To the Question of the Development of a Methodology for Assessing

the Sustainability of Economic Network Structures

Natalya V. Efanova

, Elena A. Ivanova

and Ivan V. Slesarenko

Kuban State Agrarian University, Krasnodar, Russia

Keywords: Network Structure, Enterprise, Sustainability, Model, Node, Central Element, Fuzzy Classifier, Linguistic

Variable.

Abstract: The article is devoted to the issues of mathematical modeling of the network economic structures

sustainability. The network form of enterprises organization is a reflection of integration processes and

connections. Network sustainability can be viewed from different perspectives, taking into account different

aspects, including organizational. Therefore, research in this direction is relevant. The following models have

been developed to assess the organizational sustainability of the network: a model for assessing elementary

sustainability with an emphasis on the central element of the network, a model and methodology for assessing

integration sustainability. The issues of modeling elementary and integration stability have not been studied

before. A scale of stability levels of a network enterprise has been developed on the basis of the mathematical

apparatus of fuzzy sets theory. Sustainability can be represented as a linguistic variable. The scale in the first

approximation contains three levels to determine the degree of enterprise sustainability. To formalize the

semantics of the scale values, the adaptation of the standard fuzzy three-level 01-classifier is performed.

1 INTRODUCTION

In the era of economic globalization, the boundaries

between the national economies of different countries

are erased, the merger of individual national markets

into one world market is observed, the role of

integration processes is growing. Any enterprise at

the stage of formation and development makes the

transition from small to medium business and further

to large. This transition, as a rule, is carried out

through integration processes and connections, thus

ensuring the formation of networked business

structures (Efanova, 2020; Gerasimova, 2016).

Today, the networked form of business organization

is considered the most effective and promising form

that provides the organization with progressive

development and a stable position in the market.

Network structures are specific, which allows for a

new interpretation of the concept of economic

sustainability. A network enterprise is stable when it

has enough resources to maintain every aspect of its

activities in optimal condition, in the face of

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https://orcid.org/0000-0001-5552-1987

resistance to adverse changes in the external

environment. Each aspect is important, as the stability

of the network as a whole depends on it. Thus, it is

important to conduct a comprehensive assessment of

the network structures sustainability with an

emphasis on various aspects of activities

(Baranovskaya, 2017; Melkonyan, 2017; Patalas-

Maliszewska, 2020).

The purpose of this article is to study and assess

the sustainability of economic network structures as

the most promising and little-studied form of

organization of small and medium-sized businesses,

including the development of new promising methods

and techniques to improve the quality of management

of such structures.

In accordance with the set goal, it is necessary to

solve the following tasks:

1) develop a model for assessing elementary and

structural sustainability, as well as propose a model

and methodology for integration sustainability

assessing;

278

Efanova, N., Ivanova, E. and Slesarenko, I.

To the Question of the Development of a Methodology for Assessing the Sustainability of Economic Network Structures.

DOI: 10.5220/0010589402780285

In Proceedings of the International Scientiﬁc and Practical Conference on Sustainable Development of Regional Infrastructure (ISSDRI 2021), pages 278-285

ISBN: 978-989-758-519-7

2) build a scale of stability levels based on the

mathematical apparatus of the fuzzy sets theory as

one of the most promising areas of research for

weakly formalized concepts and criteria.

2 METHODS

In the process of work, the following methods will be

used: analytical (in the process of studying the

concept of sustainability in the context of the network

form of organization), solving multicriteria problems

and mapping (when developing a model for assessing

elementary, integration stability), fuzzy sets (to build

a scale of levels of stability of the economic network

structure).

All definitions of stability (Banerjee, 2011;

Efanova, 2020; Thierling, 2020), one way or another,

have similar features in a number of criteria. Such

criteria are:

 Influence of external and internal environment;

 Stability of economic activity;

 Availability of compensation mechanisms.

According to the structural model of a network

enterprise (Efanova, 2020; Pereira, 2019), a business

network is considered as an association of business

elements (nodes) of a network and subnets with a

common central element. The integration of business

elements into a network or subnet is carried out on the

basis of vertical or horizontal integration (Loyko,

2015). Thus, by integration stability we mean the

ability of a business network to function under the

influence of internal and external destabilizing factors

or to function when an internal crisis occurs in any

particular business element (Efanova, 2020). That is,

the business network is able to keep in time within the

established limits the values of all control parameters

characterizing the activities of the enterprise.

