Modeling the selection of innovative strategy for development of

industrial enterprises

NADYA MIRONOVA

Department of Management

University of National and World Economy

str. "December 8th", 1700 Student Complex, Sofia

BULGARIA

HANNA KOPTIEVA

Department of Management and Taxation

National Technical University «Kharkiv Polytechnic Institute»

2, Kyrpychova str., 61002, Kharkiv

UKRAINE

IRYNA LIGANENKO

Deputy Director for Educational and Methodical Work

Prydunai Branch of Private joint-stock company “Higher educational institution

“Interregional Academy of Personnel Management”

str. Klushina, 3A, 68607, Izmail,

UKRAINE

AYTA SAKUN

Department of Philosophy, Political Science and Ukrainian Studies

Kyiv National University of Technologies and Design

Nemyrovycha-Danchenka Street, 2, 01011, Kyiv,

UKRAINE

DARYNA CHERNYAK

Department of Philosophy and Cultural Studies

Kyiv National University of Technologies and Design

Nemyrovycha-Danchenka Street, 2, 01011, Kyiv,

UKRAINE

Abstract: - The assessment of the state of the innovation sphere of Poland in relation to the world level shows

that Poland has educational and scientific potential allowing to produce scientific ideas and developments but

the level of their commercialization remains low. As a result, Poland lags in terms of such criteria for the

development of innovation sphere as labor productivity and financial support for innovation activities. The

methodological basis of the study is the theory of fuzzy sets and the matrix approach — in modeling the

selection of strategies to stimulate innovative development of industrial enterprises. The construction of a

matrix of strategies is based on the diagnosis of the total potential of industrial enterprises and the level of its

implementation in the innovation sphere. Modeling of the selection of innovation development strategy for

industrial entities based on the use of fuzzy set theory in assessing the level of investment attractiveness and

innovation potential of enterprises is carried out. Based on the proposed methodological approach, the strategic

directions of innovative development of three Polish industrial enterprises are substantiated.

Keywords: - Innovative Strategy; Industrial Enterprise; Management; Development; Potential; Matrix.

Received: May 30, 2021. Revised: December 7, 2021. Accepted: January 14, 2022. Published: January 16, 2022.

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1 Introduction

The current period of economic development is

characterized by active interaction and rapid

changes in production and digital technologies,

processes of intellectualization of labor, which are

defined by the concepts of the fourth industrial

revolution [1]. Economic growth and rating of the

country in the world economy are determined by its

intellectual capital, ability to generate new ideas and

implement them through innovation and investment

model of development [2, 3, 4]. The high level of

global competition in the market of industrial

products, the accelerated dynamics of its

technological renewal and digitalization determine

the urgency of the problems of effective stimulation

of innovation, the main subject of which is

traditionally industrial enterprises [5, 6, 7].

The global pandemic of 2020 exacerbated the

problems of access to financial resources and capital

markets but at the same time identified strategic

importance for each country of state support for

high-tech industries, including pharmaceuticals,

electronics and telecommunications equipment,

medical, high-precision and optical technology. The

development of such activities is based on

increasing the intellectualization of labor and

requires additional investment in the

commercialization of knowledge and therefore in

the innovation [8, 9, 10].

Stimulation of innovative activity in modern

economies is carried out by means of a complex of

economic tools and levers both in the system of

state regulation and market relations [5]. Of

particular importance are the issues of streamlining

economic instruments and levers to intensify

innovation. The solution of the outlined problems

requires the implementation of a systematic and

balanced state policy in order to increase the

efficiency of economic regulation of the innovation

sphere [11, 12, 13].

The mechanism for stimulating the innovative

activity of industrial enterprises is a component of

the model of innovative development of industry,

the economy as a whole and its regions, which

should ensure sustainable development [14, 15].

Sustainability (equilibrium, balance) is a state of

system development in which the actions of various

economic and other factors do not cause significant

deviations, i.e., development parameters remain

within acceptable limits or do not exceed the

allowable limits of the system according to its

development strategy [16].

On the other hand, the mechanism of

stimulating innovation should provide such

development that would be most effective for the

current generation, while not harming any future

generation, therefore, the innovation mechanism

should be aimed at saving resources, both natural

and material, and increasing the welfare of the

population at the present stage [17, 18, 19].

