The article presents the results of the study of the factors influence on the printing process of a photo image, including the possible deformation of photopaper. The main factors influencing the printing process quality are established, the oriented graph of the influence and dependencies of these factors is constructed. The analysis of the graph is carried out by the ranking method, which takes into account direct and indirect influences and dependencies between the factors; their priority is calculated. It has been found that the most priority factors are the photopaper weight, the print resolution and the filling area with the following calculated weights: 85, 105, 80 units respectively. These factors have been used to analyse their impact on the inkjet printing process by fuzzy logic. Accordingly, a universal set and corresponding terms have been established in the form of linguistic variables for these factors. Based on the analysis results of the inkjet printing process, a fuzzy knowledge base with the condition "If-Then" has been formed, fuzzy logical equations have been constructed and one of the variants of the factors influence on the inkjet printing process of a photo image is calculated by the defuzzyfication operation according to the "centre of gravity" principle. The formed knowledge base has been verified with the help of the Fuzzy Logic Toolbox system of the Matlab technological calculation environment and the corresponding models have been constructed.
The peculiarity of photo images printing is the use of dyes and pigments water-based inks-jet [
If the inkjet printing process is considered, it primarily depends on such factors as the print
resolution, i.e. the capabilities of the photo printer and its printing heads. Most photo printers allow
one to print with a maximum resolution of up to 5760 dpi and receive high quality photos
accordingly. The minimum ink droplet volume is approximately 1.5 picoliter. As mentioned above, a
significant role in obtaining a high-quality photo image is played by the surface type and the
photopaper weight. There are guidelines for selecting the photopaper depending on the print
resolution, because the more droplets are injected per inch of the image media, the more water it will
absorb. Photopaper weighing 150 g/m2 is recommended for photo images printing with the resolution
of up to 2880 dpi. Thinner paper is easily deformed, torn, and it quickly fades. Consumables of larger
weight – 300 g/m2 – are needed for photos with the resolution of up to 5760 dpi [
Thus, photopaper is a multilayer system whose task is to ensure the accuracy of a digital image reproduction and prevent its distortion during the operation, primarily to minimize its deformation during the application of water inks.
Another factor that affects the photopaper deformation during printing is the image filling area. To
determine the impact of this parameter, a survey has been conducted among owners of photo printers
and companies specializing in the provision of photo printing services. The experts were offered a
questionnaire where it was necessary to indicate how the image filling area from 40 to 100% affects
the printing process quality in which the photopaper has no deformation. The answers have a fuzzy
form, because it is indicated by the terms <high, medium, low>, which allowed the use of survey
results for modelling by fuzzy logic. The examples of successful use of the fuzzy logic principles in
the printing sphere are well known, namely for quantitative assessment of the flexographic printing
quality [
At insignificant filling of photopaper there is a question of expediency of use of high weight photopaper, which is usually more expensive and accordingly, increases the photo cost.
This paper is devoted to constructing models to establish the factors priority and determine their optimal parameters for the inkjet printing process of photographs by using the fuzzy logic tool.
Identification of funding sources and other support, and thanks to individuals and groups that
assisted At the first stage of our study, the factors priority is established by the ranking method [
The set of factors F and possible relationships between them are presented in the form of an oriented graph (Figure 1). The vertices of the graph indicate the presence of the set elements, and the arcs connect these vertices according to the established connections.
Resolution, f2
Weight, f1
Type, f3
Area, f5
Deformation, f6
f4 3. The total weight values are denoted by Sij :
Sij kijwi (i 1,2,3,4; j 1,...,n) , (1) where n – is the number of the factor.
4. For the oriented graph (Fig. 1) in view of (1), the formula for calculating the total weight values for each factor is received: are determined by obtaining the coefficients k3 j . The combined consideration of indirect influences or dependencies of the factor (i.e. the influence or dependency due to other factors) determines the coefficients k2 j and k4 j . 0 0 -10 -10 0 -15
SFJ each of the rows to the sum of the values in the columns S1 j , S2 j S3 j , and S4 j . Finally, the resulting weight of the factor is obtained, which serves as a basis for establishing the factor rank, which is equivalent to the priority of its influence on the inkjet printing process. The maximum rank belongs to the factor with the highest weight value SFj . According to the obtained result, a multilevel model of the influence of the studied factors is constructed (Figure 4).
Level 1
Level 2
2 f , n o t ti u irn l P seo R rep ,f1 ; ap t h thooP iegW 5 f g ,, in ea l r l iF A ace f,e3 f r p uS yT jte f,4 e Ink ypT 6 re f,n app ti o o a to r m hP feo D
In general, fuzzy logic is the logic that operates with linguistic variables using rules that reflect the
principles of human reasoning and are close to ordinary spoken language in their structure [
The quality of the photo inkjet printing process Q depends on the priority factors presented as linguistic variables such as photopaper weight (PW), print resolution (PR) and image filling area (AR):
Q = f (PW, PR, AR) (4)
These linguistic variables, which ensure the quality of the photo images printing process and assessment terms, are presented in Table 2.
Table 2 Linguistic variables of of factors influence on the photo inkjet printing quality № Variable Universal set 1 2 3
Photopaper Weight (PW), g/m2
150-300 Print Resolution (PR), dpi
The logical scheme of the influence of priority factors of the process of inkjet printing of photographic images is shown in Figure 5.
