=Paper=
{{Paper
|id=Vol-2533/paper24
|storemode=property
|title=Models of Postpress Processes Designing
|pdfUrl=https://ceur-ws.org/Vol-2533/paper24.pdf
|volume=Vol-2533
|authors=Vsevolod Senkivskyi,Alona Kudriashova,Iryna Pikh,Ivan Hileta,Oleh Lytovchenko
|dblpUrl=https://dblp.org/rec/conf/dcsmart/SenkivskyiKPHL19
}}
==Models of Postpress Processes Designing==
https://ceur-ws.org/Vol-2533/paper24.pdf
Models of Postpress Processes Designing
Vsevolod Senkivskyi[0000-0002-4510-540X], Alona Kudriashova[0000-0002-0496-1381],
Iryna Pikh[0000-0002-9909-84444], Ivan Hileta[0000-0001-6935-2854],
Oleh Lytovchenko [0000-0002-5637-6934]
Ukrainian Academy of Printing, 19, Pid Holoskom St., Lviv, 79020, Ukraine
senk.vm@gmail.com,kudriashovaaliona@gmail.com,
pikhirena@gmail.com, hileta@gmail.com, lytowchenko@gmail.com
Abstract. The study has highlighted a set of factors influencing the quality of
postpress processes designing. A fuzzy preference relations on a given set of al-
ternatives has been formed. The matrices of relations of alternatives by Pareto-
oriented factors have been constructed and the non-dominant subset has been
defined. Based on a fuzzy preference relation, the corresponding sets of non-
dominated alternatives have been distinguished. The optimal variant of the ana-
lysed process has been selected according to the maximum value of the utility
function. Modelling of key operations and functions of postpress processes de-
signing has been implemented through the development of a context diagram
and a decomposition diagram of IDEF0 models, one of the elements of which
are alternatives for this process implementation.
Keywords: postpress process, factor, alternative, fuzzy preference relation, uti-
lity function, optimization, model, IDEF0 modelling.
1 Introduction
The final stage of the book production technology which includes finishing and bin-
ding processes is often mistakenly identified with a set of mechanical, cyclically re-
petitive actions, depriving them of a highly intellectual information component. This
approach increases the likelihood of partial or total rejection of the print run. A typical
mistake is also the mismatch of manufactured products to their functional and opera-
tional characteristics. Thus, for example, for an edition that should serve for decades,
one can use an adhesive binding of organic origin that is not suitable to meet the re-
quirements and choose the wrong finishing material.
Computer-aided automation does not presents the expected results, since the pro-
cedures used are not integrated into a single, indivisible system. Under such condi-
tions, post-operational information support is appropriate and necessary, which will
result in a predictive assessment of the future products quality. Such an approach in
the presence of uncertainty conditions requires the formation, calculation and multi-
criteria assessment of alternative options for the implementation of postpress pro-
cesses on the basis of fuzzy preference relations and determining the optimal one,
which will result in obtaining the proper quality products. The specified procedure
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0)
2019 DCSMart Workshop.
becomes an important component of IDEF0 models of the implementation of post-
press processes designing.
2 Formal problem statement
An important point in the study of postpress processes is considered the presence of
technological characteristics or parameters, on which the effectiveness of the publi-
cation in the general cycle of its production depends. Generalizing such factors, we
introduce the concepts of factors that become the main elements of models for de-
termining the priority of the factors influence on the course of implementation and
predictive assessment of the quality of postpress processes.
Eventually, a set of the designing factors of the postpress processes will be pre-
sented in the form R R1 , R2 , R3 , R4 , R5 , R6 , R7 , R8 , where R1 are the edition param-
eters; R2 are structural features; R3 are operating conditions; R4 is a type of production;
R5 are materials; R6 is a type of equipment; R7 are technological and economic cal-
culations; R8 is a technological process diagram [12]. The initial step to prioritizing
the influence of these factors on the process is to design a semantic network, the es-
sence of which is to capture the existing relations between the factors. It becomes the
basis for the construction of a matrix of pairwise comparisons, processing of which
leads to obtaining conditional weight values that determine the numerical priorities of
factors — their importance value for the technological process. Next is the calculation
and the determination of the optimal (among alternative) options for the implemen-
tation of post-press processes designing.