The mechanism of stimulation of innovative

activity is a set of actions of administrative character

which interconnect and direct development of

innovative activity of economic entities in

accordance with mission and hierarchy of the long-

term purposes of development of entities [20].

Analysis of the organization of the functioning

of bodies for regulation of innovation activities

gives grounds to assert the lack of systemacity both

at the level of formation of the regulatory

framework and the activities of regulatory

institutions, in particular in the use of appropriate

tools [21, 22, 23]. Therefore, methodological

approaches to the formation of a system of

economic regulation of innovation processes in

Poland need improvement. Given the existing

approaches to understanding the essence of tools to

support innovation in industry, the following

definitions of the economic mechanism for

stimulating innovation in industrial enterprises are

proposed.

From the point of view of the system-structural

approach, the economic mechanism of stimulation

of innovative activity is a set of economic methods,

approaches, tools and levers of influence on

innovative activity at all stages of industrial activity

for the purpose of ensuring its competitiveness and

increasing its contribution to sustainable economic

development [24].

From the point of view of understanding the

economy and its mechanisms as a system of

relations, the economic mechanism of stimulation of

innovative activity is a set of procedures and rules

of economic relations of economic entities,

government institutions and other stakeholders

regarding increase in innovation activity at all stages

of industrial activity for the purpose of ensuring its

competitiveness and increasing its contribution to

sustainable economic development [26, 26].

The complexity of the processes of innovation

of industrial enterprises necessitates the use of a set

of criteria and indicators in the management of these

processes [27]. Another requirement, in addition to

systemacity, the availability of quality and regular

information for decision-making at various levels of

management and support for innovation. One of the

tools that is actively used in modern management

systems, taking into account the above

requirements, is the introduction of a monitoring

system [28].

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In a general sense, monitoring is a set of

program-methodological, organizational,

technological and other tools that provide regular

monitoring of the state of a particular object

according to a pre-developed methodology and

system of indicators [29].

Thus, as of today the theoretical and

methodological basis for the study of the innovation

sphere and its state regulation has been formed.

However, modern trends in the development of the

institutional structure of the innovation sphere, new

forms of stimulating the innovative activity of

industrial enterprises, taking into account their

specifics and the potential for development of

strategic industries, require a further study. The

importance of the studied issues for the domestic

economy is increased by the threatening trend of

declining industrial production, low share of

innovative products, the need to modernize industry

and find new models of its development. The

relevance, theoretical and practical significance of

these problems led to the selection of the topic of

the paper, its purpose, subject, object, and logic of

scientific study.

The purpose of the paper is to deepen the

theoretical and methodological principles and

develop scientific and practical recommendations

for modeling the selection of strategies for

innovative development of industrial entities in

order to justify the directions of their economic

stimulation and taking into account investment

attractiveness and innovation potential.

2 Methodology

Effective implementation of strategies for

innovative development of industries requires the

presence of internal economic incentives, primarily

at the enterprise level. Appropriate management

decisions on the selection of strategies for

innovative development at the micro level should be

based on factors related to the internal and external

environment of the enterprise, indicators of its

investment attractiveness. Such decisions require the

use of a broader information and analytical

framework, which is based on financial and other

types of reporting of the economic entity. In this

regard, it is proposed to carry out modeling of the

selection of innovation development strategy and

stimulation of its implementation at the micro level

taking into account two criteria: investment

attractiveness (X); innovation potential (У).

Given the complex nature of these criteria and

the level of testing of existing scientific and

methodological approaches to their evaluation, it is

proposed to measure the level of investment

attractiveness and innovation potential of the

enterprise using fuzzy set theory and to classify the

obtained integrated assessments as follows:

1) for the criterion of "investment

attractiveness of the enterprise", to use three levels

of values of integrated assessment: "very good",

"good", "bad";

2) for the criterion of "innovation potential of

the enterprise", to use four levels of values of

integrated assessment: "very good", "good",

"satisfactory", "bad".

