8134-8014 (Petro Shepita)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
The main problem is the strict requirements for standardization and normalization of all processes,
materials, machines and the availability of expensive multi-channel systems for zonal adjustment of
the supply of paint to a given circulation, which significantly limits the introduction of alternative
screening methods not only in Ukraine but also in other countries.
The theoretical foundations of raster transformation, which mathematically describe the
transformation of a continuous image (illustrations) into a discrete raster, lag far behind the theory of
digital processing and image conversion, which is widely developed, has different processing methods
that can significantly improve visual quality are illuminated on the monitor screen. Note that the
digital image is represented by arrays of numbers and corresponds to [0; 255] grayscale, which are
used in digital image processing [1, 2, 11-14]. Instead, in printing with raster transformation, raster
elements of different geometric sizes, different shapes and lines are used, and the main carrier of
image information is the relative area of the raster element, which is within [0;1]. Therefore, existing
digital image processing methods cannot be directly applied to bitmap conversion.
The physical processes that occur during rasterization, mold making and printing are diverse and
complex, so little is studied. Experimental research is time consuming and expensive, requiring
complex measuring equipment. In addition, the effects of various perturbations can significantly
distort the results of research. On the basis of experimental researches and densitometric
measurements build and analyze gradational characteristics of printing, carry out adjustment of
rasterization. However, on based on experimental data, it is impossible to make optimal adjustments
and compensation for different effects for different lines and shapes of the raster element.
Mathematical models of raster transformation, raster characteristics for elements of different
shapes and lines and adjustments and properties characteristic of a given line and shape of raster
elements are presented in available sources [3]. In the presented and other sources there is no general
approach to the analysis and synthesis of raster transformation, in particular to the synthesis of
parameters of the corrective link of different lines and shapes of raster elements. disadvantage. An
even more difficult problem is the optimization of raster parameters and adjustment parameters. To
solve these problems, it is necessary to develop models of raster transformation.
Thus, the urgent problem is to develop a normalized raster transformation, which would
adequately describe the raster transformation regardless of the raster line, allow to build raster
characteristics, synthesize the adjustment link, compensate and optimize the raster. Reproduction of
the tonality of the image by printing means is carried out by changing the relative areas of printing
and blank elements. To do this, printing originals (photographs, drawings, images, digital images) are
sampled and converted into growth. ditch form, which has a regular raster lattice structure in which
the raster elements are located. In general mathematical terms, the traditional raster image
transformation is expressed by the gradation transformation function where the basic value is the
geometric size of the raster element, which is placed in a raster cell (raster square), the dimensions of
which are set by the raster line, maximum raster element size element obtained after conversion,
which corresponds to the optical density of the image.
The shape of raster elements and raster lineage depend on the type of printed products (books,
magazines, newspapers) and materials that significantly affect the quality of printed products.
Traditionally, the raster transformation of a given lineage is analyzed, which can be set in a wide
range (from 30 to 120) lines / cm. Raster conversion is indicated on a limited tone interval, which is
set by the variables DM and XM for a given line. The results of analysis and synthesis and the
parameters of the corrective link in the traditional raster transformation depends on the shape of the
raster elements and the raster line, which is a disadvantage and is inconvenient for practical
applications and adjustment of tone.
To generalize the analysis and synthesis of raster transformation, a mathematical model of
normalized raster transformation in the form of a two-digit function with a domain - closed single
raster square and many values of relative areas closed closed interval [0;1]. The square raster cell has
constant unit dimensions. The raster element of a given shape is located in the center of the cell. In the
process of raster transformation, its geometric dimensions change within [0;1].
Modern computer publishing systems allow one to choose the shape of the raster element and
adjust the tone transfer. However, the gradational content of images can be varied. They can be light,
gray, dark and differ in contrast, maximum and minimum values of optical density [3]. If the interval
of optical densities of the original and reproduction is set during the tone transfer synthesis, depending
on the technological capabilities of a particular offset printing method, the tone transfer synthesis can
be performed using the Adobe package in its working window, adjust and form the desired gradation
characteristics of the tone transfer depending on the experience and intuition of the operator,
technologist or customer, for each specific image [1–4].
One should note that the operator does not have enough quantitative data on the information
content of the image, and verbal tone estimates as "light tones" or "shadows" are insufficient to form
an optical gradation characteristic, so the operator makes selection based on his own experience and
skills. The complete procedure of preparing images for printing is quite complex, lengthy and is used
in the case of increased requirements for imprint quality [3–7]. Therefore, the use of fuzzy sets and
fuzzy logic in order to obtain additional and quantitative information about the image is an urgent
task.