As a result, the expert knowledge base which corresponds to the inkjet photo printing process for the highest level can be presented as follows:
if (PW = Low) or (PW = Medium) or (PW = Big) and (PR = Low) or (PR = Satisfactory) or (PR = High) and (AR = Low) or (AR = Medium) or (AR = High)
then (Q = Low) or (Q = Мedium) or (Q = High)
Based on technical recommendations and expert statements on the factors influence on the inkjet printing quality, in which the photopaper deformation will be minimal, the membership functions are constructed. Accordingly, the value of the variable "Photopaper Weight" is determined on the universal set: u1= 150 g/m2; u2= 190 g/m2; u3= 230 g/m2; u4= 270 g/m2; u5= 300 g/m2.
To linguistically assess this parameter, a set of fuzzy terms is used: T (x) = <Low, Medium, Big>. In accordance with these terms, the membership functions of the linguistic variable "Photopaper Weight" are obtained. The value of the variable in the form of fuzzy sets is as follows:
Photopaper Weight is Low = 1510 ; 01,9809 ; 02,3708 ; 02,7202 ; 03,0101 , g/m2; Photopaper Weight is Medium = 01,5101 ; 01,9708 ; 2130 ; 02,7708 ; 31010 , g/m2;
Photopaper Weight is Big = 01,5101 ; 01,9202 ; 02,3708 ; 02,7809 ; 3100 , g/m2.
For the linguistic variable "Print Resolution", the parameter is defined on the universal set: u1= 1440 dpi; u2= 2520 dpi; u3= 3600 dpi; u4= 4680 dpi; u5= 5760 dpi. To assess the variable, a set of fuzzy terms is used: T (y) = <Low, Satisfactory, High>. Therefore, in relation to this parameter according to these terms, the value of this variable in the form of fuzzy sets is received as follows:
Print Resolution is Low = 14140 ; 205,8280 ; 306,5050 ; 406,3830 ; 507,1610 , dpi; Print Resolution is Satisfactory = 104,1410 ; 205,5250 ; 36100 ; 406,5850 ; 507,1610 , dpi;
Print Resolution is High = 104,1410 ; 205,3230 ; 306,5050 ; 406,8880 ; 57160 , dpi.
The linguistic variable "Filling Area", as another factor in the inkjet process quality, is defined on the universal set: u1= 40 %; u2= 55 %; u3= 70 %; u4= 85 %; u5= 100 %. For linguistic assessment of the parameter, a set of fuzzy terms is used: T (z) = <Low, Medium, High>.
Different values of the variable "Filling Area" are presented in the form of fuzzy sets: Filling Area is Low = 1 ; 0, 89 ; 0, 78 ; 0, 22 ; 0,11 , %;
40 55 70 85 100 low (Q) low (PW) high (PR) high (AR) med (PW) sat (PR) high(AR); med (Q) med (PW) sat (PR) med (AR) low (PW) sat (PR) low (AR); high (Q) big (PW) high (PR) high (AD) big (PW) sat (PR) med (AR). (5)
When substituting the degrees of belonging to the system of fuzzy logical equations, one of the options for calculating the quality of the printing process of a photo image is obtained: low 0, 89 0, 33 0, 22 0, 78 0, 55 0, 22 0, 22 med 0, 78 0, 55 0, 78 0, 89 0, 55 0,89 0, 55 high 0,89 0,88 0,89 0,89 0,55 0,78 0,88
The notation and are the operations of determining the minimum and maximum in logical equations.
Let one set the upper and lower limit of the inkjet printing process quality Q , namely: lower is 1%, upper is 100%.
After performing the defuzzyfication operation using the factors values, the numerical value of the
quality parameter of the inkjet printing process is obtained. To do this, the formula according to the
"centre of gravity" principle is used [
Therefore, having performed the defuzzyfication operation, a quantitative parameter of the process quality is obtained:
Q 1 0, 22 50 0, 55 100 0, 88 0, 22 0, 55 0,88 70,13%
To test the knowledge base and construct a model of the influence of priority factors, a system for
developing fuzzy control systems – Fuzzy Logic Toolbox system of the Matlab technological
calculation environment and Mamdani principle is used [
The simulation results (Figure 7) show the adequacy of the developed knowledge base and the possibility of its use for forecasting assessment of the process quality when selecting the photopaper weight depending on the print resolution and the image filling area.
Thus, the quality factors of inkjet printing of photo images have been studied in the paper. By constructing an oriented graph of the influence and dependencies of factors and the ranking method, the factors priority has been established by giving them the appropriate weight value and constructing the appropriate model. The advantage of the ranking method used is that it takes into account not only direct influences and dependencies between factors, but also indirect ones, which allows to clearly establish their weight values, i.e. priority. Thus, the highest priority is given to the photopaper weight, the print resolution and the filling area with the following calculated weights: 85, 105, 80 units, respectively.
As a result of the simulation process of the influence of priority factors, implemented using fuzzy logic, a matrix of knowledge and fuzzy logical equations are formed to calculate the membership functions of linguistic variables with the corresponding given terms. Their analysis using the "IfThen" condition and the defuzzyfication operation has allowed obtaining a quantitative assessment of the quality of the inkjet printing process. In addition, with the help of Fuzzy Logic Toolbox system of the Matlab technological calculation environment, models of the influence of the print resolution, the photopaper weight and the image filling area have been constructed, which will allow to select the paper weight a priori depending on other factors to ensure sufficient quality of photo printing process. 5. References