Determining the level of investment

attractiveness of the enterprise involves assessing a

set of indicators of its financial and economic

condition. A well-constructed model of

comprehensive analysis of investment attractiveness

should contain the optimal number of indicators that

reflect only those data that are of interest to the

manager or potential investor. In addition, the list of

indicators of the model should not include those

indicators that duplicate information. In opinion of

the authors, the balanced list of investment

attractiveness indicators is as follows [31, 32, 33]:

1. The financial independence/autonomy ratio

(

1

x

) that shows the share of own capital in the total

capital. The economically feasible value of this ratio

should be more than 0.5, i.e., the share of own

capital should be at least half of the total capital. It

is believed that the investor will be more willing to

invest in the company, the greater the share of own

capital in the total capital. As then the company is

more likely to be able to pay its obligations on its

own.

On the other hand, it should be understood that

the company will not be able to develop normally if

it does not attract external resources, at least in order

to replenish working capital.

2. Investment ratio (

2

x

) that characterizes the

adequacy of the own capital for covering fixed

assets and the participation of own capital in the

formation of assets. Economically feasible value is

more than 1. The higher the value of the indicator

compared to 1, the more stable the financial

condition of the enterprise.

3. Maneuverability coefficient (

3

x

). Standard

value: 0.40–0.60. The increase in the value of this

coefficient characterizes the positive changes in the

financial condition of the enterprise, as it means that

it increases the ability to maneuver with own funds.

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4. Current liquidity ratio (

4

x

) that determines

the ability of the company to meet its obligations at

the expense of current assets. It is believed that

current assets should be 1.5–2.5 times more than

debt obligations, i.e., the standard value of this

indicator is 1.5–2.5. In this case, the sale of current

assets provides settlement of liabilities. A very low

value of the ratio indicates a high probability of loss

of solvency, and too high value of the ratio indicates

an inefficient use of borrowed capital. The current

liquidity ratio shows how short-term liabilities are

covered by short-term assets, which will have to be

converted into money for a period equal to the

maturity of liabilities.

5. Return on assets (

5

x

) that shows the

amount of revenue from sales of products per 1 euro

of fixed assets. The greater the return on assets, the

more efficient the use of fixed assets, i.e., the capital

invested in them.

6. Along with the return on assets, it is

important to estimate the ratio of renewal of fixed

assets (

6

x

), which characterizes the level of

physical and moral renewal of fixed assets. This

figure should be constantly increased but always

taking into account inflation.

7. Return on equity (

7

x

) that characterizes the

efficiency of use of equity. It is believed that equity

is used effectively when its return exceeds the return

on long-term investments in the bank.

8. Return on total capital (

8

x

) that assesses

the operating efficiency of the enterprise.

9. Payables period (

9

x

). This is the average

payment period of short-term debt. An increase in

the indicator indicates an increase in debt, but in

case of this increase it is necessary to pay attention

to the ratios of financial dependence and financial

stability.

10. Ratio of short-term receivables and payables

(

10

x

) that shows what part of the accounts payable

the company can pay at the expense of its debtors

during the year. The standard value of this indicator

is equal to 1. The lower its value relative to 1, the

greater the likelihood of problems with credit

repayment.

11. Production profitability (

11

x

) that shows

the efficiency of production costs. This indicator is

the most qualitative measure of the economic

efficiency of production, because it most accurately

compares the amount of profit with the size of the

costs at which it is obtained.

12. Net profit ratio (

12

x

) allowing the company

to increase its working capital and solvency. To

ensure self-sufficiency, the company must provide a

level of profitability of more than 5 % of turnover.

Analysis of these indicators does not require too

broad an information base and does not require

much time, it can be regarded as a rapid analysis.

Certainly, to make a final decision on the feasibility

of investing in the company, the investor may need

more information. But in order to take in the

situation and draw a minimum of conclusions, this

set of indicators is enough.

To assess the innovative potential of the

enterprise there is a need to take into account many

factors that are the basis for further calculation of

the integrated indicator of its level. As indicators of

resource provision of the enterprise for the purposes

of realization of its innovative potential it is

proposed to use a number of such indicators [34]:

1. Intellectual property ratio (

1

y

), which is

calculated as the ratio of the value of rights to

commercial designations, industrial property,

copyright and related rights to the value of

intangible assets of the enterprise.

2. Proficiency ratio of personnel (

2

y

)

involved in the innovation activities of the

enterprise, which is the ratio of the number of

employees with higher education to the total number

of employees involved in the innovation activities.