By elementary stability we mean the ability of an

individual business element of a network or

subnetwork to maintain the ability to function under

the influence of internal destabilizing factors or to

restore its equilibrium state over time when a crisis

occurs (Efanova, 2020). The emphasis is on internal

destabilizing factors, since external ones are more

related to integration stability.

It should also be borne in mind that sustainability

can be influenced not only by the current state of

activity, but also by its stability.

To assess the integration stability, it is proposed

to use the integral indicator S



f





, S





, (1)

whereS



is an indicator of "elementary sustainability

" of a separate business element of the network;



– aggregate index of the center element

sustainability;

f – functional that allows to determine the value

for individual indicators of sustainability S



and S



In the simplest approximation, as the functional f,

we can denote the weighted sum over all S



and S



that form the network, then formula (1) takes the

form:





∑

w∙S







w



∙S



, (2)

where w is the weight of the i-th business element, for

which the elementary sustainability S



is already

calculated; w

– weight of the central element, for

which S



is already known. The sum of the weights in

(2) is equal to one. Towards S



, the weights are

distributed in proportion to their share of influence.

The central element plays the role of the main

strategic management element. Therefore, to

calculate its sustainability, a separate indicator S



different from S



, is used. So S



, is an aggregate

indicator for assessing the management aspect, while



is used to assess the operational or performance

aspect. The formation of a set of evaluation criteria

depends on this.

If the central element or any other element of the

network is presented not just as an abstract entity, but

as an object with its own internal structure, then its

sustainability depends mainly on the elements that

form this structure. The sustainability of the central

element is based on the sustainability of departments

and key performance indicators.

As a result of the above reasoning, Figure 1 shows

a methodology for assessing integration

sustainability.

To the Question of the Development of a Methodology for Assessing the Sustainability of Economic Network Structures

279

Figure 1: Integration sustainability assessment method.

As can be seen from this figure, in order to assess

the integration sustainability, it is necessary to

determine the functional for assessing the elementary

sustainability and with the functional for assessing the

sustainability of the central element.

To assess the sustainability of the central element,

we can propose a model based on the data analysis of

the organization effectiveness and including:

 Model of sustainability of the activity’slevel

element (assumes the calculation of the

activity’s efficiency level and the stability

coefficient of this level according to the given

rules, as well as a model for calculating

sustainability based on the level and stability);

 Model of a department-level element

sustainability (based on the rules for

sustainability calculating based on the

activities of the department);

 Model of sustainabilityof the element of the

central element level (uses the rules for

sustainabilitycalculating based on the

departmentsustainability, as well as on the

basis of the critical activity’s sustainability).

The input of the model is information about the

effectiveness of the organization, the output indicator

is the sustainabilitylevel of the central element.

Figure 2 shows the stages which formalize the

model for assessing the central elementsustainability.

Figure 2: Formalization of the stages of the model for

assessing the central element sustainability.

The primary definition of activity’s sustainability

in this model involves an assessment of its

ISSDRI 2021 - International Scientiﬁc and Practical Conference on Sustainable Development of Regional Infrastructure

280

dependence on the efficiency levels of activities and

the values of activity levels stability. With the

secondary definition, the functional of the

dependence of the final indicator on the stability of

another activity is added to the calculations, taking

into account the influence of various types of activity

on each other.

The calculation of the department’s sustainability

is based on the assessment of its activities

sustainability, as well as their weight coefficients.

The central element’s sustainability is determined

by the dependence on the sustainability of the

departments and activities of the organization, also

taking into account their weights.

This model can be adapted to assess elementary

sustainability, where the focus of attention shifts from

the managerial to the executive aspect of the activity.

To determine the level of sustainability, you can

use several options for using these indicators as

variables.

The main problem in this case is that it is possible

to get an answer to the question "How sustainable is

the activity?", but it is difficult to give an answer to

the fuzzy ambiguous question "Is the activity

sustainable?"

