The study has highlighted a set of factors influencing the quality of postpress processes designing. A fuzzy preference relations on a given set of alternatives has been formed. The matrices of relations of alternatives by Paretooriented factors have been constructed and the non-dominant subset has been defined. Based on a fuzzy preference relation, the corresponding sets of nondominated alternatives have been distinguished. The optimal variant of the analysed process has been selected according to the maximum value of the utility function. Modelling of key operations and functions of postpress processes designing 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.
The final stage of the book production technology which includes finishing and binding processes is often mistakenly identified with a set of mechanical, cyclically repetitive 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 operational 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 requirements and choose the wrong finishing material.
Computer-aided automation does not presents the expected results, since the procedures used are not integrated into a single, indivisible system. Under such conditions, 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 multicriteria assessment of alternative options for the implementation of postpress processes on the basis of fuzzy preference relations and determining the optimal one, which will result in obtaining the proper quality products. The specified procedure becomes an important component of IDEF0 models of the implementation of postpress processes designing. 2
An important point in the study of postpress processes is considered the presence of technological characteristics or parameters, on which the effectiveness of the publication 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 determining 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
presented in the form R R1, R2 , R3 , R4 , R5 , R6 , R7 , R8 , where R1 are the edition
parameters; 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
calculations; R8 is a technological process diagram [
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.
AccorxD
dingly, by the method of linear minimization of the criteria, combining partial target
functionals r1, ..., rn is carried out according to the formula [
For the factors independent in utility and preference, the following utility function
exists [
n R v, x vi ri x max; v V ,
i1 xD V v v1, ..., vn Q ; vi 0; n vi 1, i1
n U x viui yi , i1 (1) (2) 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 utilii1 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
The analysis of literary sources shows the necessity of a reasonable selection of
factors influencing the quality of printed products [
The formation and multicriteria assessment of alternative options for the implementtation of postpress processes based on fuzzy preference relationships. The determination of Pareto-optimal alternative on the basis of the results analysis of the nondominant sets intersection of the relation convolutions and the maximum value of the membership function of a common set. Modelling of designing procedures of postpress 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.
Making management decisions regarding the alternative implementation of
technological 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
technological process are the criteria. According to Pareto principle [
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 alternatives (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 :
Rj x, y : rj x rj y , x, y X
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: (1) (2) rj x0 rj y , j 1, m; y X
The convolution of all the criteria of formed Pareto set into a single scalar is
carried out by the intersection method [
m We denote Q1
Rj . Thus, the set of alternatives X x1, ..., xn with prej1 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 Rj 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:
Accordingly, the membership function of the convolution Q1 is written as follows: 1, if rj x rj y , then x, y Rj j x, y
0, if x, y R Q1 x, y min1 x, y,2 x, y,...,n x, y
Q x min vj rj x
j
The convolution of the criteria, taking into account the weight values of the process factors v j and the corresponding utility functions, will be:
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:
(3)
(4)
(5)
(6)
(7)
It corresponds to the following membership function: [
m m Q2 v j rj x, where v j 1, v j 0 j1 j1
m Q2 x, y j1 vj j x, y
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 decomposition 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, ..., In , the arrows of the control type (procedures and management strategies) will be the set C C1, ...,Cn , the arrows 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, ..., Mn . 6
We determine the quality of postpress processes designing by assessing fuzzy preference relations Ri on the set of alternatives X x1, x2 , x3 : R1 (the edition parameters) — x1 x2 , x2 x3 ; R2 (operating conditions) — x1 x3 , x2 x3 ; R3 (structural 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. R1 xi , xj = R3 xi , x j = Q1 xi , xj = R2 xi , xj = R2 xi , xj =
According to the convolution of relations Q1 , a subset of non-dominant
alternatives will look like this [
Qнд Qнд 1
Qнд
2 нд x minQнд x ,Qнд x 1 2 (11) (12) (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 processes designing are of the control type (procedures and management strategies), we obtain the following context diagram of IDEF0 model (Fig. 1).
C1
C2
C3 Implementation alternatives I I1 Printed sheets 2
Postpress processes designing
M1 M 2
As a result of the corresponding calculations, we get a subset of non-dominant alternatives of the following form: Qн1д x1 1 sup0 0; 0 0 1;
yX Qнд x2 1 sup0 0; 0 0 1;
1 yX Qнд x3 1 sup0 0; 0 0 1.
1 yX 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: Q2 xi , x j = 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).
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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 [
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
volume indicates the number of paper sheets or pages within a single copy [
– I2 (printed sheets). The result of prepress processing of the originals and printing 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
operating intensity of the finished edition [
– C3 (implementation alternatives). Pareto-optimal alternatives, determined by the
assessment of fuzzy relations on a given set of alternatives [
– 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.
– M1 (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
production workers in the design. If necessary, the authors and customers of the book
edition are involved [
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 selection of the most efficient alternative according to the maximum value of the membership function of the convolutions has been implemented.
Modelling of key operations and functions provides the basis for predictive assessment of the quality of the studied process. 21. Velychko, O. M., Skyba, V. M., Shanhin, A. V.: Designing of technological processes of publishing and printing production: Educational textbook. NTUU "KPI", Kyiv. 235 p. (2014) (In Ukrainian). 22. Keif, M. G.: Designer’s postpress companion. National Association for Printing. 170 p.
(2003). 23. Kipphan, H.: Handbook of Printed Media: technologies and production methods. Springer.
1207 p. (2001). 24. Kokot, J.: Digital Printing, Finishing and Post-press: Process Chains with Modular System
Components. BdgW Agency. 178 p. (2018). 25. Havenko, S., Lazarenko, E., Mamut, B., Sambulskyi, M., Tsymanek, Ya., Yakutsevich, S., Yarema, S.: Decoration of printed products: technology, equipment, materials. University “Ukraine”, UAP, Kyiv-Lviv. 180 p. (2003) (In Ukrainian). 26. Romano, F.: Print Media Business / Translated from English. M. Bradis, V. Voblenko, N. Druzieva; Ed. B. A. Kuzmin. PRINT MEDIA, Moscow. Center, 456 p. (2006) (In Russian). 27. Malcolm, J. Keif: Postpress technologies / Translated from with English. S. I. Kuptsova; Ed. S. I. Stefanova. PRINT MEDIA Center, Moscow. 280 p. (2005) (In Russian).