3. Ratio of enterprise provision with

equipment necessary for the innovation activities

(

3

y

), which is calculated as the ratio of the cost of

production equipment related to technological

innovations to the cost of all production equipment.

4. New technology insertion ratio (

4

y

), which

is the ratio of the value of the introduced fixed

assets to the average annual value of fixed assets of

the machine-building enterprise.

5. Ratio of mastering of new products (

5

y

),

which is the volume of sales of new products in

value terms divided by the total sales of the

enterprise for a certain period of time.

6. Innovation growth ratio (

6

y

), which is

calculated as the ratio of enterprise costs for

innovation for a certain period of time to the total

costs of the enterprise for the same period.

Given the complex nature of the criteria of

investment attractiveness and innovation potential, it

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is proposed to quantify them using fuzzy set theory

and methods of integrated assessment, in particular,

double convolution formulas:

),x(RBAm_x i

m

1i

5

1j

ijji

 

 



(1)

),y(RBAn_y k

n

1k

5

1j

kjjk

 

 



(2)

where

i

A

and

k

A

– weights of

i

-th and

k

-th

basic indicators in the convolution;

)x(R iij

and

)x(R kkj

– values of membership functions of

j

-th

quality level relative to the current value of

i

-th and

k

-th basic indicators;

j

B

– nodal points of the

standard five-level fuzzy 01-classifier, which value

for indicators for which the increase in the value of

the indicator corresponds to the improvement of the

characteristic is calculated by the formula:

),1j(2.01.0Bj



(3)

and for indicators for which the increase in the

value of the indicator corresponds to the

deterioration of the characteristic — by the formula:

).1j(2.09.0Bj



(4)

The standard five-level fuzzy 01-classifier is

based on 01-support and allows to describe the five

values of the linguistic variable "indicator level":

"very low", "low", "medium", "high" and "very

high".

A system of five trapezoidal membership functions is used to describe subsets of the values of the

linguistic variable "indicator level":

"very low":



















1x25.0if,0

25.0x15.0if),x25.0(10

15.0x0if,1

)x(R

i

ii

i

i1i

(5)

"low":























1x45.0if,0

45.0x35.0if),x45.0(10

35.0x25.0if,1

25.0x15.0if),x25.0(10

15.0x0if,1

)x(R

i

ii

i

ii

i

i2i

(6)

"medium":























1x46.0if,0

65.0x55.0if),x65.0(10

55.0x45.0if,1

45.0x35.0if),35.0x(10

35.0x0if,0

)x(R

i

ii

i

ii

i

i3i

(7)

"high":























1x85.0if,0

85.0x75.0if),x85.0(10

75.0x65.0if,1

65.0x55.0if),55.0x(10

55.0x0if,0

)x(R

i

ii

i

ii

i

i4i

(8)

"very high":

















1x85.0if,1

85.0x75.0if),75.0x(10

75.0x0if,0

)x(R

i

ii

i

i5i

(9)

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In formula (1)

)y(x ki

is 01-support, and membership functions built on the basis of this system are given

in Figure 1.

Figure 1. Standard five-level fuzzy 01-classifier built on the basis of trapezoidal membership functions

The nodal points of the standard five-level fuzzy

01-classifier

)x(R iij

are, on the one hand, the

abscissas of the maxima of the corresponding

membership functions on 01-support, and, on the

other hand, evenly spaced on 01-support and

symmetric with respect to the nodal point 0.5,

namely these are points 0.1; 0.3; 0.5; 0.7; 0.9. These

points act as weights when aggregating the system

of indicators at the level of their qualitative states.

Thus, the nodal points reduce the set of non-

standard classifiers (with their asymmetrically

located nodal points) to a single classifier of

standard form, with the simultaneous transition from

a set of non-standard supports of individual factors

to the standard 01-support.

The essence of the five-level fuzzy 01-classifier

is that if nothing is known about the indicator,

except that it can take any value within the 01-

support, and it is necessary to make an association

between qualitative and quantitative estimates of the

indicator, the proposed classifier does so with

maximum reliability. With that the sum of all

membership functions for any

i

A

or

k

A

is equal to

one, which indicates the consistency of the

classifier.