A multicriteria optimization of functions r x r1 x , ..., rn x on the set B is to
distinguish the maximum value of the utility functions ri x max, i 1, n. Accor-
xD
dingly, by the method of linear minimization of the criteria, combining partial target
functionals r1 , ..., rn is carried out according to the formula [13-16]:
n
R v, x vi ri x max; v V , (1)
xD
i 1
n
V v v1 , ..., vn ; vi 0; vi 1 ,
Q
i 1
where vi are weights of the factors of Pareto set.
For the factors independent in utility and preference, the following utility function
exists [17, 18]:
n
U x vi ui yi , (2)
i 1
where: U x is a multicriteria utility function; 0 U x 1 are alternatives x ; vi
n
is the weight of the i -th criterion, moreover 0 vi 1, vi 1 ; ui yi ; is the utili-
i 1
ty function of the i -th criterion 0 ui yi 1 ; yi is the value of the alternative x
by the i -th criterion.
3 Literature review
The analysis of literary sources shows the necessity of a reasonable selection of fac-
tors influencing the quality of printed products [1-7]. In recent years, the simulation of
postpress processes with the help of computer equipment and specific software has
been used [8-11]. As risk and uncertainty are peculiar to complex processes, quantita-
tive parameters for making a sound decision about the implementation of the studied
process can be obtained on the basis of the methods of the operations research [12-
16]. The design of the studied processes is performed through the calculation of alter-
native options for their implementation [17, 18]. It is important to take into account
the fact that the equipment for performing separate operations of finishing and bind-
ing processes and the materials used for different types of products are individual [19-
23]. The principle of vertical design is actively applied, which distinguishes between
the procedures of analysis and synthesis. The synthesis creates the descriptions of
objects that reflect their structure and parameters [25]. The selection of technology
and postpress equipment depends on the type of printed matter, its purpose, produc-
tion volumes, economic and financial indicators of the printing company activities
[26, 27]. A significant problem is the adherence to standards for the edition produc-
tion, metrological characteristics related to the quality in printing, modelling of busi-
ness processes, which are important factors of planning and effective functioning of
printing companies. The performed analysis indicates that there is no information
approach to the problem of forming the book quality, the final stage of which is the
postpress process. The essence of the new methodology is the use of methods and
means of theory of operations research, modelling theory, expert assessment of publi-
shing and printing processes, which will ensure the proper quality of printed products.
4 Objectives of the work (problem setting)
The formation and multicriteria assessment of alternative options for the implement-
tation of postpress processes based on fuzzy preference relationships. The determi-
nation of Pareto-optimal alternative on the basis of the results analysis of the non-
dominant sets intersection of the relation convolutions and the maximum value of the
membership function of a common set. Modelling of designing procedures of post-
press process by means of context diagrams for the corresponding decomposition
levels of IDEF0 models. Obtaining a model-basis for further predictive assessment of
the quality of the postpress process.
5 Materials and methods
Making management decisions regarding the alternative implementation of techno-
logical processes can be complicated by the lack of information about their priority
and the inability to quantify the benefits. Instead, it is possible to pair the alternatives
in the segment [0; 1] and to represent the data in numerical form. The assessment is
carried out on the basis of multicriteria optimization, where the factors of the tech-
nological process are the criteria. According to Pareto principle [17, 18], it is suffi-
cient to select only the dominant factors with the highest weight parameters, which
form Pareto set P( D) , where D Ri is a set of valid values. Accordingly, with a
fuzzy preference relation, decision-making will be exercised by Pareto-optimal alter-
natives for a set of alternatives.