2. Literature Review
The choice of the form of raster elements depends on the type of printed products, as the raster
image is related to the structure of raster elements and their shape [3–6]. The clearest image is
provided by a regular raster structure with a square raster element. An image with a checkerboard
structure and a square element is visually perceived as a solid gray surface than an image with linear
dashed elements. Therefore, the square shape of the raster element is considered one of the best for
reproducing raster images by printing means [1, 2]. Graphical representation of the geometry scheme
of the normalized raster transformation for a square element located in the center of a single cell of
the raster grid.
Nowadays, the experience has been gained in the use of fuzzy logic to solve many problems that
are difficult to solve by traditional mathematics [1, 7, 8, 9, 10, 11]. The ability to properly evaluate
the original makes it possible to draw conclusions about the interval and ranges of tone. To do this,
the characteristics of tone reproduction are divided into seven bands, which helps during tonal image
correction, and tones are given in the processes: light areas - 2-10%, quarter tones - from 18% to 35%
with a center of 25%, ordinal tones - from 35 to 65% with a center of 5%, three-quarter tones - from
65 to 80% ofaverage value of 75%, shadows - dark areas, which for high-quality offset can be up to
97%, which corresponds to the range of optical densities of the print 0-1.4 B [1, 4].
With the advent of digital images, their interval is given by the number of discrete levels
(grayscale 0–255), which are called eight-bit [2, 5]. Some applications of fuzzy sets for image contrast
in general are presented in the monograph [2], there is also described the use of fuzzy sets for spatial
filtering on a simple example of four neighbors and provides an illustration that confirms the
effectiveness of spatial filtering based on fuzzy logic Some applications of fuzzy logic models to the
image transformation are presented in the monograph [5, 13, 15], where red, yellow and green are
used as linguistic values of the corresponding membership functions which are formalized by fuzzy
rules IF-THEN and logic inference rules. Based on them, the problem of increasing the contrast of a
halftone black and white image is solved, applying a fuzzy base of rules: if a pixel is dark, make it
darker, if a pixel is light, then make it lighter. An example of the use of fuzzy sets is presented for
raster filtering on the example of four neighbours as well as the illustration that confirms the
effectiveness of spatial filtering to increase contrast.
In the work of the author [3, 19-22] Mamdani fuzzy model of the ranges of optical densities of the
originals and reproductions associated with technological transformations in offset printing is
constructed. A simulator has been developed that simultaneously calculates three membership
functions of the optical density interval and performs their visualization. The properties of the model
are considered, which quantitatively, and therefore objectively describes the fuzzy smooth ranges of
tone transfer, which is the advantage of the fuzzy model over the traditional one [18, 19, 23].
There are various fuzzy models that describe different phenomena, processes, objects, and
systems. The choice of model type depends on the object, the purpose of the study, the accuracy and
the available information about the object.
Since the graphic characteristics of the tones of the originals, reproductions and raster prints are
known or can be determined experimentally, we believe that the model of the object is known. In this
case, the construction of a fuzzy model is called fusification (blurring) of the original model. To fusify
the interval of optical densities, we use one of the most popular models - the Mamdani model [2, 7,
8], which should reproduce the input in output in the form of a set of rules, each of which defines one
blurred point. Sets of blurred points create a blurred pattern in which the interpolation between points
depends on the accepted apparatus of fuzzy logic, in particular the membership function, which can
be segmental-linear or continuous [9, 11].
3. Models & Methods & Technology
3.1. Methodology of research
Rasterization There are various fuzzy models that describe different processes, objects, and
systems based on their mathematical models or relevant data. In the process of raster transformation,
the image (original) is transformed into discrete-continuous (raster) one, which is described by the
area of the raster element, which is an information carrier about the image and is given by the
analytical expression in general [2, 17]:
𝑆𝑎(𝑥) = 𝐹(𝑥, 𝑎, 𝐿), 𝐼𝐹 0 ≤ 𝑥 ≤ 𝑎, (1)
where Sa(x) - is the area of the raster element, a – is a raster constant, which is equal to the size of the
raster grid, L- is the raster lineature, x - is the geometric size of the raster element (control effect),
F(·)- is a nonlinear function.