As for the weights of the basic indicators in the

convolution a, and "a", in this case it is advisable to

determine them by expertise using the Fishburne

scale [35].

Each basic indicator of the enterprise

)m,1i(xi

and

)n,1i(yk

is matched with the

estimate of weight, that is the following system of

weights is constructed:

































.n,1k

,0A

,1A

and

m,1i

,0A

,1A

k

i

(10)

where

i

A

and

k

A

–

i

-th and

k

-th basic

indicators;

i

and

k

– ordinal numbers of the

indicators; п and т – number of the basic indicators

on the basis of which integrated indicators X and Y

are determined.

According to the Fishburne principle, the basic indicators are ranked in descending order of weight

of

mi321 x...x...x~xx 

and

nk321 y...y...y~yy 

(the sign "~" means that

the expert considers a certain pair of indicators to be equivalent), and after ranking their weights are calculated

by formulas:

)1n(n

1kn(2

Aand

)1m(m

)1im(2

Aki 











(11)

The Fishburne rule reflects the fact that nothing

is known about the level of weight of indicators

except their hierarchy. Then the estimate (11)

corresponds to the maximum entropy of the

available information uncertainty about the object of

study.

The resulting weighting factor is calculated as

the arithmetic mean of the weights determined by

each of the experts.

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3 Results and Discussion

The selection of innovation development strategy taking into account the levels of investment

attractiveness and innovation potential of an industrial enterprise is proposed to be carried out using the matrix

given in Table 1.

Table 1. Matrix for selection of the strategy of innovative development of an industrial enterprise taking into

account its investment attractiveness and innovation potential

Enterprise innovation potential level (У)

Very

good

Market niche strategy

Active innovator strategy

Active generator strategy

Good

Strategy for targeting knowledge-

intensive firms

"Preemptive strike" strategy

Challenge strategy

Satisfactory

Opportunistic strategy

Differentiation strategy

Price leadership strategy

Bad

Innovative change strategy

Expectation strategy

Simulation strategy

Bad

Good

Very good

Enterprise investment attractiveness level in the market (X)

Enterprises with a high level of investment

attractiveness and innovation potential are proposed

to select the generator active strategy (leadership

strategy) for innovative development. This strategy

is applied to a limited range of products for which

release favorable conditions (scientific and technical

potential, resources, environment) are created.

Scientific studies conducted by economic entities —

innovation generators — are aimed at production of

innovative products in order to displace competitors

and enter new markets. Technological and market

leadership is based on the development of basic,

radical innovations. The implementation of the

leadership strategy requires thorough research: a

wide front of research work; constant review of the

most important results of research in order to

implement them in production; operational changes

in funding priorities depending on the expected

marketing results [12]. Patent licensing measures

require special attention.

The active innovator strategy (follow the leader)

focuses attention on expanding market positions

[16]. An enterprise concentrates on innovations

(products) that have recently appeared in the market.

An economic entity needs to keep in the second

position in the group of applicants for the first

position, to implement an effective innovation

policy, constantly monitor the research and

development of the technological leader and focus

on creating scientific achievements in these

activities to reduce time and effort of scientific and

technical preparation of innovative products before

entering the market. Economic entities that adhere

to this strategy patent their own innovations, which

are based on the innovations of the technological

leader [14]. The active innovator strategy is

proposed for industrial entities with a satisfactory

level of investment attractiveness and high

innovation potential.

A differentiation strategy implies the company's

desire for uniqueness in any aspect important to

customers [24]. Differentiation strategies become

relevant when consumer demands become diverse

and cannot be met by standard products. A

successful differentiation strategy can only be based

on a study of consumer demand. A competitive

advantage can be expected in the case when a large

number of buyers will be interested in purchasing

products with differentiated (i.e., different from

those produced by competitors) characteristics.

Differentiation can be based on differences in the

taste properties of the product, its design, service,

completeness of the range, reliability, safety.

An innovative change strategy is characteristic of

enterprises with low innovation potential and

investment attractiveness. The main reason for this

situation is outdated uncompetitive products on the

market. For innovative development of such

enterprise it is important to carry out economic

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stimulation of professional development of the

personnel of an enterprises in a part of its innovative

culture, generation of new ideas and developments

for updating of products.