Introducing a clear relation of non-strict preference Ri for a set of alternatives
X x1 , ..., xn allows making one of the following statements for any pair of alterna-
tives ( x, y) : x is not worse than y , that is x y, x, y R ; y is not worse than x
being written as y x, y, x R , x and y are not comparable, x, y R,
y, x R. This approach makes it possible to narrow down the rational selection class.
If there is a strict preference x, y Rz the alternative x prevails y , that is
x y . With clear utility functions rj of the set X , the alternative x with a higher
assessment rj x by the factor j is better than the alternative y whose assessment
is rj y . The above statement is described by a clear relation of the advantage R j of
the set X :
R j x, y : rj x rj y , x, y X (1)
To single out Pareto-optimal alternative, it is necessary to select the alternative
x0 X with the highest utility ranking on the set of all factors:
rj x0 rj y , j 1, m; y X (2)
The convolution of all the criteria of formed Pareto set into a single scalar is car-
ried out by the intersection method [17].
m
We denote Q1 R j . Thus, the set of alternatives X x1 , ..., xn with pre-
j 1
ference relation Q1 corresponds to the set of alternatives with utility functions rj x .
Identifying non-dominant alternatives by a fuzzy preference relation Q1 is to replace
several relations R j j 1, m by the intersection between them. We will assume that
j x, y is a membership function of a clear preference relation rj . We form the
condition:
1, if rj x rj y , then x, y R j
j x, y (3)
0, if x, y R
Accordingly, the membership function of the convolution Q1 is written as follows:
Q x, y min 1 x, y , 2 x, y ,..., n x, y
1
(4)
The convolution of the criteria, taking into account the weight values of the process
factors v j and the corresponding utility functions, will be:
Q x min v j rj x (5)
j
The convolution of the initial relations Q2 is also formed by the weight values of
the analysed factors v j and the corresponding utility functions:
m m
Q2 v j rj x , where v j 1, v j 0 (6)
j 1 j 1
It corresponds to the following membership function: [15-18]
m
Q x, y v j j x, y
2
(7)
j 1
The methodology of IDEF0 modelling has been used to model the studied process,
which involves the construction of context diagrams of a tree structure, created on the
principle of decomposition. Next, we denote the context diagram A-0, and the de-
composition diagram of the first level — A-1. The arrows of the input type (what is
being processed) will be the set of values I I1 , ..., I n , the arrows of the control
type (procedures and management strategies) will be the set C C1 , ..., Cn , the ar-
rows of the output type (result) will be the set O O1 , ..., On , and the arrows of the
mechanism type (required resources) will be the set M M1 , ..., M n .
6 Experiment
We determine the quality of postpress processes designing by assessing fuzzy prefe-
rence relations Ri on the set of alternatives X x1 , x2 , x3 : R1 (the edition parame-
ters) — x1 x2 , x2 x3 ; R2 (operating conditions) — x1 x3 , x2 x3 ; R3 (structu-
ral features) — x1 x2 , x2 x3 ; R4 (a type of production) — x1 x2 , x2 x3 .
We form the matrices of relations for the factors R1 , R2 , R3 and R4 . We use two
types of numeric visualizers: 0 and 1, where 0 is the absence of preference.
x1 x2 x3 x1 x2 x3
R xi , x j = R xi , x j =
x1 1 1 0 x1 1 0 0
1
x2 1 1 0 2
x2 1 1 1
x3 1 1 1 x3 1 0 1
x1 x2 x3 x1 x2 x3
R xi , x j = R xi , x j =
x1 1 1 1 x1 1 1 1
3 2
x2 0 1 1 x2 0 1 1
x3 0 1 1 x3 0 1 1
We construct the convolution of relations Q1 R1 R2 R3 R4 . The absence of
preference of the xi -th alternative is considered to be zero by the factor analysed.
x1 x2 x3
Q xi , x j =
x1 1 0 0
1
x2 0 1 0
x3 0 0 1
According to the convolution of relations Q1 , a subset of non-dominant alterna-
tives will look like this [14-17]:
4
Qнд x 1 sup Q y, x Q x, y (8)
j 1
1 1 1
y X
Having used these matrices of relations and (8), we get:
Qнд x1 1 sup x2 x1 x1 x2 ; x3 x1 x1 x3 ;
1
y X
нд
Q1 x2 1 sup x1 x2 x2 x1 ; x3 x2 x2 x3 ;
y X
Qнд x3 1 sup x1 x3 x3 x1 ; x2 x3 x3 x2 .