This problem can be solved through the use of

fuzzy logic methods. In particular, the presentation of

the efficiency and sustainability concepts in the form

of linguistic variables with their own term-sets and

the use of standard 01-classifiers to cover the

universal set, where the semantics of the terms

meanings is formalized. The first step in this direction

is the development of a scale of sustainability levels

based on the mathematical apparatus of the fuzzy sets

theory.

In the general case, the scale assumes that a

mapping is given that sets the corresponding scale

value in accordance with real situations. If we

consider the concept of sustainability as a linguistic

variable, then the term-set, which formalizes the

semantic load of terms, will just be the scale of values

that completely overlaps the universal set of the

linguistic variable. As a first approximation, three

levels are sufficient to determine the degree of

enterprise sustainability: "critical", "borderline state",

"normal". The range [0..1] has some versatility, so it

is convenient to use it as a universal set for setting

stability levels. This makes it possible to adapt the

standard three-level 01-classifier to the selected

levels of the sustainability scale (table 1). The

membership function formalizes the meaning of the

scale values. It should be noted that there can be more

scale levels, and other types, for example, triangular

membership functions, can also be used. The main

thing is that the adequacy of the comparison does not

suffer. More fine tuning of the scale levels is possible

with the assistance of experts.

Table 1: Comparison of sustainability levels and levels of

the standard 01-classifier.

Sustainability

level value

01-

classifier

level

value

Designation

Membersh

ip function

type

Critical Low

Z-sha

Borderline

state

Medium T

Trapezoid

Acce

table Hi

S-sha

Each of the proposed types of membership

functions has its own analytical form, represented by

the corresponding formula and depending on certain

sets of parameters.

The Z-shaped function is determined by the

formula (3), the trapezoidal function – by the formula

(4), the S-shaped function – by the formula (5)





















1,0

0,1

),,(

bxa

bax



(3)



























1,0

0,0

),,,,(

dxc

cxb

bxa

dcbax



(4)





















1,1

0,0

),,(

bxa

bax



(5)

As an example, we can build and visually evaluate

the graphs of the reduced membership functions with

the following parameter values:

 Z- shaped: a = 0,3; b = 0,7;

 trapezoidal: a = 0,2; b = 0,4; c = 0,6; d = 0,8;

 S- shaped: a = 0,5; b = 0,8.

A universal set in this case will be a certain

hypothetical level of sustainability, measured on a

scale from 0 to 1. The calculated values of

membership functions for three levels of

sustainability are shown in Table 2, and the graphs of

functions are shown in Figure 3.

For real use, the considered example requires

adjusting the parameters of the membership functions

in order to comply with the model adequacy.

To the Question of the Development of a Methodology for Assessing the Sustainability of Economic Network Structures

281

Table 2: An example of describing the linguistic variable

"Sustainability".

Sustainability

level (0-1)

Membershipfunctionvalues

Critical

Borderline

state

Acceptable

0 1 0 0

0,1 1 0 0

0,2 1 0 0

0,3 1 0,5 0

0,4 0,75 1 0

0,5 0,5 1 0

0,6 0,25 1 0,33

0,7 0 0,5 0,67

0,8 0 0 1

0,9 0 0 1

1 0 0 1

Figure 3: Graphs of membership functions of the stability

scale levels.

3 RESULTS

The technique of using a linguistic variable to

determine the sustainability of organizations

described in the previous section can be applied to

both traditional and networked enterprises.

Table 3 shows an example of setting intervals for

sustainability levels based on an adapted standard

three-level fuzzy 01-classifier.

Table 3: Classification of the sustainability level based on

the adapted standard three-level fuzzy 01-classifier.

Interval of

sustainability

level (SL)

values

Sustainability

level value

Degree of

estimated

confidence

(membership

function)

0 SL 0,2

Critical

0,2 <SL< 0,4

Critical



Т1

= 5  (0.4 -

)

Borderline

state

1- 

Т1

= 

Т2

0,4 SL 0,6

Borderline

state

0,6 <SL< 0,8

Borderline

state



Т2

= 5 (0.8 -

)

Acceptable

1- 

Т2

= 

Т3

0,8 SL 1,0

Acceptable 1

Based on the results of the classification carried

out, it is possible to calculate the values of the

membership functions for different sustainability

levels on a universal set of values of the sustainability

index from 0 to 1 (Table 4), as well as build graphs of

these functions (Figure 4).