Table 2 presents the resulting weighting

coefficients of the basic/partial indicators of

investment attractiveness of an enterprise calculated

by formula (11) according to their ranking by

experts.

Table 2. Calculation of the weighting coefficients of the basic indicators that characterize the investment

attractiveness of an enterprise, according to their ranking by experts

Expert

Weighting coefficients of the basic indicators that characterize the investment attractiveness of an

enterprise

1

x

2

x

3

x

4

x

5

x

6

x

7

x

8

x

9

x

10

x

11

x

12

x

1

0.122

0.013

0.077

0.064

0.026

0.154

0.141

0.044

0.103

0.090

2

0.154

0.045

0.141

0.103

0.090

0.121

0.064

0.077

0.026

0.013

3

0.096

0.019

0.090

0.077

0.064

0.154

0.121

0.045

0.121

0.142

4

0.103

0.051

0.038

0.090

0.071

0.141

0.154

0.019

0.122

5

0.141

0.122

0.013

0.154

0.096

0.077

0.122

0.045

0.025

0.045

0.064

6

0.141

0.090

0.019

0.154

0.051

0.122

0.103

0.038

0.077

0.064

7

0.122

0.051

0.019

0.122

0.071

0.096

0.154

0.038

0.019

0.096

0.141

Resulting

weighting

coefficient

0.126

0.071

0.024

0.100

0.091

0.067

0.124

0.134

0.051

0.038

0.084

0.090

Table 3 presents the resulting weighting coefficients of the basic/partial indicators of the level of innovation

potential of an enterprise calculated by Formula (11), according to the data on their ranking by experts.

Table 3. Calculation of weighting coefficients of the basic indicators that characterize the level of innovation

potential of an enterprise, according to their ranking by experts

Expert

Weighting coefficients of the basic indicators

that characterize the level of innovation potential of an enterprise

1

y

2

y

3

y

4

y

5

y

6

y

1

0.048

0.262

0.167

0.094

2

0.071

0.262

0.191

0.143

3

0.049

0.095

0.190

0.286

4

0.095

0.286

0.238

0.166

0.049

0.166

5

0.048

0.238

0.286

0.190

0.145

0.095

6

0.167

0.071

0.262

0.167

0.262

7

0.190

0.143

0.238

0.095

0.048

0.286

Resulting

weighting

coefficient

0.095

0.167

0.221

0.190

0.137

0.190

The method of modeling the selection of the strategy of innovative development of three machine-building

enterprises of Poland is tested in the paper: ‘Еlectron’ LLC, LEONI LLC and ‘Аtom’ PJSC. The calculation of

the integrated indicators for the positioning of the enterprises in the matrix for the selection of a strategy to

stimulate innovation activity was carried out in the application software package Math CAD. To illustrate the

sequence of their calculation, an example of calculating the integrated indicators of the matrix for the selection

of an innovation development strategy for ‘Еlectron’ LLC is given in tabular form (Table 4-5).

Table 4. Data for estimating the integrated indicator X_m

Normalized values

of basic indicators

Weighting

coefficients of

basic indicators

Membership functions for values of basic indicators according to the standard five-

level fuzzy 01-classifier

"Very low"

)x(R i1i

"Low"

)x(R i2i

"Medium"

)x(R i3i

"High"

)x(R i4i

"Very

high"

)x(R i5i

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1

x

= 0.90

1

A

= 0.126

0

1

2

x

= 0.90

2

A

= 0.071

0

1

3

x

= 0.78

3

A

= 0.024

0

0.62

0.38

4

x

= 0.67

4

A

= 0.100

0

0.14

0.86

0

5

x

= 0.37

5

A

= 0.091

0

0.64

0.36

0

6

x

= 0.27

6

A

= 0.067

0.18

0.82

0

7

x

= 0.28

7

A

= 0.124

0.11

0.89

0

8

x

= 0.30

8

A

= 0.134

+ 0

1

0

10

x

= 0.70

10

A

= 0.038

0

1

0

11

x

= 0.30

11

A

= 0.084

0

1

0

12

x

= 0.57

12

A

= 0.090

0

0.66

0.34

0

Nodal points

)B( j



0.1

0.3

0.5

0.7

0.9

9

x

= 0.52

9

A

= 0.051

0

0.1

0.9

0

Nodal points

)B( j



0.9

0.7

0.5

0.3

0.1

Table 5. Data for estimating the integrated indicator Y_n

Normalized

values of basic

indicators

Weighting

coefficients of

basic indicators

Membership functions for values of basic indicators according to the standard five-

level fuzzy 01-classifier

"Very low"