1
y X
Now we set the fuzzy preference relation Q2 , j 1, 4 :
4
Q2 v j rj x (9)
j 1
We form the membership functions for the convolution of relations Q2 and the
corresponding sets of non-dominant alternatives:
4 4
Q x, y w j j x, y , w j 1, w j 0
2
(10)
j 1 j 1
Q x1 , x2 v1 R x1 , x2 v2 R x1 , x2 v3 R x1 , x2 v4 R x1 , x2
2 1 2 3 4
Q x1 , x3 v1 R x1 , x3 v2 R x1 , x3 v3 R x1 , x3 v4 R x1 , x3
2 1 2 3 4
Q x2 , x1 v1 R x2 , x1 v2 R x2 , x1 v3 R x2 , x1 v4 R x2 , x1
2 1 2 3 4
Q x2 , x3 v1 R x2 , x3 v2 R x2 , x3 v3 R x2 , x3 v4 R x2 , x3
2 1 2 3 4
Q x3 , x1 v1 R x3 , x1 v2 R x3 , x1 v3 R x3 , x1 v4 R x3 , x1
2 1 2 3 4
Q x3 , x2 v1 R x3 , x2 v2 R x3 , x2 v3 R x3 , x2 v4 R x3 , x2
2 1 2 3 4
4
Qнд x 1 sup Q y, x Q x, y (11)
j 1
2 2 2
y X
2 2
Qнд x1 1 sup Q x2 , x1 Q x1 , x2 ; Q x3 , x1 Q x1 , x3
2 2 2
x 1 sup x , x x , x ; x , x x , x
нд
Q2 2 Q2 1 2 Q2 2 1 Q2 3 2 Q2 2 3
x 1 sup x , x x , x ; x , x x , x
нд
Q2 3 Q2 1 3 Q2 3 1 Q2 2 3 Q2 3 2
To determine Pareto-optimal alternative, we perform the intersection of sets Q1нд
and Q2нд and define the membership function of a common set:
Qнд Q1нд Q2нд (12)
нд x min Qнд x , Qнд x
1 2
(13)
The selection of the most efficient alternative is made by the maximum numeric
value of the membership function Qнд xi . Since the alternatives for postpress pro-
cesses designing are of the control type (procedures and management strategies), we
obtain the following context diagram of IDEF0 model (Fig. 1).
C1 C2 C3
Regulatory technical Opera- Implementation
and technological ting con- alternatives
documentation ditions Quality level of
postpress processes
Edition parameters designing
I1 Postpress processes O1
I 2 Printed sheets designing Finished
O2
project
Hardware and Staff, the subject area
software, other experts, interested people
tools
M1 M2
Fig. 1. Context diagram of IDEF0 model of the postpress processes implementation
7 Results
As a result of the corresponding calculations, we get a subset of non-dominant al-
ternatives of the following form:
Qнд x1 1 sup 0 0;0 0 1;
1
y X
нд
Q1 x2 1 sup 0 0;0 0 1;
y X
Qнд x3 1 sup 0 0;0 0 1.
1
y X
Qнд x 1;1;1
1
The membership functions of the additive convolution of relations Q2 for each
planned alternative, when the values of the factors weights are set v1 0,53;
v2 0, 27; v3 0,13; v4 0,07 have such values: Q2 x1 , x2 0,73 ; Q2 x1 , x3
0, 2 ; Q2 x2 , x1 0,8 ; Q2 x2 , x3 0, 47 ; Q2 x3 , x1 0,8 ; Q2 x3 , x2 0,73 .