When transferring from light to gray and dark tones, the size of a square raster element is
gradually increased, and the area will be determined by the area of the square [2, 24]:
𝑆𝑎 = 𝑥 2 , 𝐼𝐹 0 ≤ 𝑥 ≤ 𝑎, (2)
If L line/cm is given, then the raster constant will be in μm and will be determined by the
expression:
10000
𝑎= 𝐿 , (3)
Then the relative area of the raster element will look like this:
𝑆𝑎
𝑆= = 𝑥 2 𝐿2 , (4)
𝑆𝑚
If in the expressions (2)-(4), the size of the raster element is linearly changed within the given
limits 0≤x≤a, then they can be used to calculate and form the rasterization characteristic needed to
construct a fuzzy raster transformation model. A simpler task can be solved by using object-oriented
programming in the popular Matlab: Simulink package [8, 20-25]. In accordance with the modelling
principles on the basis of the above formulas, a block diagram of the model of raster transformation
has been developed in Simulink, which is presented in Figure 1.
Figure 1 : The block diagram of the raster transformation model
The control effect generates the block Ramp and feeds it to the input of the block of mathematical
functions Fnc, which calculates the absolute value of the area of the raster element. The relative area
is determined by dividing the absolute value of the area in the block Divide by its maximum value,
which is determined by the second block of mathematical functions Fnc2 of the constant and the
rasterization is determined on the basis of the expression (3). The results of the calculations are
determined by the blocks Scope and Display.
For example, the lineature is L = 50 lines/cm. The model is adjusted to the specified lineature and
parameters. The results of modelling in the form of a characteristic of the raster transformation in
relative units of the elements area are presented in (Figure 2).
Figure 2 : The characteristic of the raster transformation in relative units
The characteristic of raster transformation is a concave quadratic curve, which corresponds to the
optical density of reproduction of a linear raster scale [2]. Traditionally, to assess the tone of the
originals and reproductions, the tone transfer interval is conventionally divided into three ranges: light
0 ≤ D ≤ 0.30; gray 0.30 ≤ D ≤ 1; dark 1.00 ≤ D ≤ 3.0.
The sensitivity of the eye in different ranges varies.
The threshold of visual perception, i.e. the minimum change in optical density is in the light tones
of the original, the largest one is in the dark [4].
Therefore, when preparing an image for printing, it is necessary to pay more attention to the
transfer of light areas than to dark ones. Since the optical density corresponds to the relative area of
the raster element, the selected ranges correspond to the following geometric dimensions of the raster
elements: light 0 ≤ x ≤ 50; gray 50 ≤ x ≤ 100; dark 100 ≤ x ≤ 200 μm.
This approach to describing the division of tone transfer ranges is useful for analysing the
distribution of tones and constructing a fuzzy model of raster transformation.
One should pay attention to features of division of the tone transfer ranges.
For example, the original having an optical density D = 1.0 is gray, and the original D = 1.01 is
already dark. Therefore, the change in density by 0.01 which is less than the threshold of visual
perception ΔD = 0.01 is not possible to be noticed by the operator who performs the tone adjustment
of the image, which is a disadvantage of using traditional tone transfer ranges.
Since Figure 1 shows the characteristics of the raster transformation for square elements, one
assumes that the model of the object is known. In this case, the structure of a typical fuzzy model is
selected, which should contain a fuzzification unit that performs the operation of blurring of the input
geometric size of the raster element.
One of the most popular Mamdani fuzzy models [1] is used for fuzzification, which corresponds to
the characteristic of raster transformation in the form of a set of rules, each of which is determined by
a blurred point.
According to the procedure, first the starting point R1 of the zero geometric size of the raster
element x = 0.0 and the end point R3 for the size x = 200 mkm are selected.
The most important is the selection of the second blurred point R2, which should determine the
most important properties of the raster transformation and corresponds to the geometric dimensions of
the raster element x = 50 mkm and the optical density D = 0.3.
The selected characteristic points on the raster characteristic are represented by asterisks, which
are closest to the reproduction of the raster transformation characteristic X → S represented by a
fuzzy model.
The Mamdani model is a set of rules, each of which defines one blurred point. The set of blurred
points creates a blurred drawing in which the interpolation between points depends on the accepted
elements of fuzzy logic [1].