)x(R k1k

"Low"

)x(R k2k

"Medium"

)x(R k3k

"High"

)x(R k4k

"Very high"

)x(R k5k

1

y

= 0.46

1

A

= 0.095

0

0.21

0.79

0

2

y

= 0.50

2

A

= 0.167

0

1

0

3

y

= 0.30

3

A

= 0.221

0

1

0

4

y

= 0.48

4

A

= 0.190

0

0.1

0.9

0

5

y

= 0.25

5

A

= 0.137

0.27

0.73

0

6

y

= 0.13

6

A

= 0.190

0.86

0.14

0

Nodal points

)B( j



0.1

0.3

0.5

0.7

0.9

The calculation based on these tables by

formulas (1) and (2) gives the following coordinates

for the positioning of "Electron” LLC in the matrix

for the selection of the strategy to encourage

innovation activity: X_m = 0.519 and Y_n = 0.343.

If the quantitative estimation of the integrated

indicators X_m and Y_n can be carried out by

formulas (1) and (2), to recognize the linguistic

levels of these indicators it is necessary to use not

the standard five-level 01-classifier, but three- and

four-level 01-classifiers, with subsets "Bad",

"Good", "Very good" of the linguistic variable

"Indicator level", in case of the three-level classifier,

and with subsets "Bad", "Satisfactory", "Good",

"Very good", in case of the four-level classifier. The

transition from five levels to three and four levels is

due to the fact that the matrix for the selection of the

strategy to encourage innovation activity of

enterprises has a dimension of 4x3 (12 positions in

total).

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The rule for recognizing the linguistic values of the integrated indicators X_m and Y_n calculated by

formulas (1) and (2) are presented in Tables 6-7, respectively.

Table 6. The rule for recognizing the linguistic values of the integrated indicator X_m – the level of investment

attractiveness of an enterprise in the market

Value range

X_m

Classification of the levels of investment

attractiveness of an enterprise in the market

Level of assessment confidence

(membership function)

0 < X_m < 0.2

Bad

1

R

= 1

0.2 < X_m < 0.4

Bad

)m_X4.0(5R1

Good

12 R1R 

0.4 < X_m < 0.6

Good

1R2

0.6 < X_m < 0.8

Good

)m_X8.0(5R2

Very good

23 R1R 

0.8 < X_m < 1.0

Very good

1R3

Table 7. The rule for recognizing the linguistic values of the integrated indicator Y_n – the level of innovation

potential of an enterprise

Y_n value range

Classification of the levels of innovation potential

of an enterprise

Level of assessment confidence

(membership function)

2.0n_Y0 

Bad

1

R

= 1

3.0n_Y2.0 

Bad

)n_Y3.0(10R1

Satisfactory

12 R1R 

45.0n_Y3.0 

Satisfactory

1R2

55.0n_Y45.0 

Satisfactory

)n_Y55.0(10R2

Good

23 R1R 

7.0n_Y55.0 

Good

1R3

8.0n_Y7.0 

Good

)n_Y8.0(10R3

Very good

34 R1R 

1n_Y8.0 

Very good

1R4

When recognizing according to these rules the

linguistic values of the integrated indicators X_m

and Y_n calculated for "Electron" LLC, one can

position the level of the indicator X_m of the

enterprise as "Good", and the level of the indicator

Y_n as "Satisfactory".

Similarly, the assessment of integrated indicators

and positioning in the matrix for the selection of the

strategy to encourage innovation activity for other

enterprises was carried out. In particular, for LEONI

X_m = 0.392, and Y_n = 0.364. Recognition of

these values

using the rules given in Table 6-7 indicates that the

level of investment attractiveness of the enterprise

in the market is 96% "Good" and 4% "Bad", and the

level of innovation potential is 100% "Satisfactory".