We present the values of the membership functions with the help of the matrix of
relations:
x1 x2 x3
Q xi , x j =
x1 1 0,73 0,2
2
x2 0,8 1 0,47
x3 0,8 0,73 1
We find the elements of the subset of non-dominant alternatives for the relation Q2 :
Qнд x1 1 sup 0,8 0, 73 ; 0,8 0, 2 0, 4
2
Qнд x2 1 sup 0, 73 0,8 ; 0, 73 0, 47 0, 74
2
Qнд x3 1 sup 0, 2 0,8 ; 0, 47 0, 73 1, 26
2
After calculations, we get:
Qнд xi 0, 4; 0,74; 1, 26.
2
According to the intersection of sets Q1нд and Q2нд the maximum value will have
the membership function Qнд x3 0, 4; 0,74; 1, 26 , i.e. the third option is consi-
dered the optimal one.
The process of functional decomposition of the context diagram shown in Fig. 1
consists in its division into lower order functions and setting of the direction of the
boundary arrows, which contributes to the detailing of activities within the studied
process. Based on the above statements, we construct the resulting decomposition
diagram of the context diagram (Fig. 2).
C1 C2 C3
Regulatory technical Implementation
Operating
and technological conditions alternatives
documentation
Edition pa-
DED Structural
rameters
I1
features
I2 Printed sheets
DRE
DSO
Formalized re- Quality level of
quirements postpress processes
designing
DPM O1
Hardware and Technological O2
Finished
software, other process diagram project
tools
Staff, the subject area ex-
perts, interested people
M1 M2
Fig. 2. Diagram of the first decomposition of IDEF0 model of the postpress processes designing
The diagram of the first decomposition of IDEF0 model of the postpress processes
designing contains the following functional blocks: DED — the determination of the
edition design, DRE — the determination of the requirements for the finished edition,
DSO — the determination of the sequence of technological operations, DPM — the
determination of the processing modes [12, 19].
We will analyse the components information load of the sets of boundary arrows in
IDEF0 model of the postpress processes designing:
– I1 (the edition parameters). The key parameters of the book editions are a kind,
type, format and volume. Editions are divided into kinds according to a number of
typological features: production method, periodicity, material structure, composition
of the main text, language feature, purpose, frequency of issue, structure, etc. The
format determines the size of the print sheets and the finished book block. The vol-
ume indicates the number of paper sheets or pages within a single copy [19].
– I 2 (printed sheets). The result of prepress processing of the originals and prin-
ting of the print run is the printed paper sheets that arrive at the postpress section.
– C1 (regulatory technical and technological documentation). Regulatory technical
documents include technical requirements and legal regulations, in particular: laws,
standards, specifications, codes of established practice, etc.
– C2 (operating conditions). Operating conditions include the lifespan and opera-
ting intensity of the finished edition [19].
– C3 (implementation alternatives). Pareto-optimal alternatives, determined by the
assessment of fuzzy relations on a given set of alternatives [18].
– O1 (quality level of postpress processes designing). The result of the post-press
processes designing is an appropriate level of the project quality.
– O2 (finished project). The project determines the progress of all technological
actions aimed at the implementation of postpress processes.
– M 1 (hardware and software, other tools). The postpress processes designing is
done using the computer technology and specific, narrow-profile software.
– M 2 (staff, the subject area experts, interested people). The participation of pro-
duction workers in the design. If necessary, the authors and customers of the book
edition are involved [19, 20].
8 Conclusions
Matrices of relations for certain factors influencing the quality of postpress processes
designing have been formed. Membership functions for the convolution of relations
and corresponding sets of non-dominant alternatives have been received. The selec-
tion of the most efficient alternative according to the maximum value of the member-
ship function of the convolutions has been implemented.
Modelling of key operations and functions provides the basis for predictive as-
sessment of the quality of the studied process.
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