Fuzzy sets А1 = neighborhood of zero, А2 = neighborhood of 50, А3 = neighborhood of 200 mkm.
correspond to the selected dots. Then the constructed fuzzy Mamdani model for raster transformation
is described by a set (base) of rules:
𝑅1: 𝑖𝑓 (𝑥 ∈ 𝐴1 ) 𝑇ℎ𝑒𝑛 (𝑦 ∈ 𝐵1 )
𝑅2: 𝑖𝑓 (𝑥 ∈ 𝐴2 ) 𝑇ℎ𝑒𝑛 (𝑦 ∈ 𝐵2 ), (5)
𝑅3: 𝑖𝑓 (𝑥 ∈ 𝐴3 ) 𝑇ℎ𝑒𝑛 (𝑦 ∈ 𝐵3 )
where x – input variable of the model (geometric shape of a raster element) which is within [0, 200
mkm], y – model output (relative area S of a raster element) within [0, 1].
Each rule defines typical properties of a raster transformation that geometrically corresponds to a
dot on the X*Y plane. The results of fuzzy model reproduction (outputs) correspond to fuzzy sets:
B1= neighborhood of zero, B2= neighborhood of 50, B3= neighborhood of 200 mkm.
The fuzzy set A of the area of geometric dimensions x of the raster element is a set of pairs:
𝐴 = [𝜇𝐴 (𝑥), 𝑥], (6)
where 𝜇𝐴 (𝑥) – is a membership function of a fuzzy set А, which assigns to each dimension of the
raster element 𝑥 ∈ 𝑋 the degree of its membership 𝜇𝐴 (𝑥) to the fuzzy set А where 𝜇𝐴 (𝑥) ∈ [0, 1]. For
three ranges of geometric dimensions of the elements we use a discrete notation of the fuzzy set A as a
sum:
𝜇 (𝑥 ) 𝜇 (𝑥 ) 𝜇 (𝑥 )
𝐴= 𝐴 1 + 𝐴 2 + 𝐴 3, (7)
𝑥1 𝑥2 𝑥3
where the set А is a sum of sets, rather than an arithmetic pair [𝜇𝐴 (𝑥)/𝑥]
To build a model of raster transformation, we apply, respectively, the linear membership functions
of a triangular shape of a fuzzy set to select three ranges of the variable x:
𝜇𝐴1 (𝑥), 𝑃1 [0, 0,50]
𝜇𝐴2 (𝑥), 𝑃2 [0, 50,200], (8)
𝜇𝐴3 (𝑥), 𝑃3 [50, 200,200]
where Pi[·] – parameters of the membership function of a triangular shape.
The membership function subordinates a certain value from the boundary [0, 1] to each value of
the geometric dimension x of the raster element.
𝜇𝐴 (𝑥): 𝑋 → [0,1], ∀𝑥 ∈ 𝑥, (9)
Based on the research results, a method of using a fuzzy model and database of raster
transformation and organization of defuzzification as well as fuzzy inference with the help of MAX
operator to obtain the results of inference has been worked on.
To build a fuzzy model, the method of simulation in the package Matlab:
Simulink [1] was used. Operating blocks of fuzzy sets and membership functions, located in library
of the Fuzzy Logic Toolbox from the Membership section, and the operation block
Triangular MF for generating the triangular membership function, and traditional visualization
blocks were used for its building.
Based on the above, the block diagram of the fuzzy raster transformation simulator has been built,
shown in Figure 3.
The main blocks are the operating Triangular MF ones which generate the membership functions
of the triangular shape at the input of which is the geometric dimension of the raster element that
forms the Ramp block.
The Scope and Display blocks visualize the membership functions after the inputs are blurred.
The simulator calculates three membership functions simultaneously and blurs the input signal.
The MAX operator is used to obtain a logical inference.
Parameters of the Triangular MF blocks were adjusted to the specified parameters of the model:
P1[0, 0, 50], P2[0, 50, 200], P2[50, 200, 200], which were set in the dialogue boxes of the blocks.
The results of simulation of fuzzy raster transformation model in the form of membership function
are presented in Figure 4.
.
Figure 3 : The block diagram of the fuzzy raster transformation simulator
Figure 4: Graphs of the membership function for raster transformation
3.2. Experiments & Results & Discussion
Graphs of the membership function after blurring are asymmetric, shifted to the left and intersect.
Different values of two membership functions correspond to the input variable x simultaneously. For
example, specific numerical values of the compatible membership functions μ = 0.6; μ = 0.4 will
correspond to the input variable x = 20
Let us assign linguistic (verbal) meanings of variables (light, gray, dark) to the graphs of
membership functions and divide the interval of tone transmission into three ranges: light tones, gray,
and dark.
The fuzzy range of light tones of A1 image is quite narrow, while the range of dark is wide and
shifted to the right.