As for "Atom" PJSC, X_m = 0.221, and Y_n =

0.167. When recognizing the linguistic values of

these integrated indicators, one can position the

level of the indicator X_m as 90% "Bad" and 10%

"Good", and the level of the indicator Y_n as 100%

"Bad".

Based on the carried out calculations one can position the machine-building enterprises under study in the

matrix for the selection of the strategy to encourage innovative activity (Figure 2).

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Електрон

LEONI

Атом

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0 0,1 0,2 0,3 0,4 0,5 0,6

Company investment potential level

Company investment attractiveness level in the market

Figure 2. Positioning of industrial enterprises in the matrix for the selection of

the strategy for innovation development

As a result of positioning of three machine-

building enterprises the following results were

obtained.

 "Atom" PJSC fell into the area of

application of the strategy of innovative changes, as

it is characterized by a low level of investment

attractiveness and innovation potential.

 "Electron" LLC and LEONI LLC fell into

the area of application of the differentiation strategy,

as they are characterized by a medium level of

investment attractiveness and a satisfactory level of

innovation potential. However, by the first

parameter, i.e., the level of investment attractiveness

of the enterprise in the market, LEONI LLC is still

quite close to the area of application of opportunistic

strategy.

Thus, based on the carried out studies and

calculations, the following strategies to stimulate

innovation activity can be proposed for each of the

machine-building enterprises considered in the

paper:

 For "Atom" PJSC, it is advisable to apply

the strategy of innovative changes, the essence of

which is to upgrade production.

 For "Electron" LLC and LEONI LLC, it is

advisable to implement a differentiation strategy,

which is more competitive than innovative. Its

essence for these machine-building enterprises

consists in the introduction of innovations that

improve the existing product range in accordance

with consumer needs.

Under conditions of limited access to financial

resources, global competition in the market of

industrial technologies, such tax incentives can

become perspective directions of the state support

for innovative activity of the above and other

industrial entities:

1) establishment of the annual rate of accelerated

depreciation of the third and fourth groups of fixed

assets for enterprises implementing innovative

projects;

2) for innovative enterprises, payment of land tax

in the amount of 50% of the current tax rate,

reduction by 50% of value added tax and tax for

income received from the implementation of

innovative projects (funds are credited to a special

account of the taxpayer and used exclusively to

finance innovation activity);

3) introduction of a research tax credit for

enterprises that do not have the innovative status.

Their stimulation consists in reduction of the

accrued income tax by an amount equal to the share

of costs for innovation activity in the current year,

but not more than 50%.

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Additional support is also required by national

enterprises that use the sixth technological mode

(biotechnology, nanotechnology, photonics,

artificial intelligence) in the production process, in

particular, in terms of exemption from customs

duties and value added tax on raw materials,

equipment, components and other products, which

are not produced in Poland.

5 Conclusion

In the paper, selection modeling of innovation

development strategy for industrial entities (micro

level) on the basis of indicators of their investment

attractiveness and innovation potential was carried

out. Such approach allows to adapt as much as

possible the process of making decisions in

uncertain market conditions, taking into account the

financial and economic condition of each enterprise,

regional and sectoral conditions of their

development and competitiveness, strengths and

weaknesses in innovation activities.

The matrix approach in selection modeling of

innovation development strategy of an economic

entity was tested for three enterprises of the

machine-building industry of Poland. It is

emphasized that to implement the proposed

innovation strategies at the enterprise level with

maximum support from the state and private

investors, it is important, firstly, to place

information on indicators of innovation activity and

investment potential on the company website,

secondly, to develop an innovative project that

implements the selected strategy, including in

cooperation with participants of an industrial or

regional cluster or innovation park, and thirdly, to

register the project with the Ministry of Science and

Higher Education of Poland, which maintains an

electronic database of such initiatives.

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Author Contributions:

Conceptualization, N.M. and H.K.; methodology,

N.M.; software, I.L.; validation, A.S.; formal

analysis, D.C.; investigation, H.K.; resources, I.L.;

data curation, A.S.; writing—original draft

preparation, D.C.; writing—review and editing,

N.M.; visualization, H.K.; supervision, I.L.; project

administration, A.S.; funding acquisition, D.C.

All authors have read and agreed to the published

version of the manuscript.

Funding:

This research received no external funding.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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