Thus, black tones dominate in the raster transformation. In other words, raster transformation
darkens the image. Instead, it distorts light images.
For example, at the output variables x = 20, the meaning 0,6 corresponds to the membership to the
"light" tone, and 0.4 to the gray one.
Thus, fuzzy models assess raster transformation more fully, quantitatively, and, therefore,
objectively.
A logical inference is organized with the help of MAX operator of the membership functions given
in percentage, which is quite often used in printing, shown in Figure 5.
Figure 5: The results of logical inference of the membership functions with the help of MAX operator
The results of the logical inference are asymmetric segments of the maximum values of the
membership function shifted to the left in light tones, and their obtained maximum values are 100%
for each fuzzy range.
The lowest value of the tone indicator is on light tones and is 50%, and for dark is 55%. Thus, light
tones have a smaller transmission range comparing to dark ones, so raster transformation reproduces
dark images better than light ones.
Thus, the conclusion is that fuzzy models assess the tone transfer of the raster transformation for
square elements more fully, quantitatively, and, therefore, objectively, which is the advantage of such
models over traditional ones.
4. Conclusions.
A fuzzy model of the image raster transformation for square elements has been developed on the
basis of characteristics of raster transformation in relative area units that correspond to optical density
of reproduction of the linear raster scale with the three characteristic dots that correspond to
neighborhood of three fuzzy sets. Parameters of membership function that describe fuzzy tone transfer
ranges were discovered.
A simulator of a fuzzy model of raster transformation in Matlab:simulink package has been
developed on the basis of Triangular MF operating blocks of fuzzy sets to generate membership
function of triangular shape that has simplified its implementation. The simulator calculates three
membership functions of fuzzy sets and visualizes them.
The results of the simulation modelling in the form of graphs of membership functions of input
and output variables on the tone transfer interval and the results of logical inference are presented. It
was found out that the graphs of membership function for raster transformation are asymmetrical,
intersect and shifted to the light range.
The results of fuzzy tone transfer are two dimensional and define the degree of membership to two
tones, e.g. 0,6 to the light tone, and 0,4 to the gray one.
Fuzzy models assess fuzzy ranges of light, gray, and dark tones reproduction during the process of
raster transformation qualitatively, and, thus, objectively, which is the advantage of fuzzy models
over traditional ones and will help to improve tone transfer adjustment.
For the printing industry, the introduction of this type of regulators will speed up the production of
printed products and reduce shortage costs. Which in today's market conditions is a sufficient
advantage over competitors in the financial sector.
5. References
[1] B.V. Durniak, Ya.O.Medenets, I.T.Strepko, O.V. Tymchenko Fuzzy control of roller rotary
printing presses with clustering of technological parameters. Ukrainian academy of printing.
Lviv (2017) 164 p.
[2] J. Wang, J. Liang, L. Zhang, X. Ding, Non‐fragile dynamic output‐feedback control for‐gain
performance of positive FM‐II model with PDT switching: An event‐triggered mechanism.
International Journal of Robust and Nonlinear Control.
[3] T. Yuvaraja, K. Ramesh. Fuzzy control in H-Bridge MLI for solar photovoltaic system to
enhance load sharing. The International Journal of Electrical Engineering & Education, 57(1)
(2020) 64-72.
[4] Y. Pan, P. Du, H. Xue, H. K. Lam, Singularity-free fixed-time fuzzy control for robotic systems
with user-defined performance. IEEE Transactions on Fuzzy Systems, 29(8) (2020) 2388-2398.
[5] K. Sun, S. Mou, J. Qiu, T. Wang, H. Gao,. Adaptive fuzzy control for nontriangular structural
stochastic switched nonlinear systems with full state constraints. IEEE Transactions on Fuzzy
systems, 27(8) (2018) 1587-1601.
[6] B. Durnyak, M. Lutskiv, P. Shepita, V. Nechepurenko, Simulation of a Combined Robust
System with a P-Fuzzy Controller. Intellectual Systems of Decision Making and Problems
of Computational Intelligence: Proceedings of the XV International Scientific Conference
1020 (2019) 570-580.
[7] B. Imamović, S.S. Halilčević, P.S. Georgilakis, Comprehensive fuzzy logic coefficient of
performance of absorption cooling system Expert Systems with Applications, 190 (2022)
116185. DOI: 10.1016/j.eswa.2021.116185.
[8] A.A. Salem, A.A. ElDesouky, A.H.K. Alaboudy, New analytical assessment for fast and
complete pre-fault restoration of grid-connected FSWTs with fuzzy-logic pitch-angle controller
International Journal of Electrical Power and Energy Systems, 136 107745 (2022). DOI:
10.1016/j.ijepes.2021.107745
[9] P. Tang & Y. Ma Exponential stabilization and non-fragile sampled-date dissipative control for
uncertain time-varying delay TS fuzzy systems with state quantization. Information Sciences,
545 (2021) 513-536.
[10] L. Wang, H. R. Karimi, J. Gu, Stability analysis for interval type-2 fuzzy systems by applying
homogenous polynomially membership functions dependent matrices and switching technique.
IEEE Transactions on Fuzzy Systems, 29(2) (2020) 203-212.
[11] M. J. Mahmoodabadi & M. Andalib Sahnehsaraei. Parametric uncertainty handling of under-
actuated nonlinear systems using an online optimal input–output feedback linearization
controller. Systems Science & Control Engineering, 9(1) 2021 209-218.
[12] J. Yoo, D. Lee, C. Son, S. Jung, B. Yoo, et al RaScaNet: Learning Tiny Models by Raster-
Scanning Images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern
Recognition 2021 13673-13682.
[13] E. Alzaghoul, M. B. Al-Zoubi, R. Obiedat, F. Alzaghoul. Applying Machine Learning to DEM
Raster Images. Technologies, 9(4) (2021) 87.
[14] E. Pérez, P. García. Monitoring soil erosion by raster images: From aerial photographs to drone
taken pictures. Eur. J. Geogr, 8 (2017) 116-128.
[15] M. Azimipour, R. J. Zawadzki, I. Gorczynska, J. Migacz, J. S. Werner, R. S. Jonnal. Intraframe
motion correction for raster-scanned adaptive optics images using strip-based cross-correlation
lag biases. PloS one, 13(10) (2018) e0206052.
[16] J. Xia, J. Zhang, J. Feng, Z. Wang, G. Zhuang, Command filter-based adaptive fuzzy control for
nonlinear systems with unknown control directions. IEEE Transactions on Systems, Man, and
Cybernetics: Systems, 51(3) (2019) 1945-1953.
[17] W.Sun, S. F. Su, Y. Wu, J. Xia. Novel adaptive fuzzy control for output constrained stochastic
nonstrict feedback nonlinear systems. IEEE Transactions on Fuzzy Systems, 29(5) (2020) 1188-
1197.
[18] C. Yang, Y. Jiang, J. Na, Z. Li, L. Cheng, C. Y. Su. Finite-time convergence adaptive fuzzy
control for dual-arm robot with unknown kinematics and dynamics. IEEE Transactions on Fuzzy
Systems, 27(3) (2018) 574-588.
[19] T. Yang, N. Sun, Y. Fang. Adaptive fuzzy control for a class of MIMO underactuated systems
with plant uncertainties and actuator deadzones: Design and experiments. IEEE Transactions on
Cybernetics (2021).
[20] X. Su, F. Xia, J. Liu, L. Wu. Event-triggered fuzzy control of nonlinear systems with its
application to inverted pendulum systems. Automatica, 94 (2018) 236-248.
[21] J. Huo, F. T. Chan, C. K. Lee, J. O. Strandhagen, B. Niu. Smart control of the assembly process
with a fuzzy control system in the context of Industry 4.0. Advanced engineering informatics, 43
(2020) 101031.
[22] D. Zhao, H. K. Lam, Y. Li, S. X. Ding, S. Liu. A novel approach to state and unknown input
estimation for Takagi–Sugeno fuzzy models with applications to fault detection. IEEE
Transactions on Circuits and Systems I: Regular Papers, 67(6) (2020) 2053-2063.
[23] А. F. Abdurakhmanova, I. V. Demianenko Using Adobe Photoshop for vector and raster
graphics creation. XIX All-Russian Student Scientific and Practical Conference of
Nizhnevartovsk State University (2017) 143-146.
[24] X. Lv, J. Fei, Y. Sun, Fuzzy PID controller design for uncertain networked control systems based
on T–S fuzzy model with random delays. International Journal of Fuzzy Systems, 21(2) (2019)
571-582.
[25] H. Yu, Y. Ma, J. Liu, Extended dissipative analysis for uncertain T–S fuzzy system with time-
varying delay and randomly occurring gain variations. Journal of the Franklin Institute, 356(15),
(2019) 8542-8568.