Table 4: Setting the linguistic variable "Sustainability"

based on the classification carried out.

Sustainability

level (0-1)

Membershipfunctionvalues

Critical

Borderline

state

Acceptable

0 1 0 0

0,05 1 0 0

0,1 1 0 0

0,15 1 0 0

0,2 1 0 0

0,25 0,75 0,25 0

0,3 0,5 0,5 0

0,35 0,25 0,75 0

0,4 0 1 0

0,45 0 1 0

0,5 0 1 0

0,55 0 1 0

0,6 0 1 0

0,65 0 0,75 0,25

0,7 0 0,5 0,5

0,75 0 0,25 0,75

0,8 0 0 1

0,85 0 0 1

0,9 0 0 1

0,95 0 0 1

1 0 0 1

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282

Figure 4: Graphs of membership functions of the linguistic

variable "Sustainability" terms (adapted fuzzy 01-

classifier).

Based on the obtained membership functions, it is

possible to analyze the sustainability indicators of

specific enterprises.

For traditional (non-networked) organizations, it

is enough to have one single indicator of

sustainability to assess it.

Suppose that the sustainability indicator was

calculated for enterprise A, and it turned out to be

equal to 0.35, and for enterprise B – 0.7.

In this case, the following conclusions can be

drawn:

 Enterprise A has a critical sustainability level

with a confidence level of 0.75, and with a

confidence level of 0.25 it is at the borderline

sustainability state;

 The sustainability of enterprise B can be

assessed as borderline with a confidence degree

of 0.5 and as acceptable with a confidence

degree of 0.5.

For network enterprises, as the initial data for

sustainability assessing, it is necessary to have data of

its individual nodes sustainability indicators,

including the central element of the network, and to

assess the integral stability indicator, it is necessary to

know the weight coefficients of each node.

The initial data and results of the experiment to

assess the sustainability of a network enterprise are

shown in Table 5.

Table 5: Evaluation of the network enterprise sustainability

based on a three-level fuzzy 01-classifier.

Node

Sustainability S

Weightw

Confidence degree for

sustainability

assessing

Critical

Borderline

state

Acceptable

Central

element

0,55 0,4 0 1 0

Node 1

0,35 0,15 0,25 0,75 0

Node2El

0,8 0,15 0 0 1

Node3El

0,65 0,1 0 0,75 0,25

Node4El

0,2 0,2 1 0 0

It can be seen from the table that the central

element of the enterprise has a borderline state of

sustainability, and, therefore, the remaining nodes can

affect the overall stability of the organization, both for

the better and for the worse. Their sustainability

assessment can be characterized as follows:

 Node 1 is at a critical level of sustainability

with a confidence level of 0.25, and in a

borderline state with a confidence level of 0.75;

 Node 2 sustainability level – unambiguously

acceptable (confidence level is equal to 1);

 Node 3 has a borderline sustainability level

rather than an acceptable one (confidence

levels are 0.75 and 0.25 respectively);

 For node 4, we can say for sure that its level of

sustainability is critical.

Next, we need to calculate and evaluate the

integral indicator of sustainability. The calculation

will use the linear convolution method given in

formula (6).

𝑆





∑

𝑤∙𝑆







𝑤



∙𝑆



, (6)

Substituting the initial data of the analyzed

enterprise into this formula, we can get the following:

int

= 0,35  0,15 + 0,8  0,15 + 0,65  0,1 + 0,2 ××

0,2 + 0,55  0,4 = 0,4875  0,5

Thus, we can conclude that the value of the

integral indicator corresponds to the borderline state

of the organization's sustainability.

To the Question of the Development of a Methodology for Assessing the Sustainability of Economic Network Structures

283

4 DISCUSSION

The results of the experiment carried out in the

previous section indicate some differences in the

sustainability assessment of traditional and

networked enterprises.

In particular, the case should be highlighted when

the calculated value of sustainability turned out to be

equal to 0.5 or less. For a traditional enterprise, this

situation is critical and requires immediate adoption

of appropriate measures to improve the situation. For

a networked enterprise, the picture may be

completely different, especially if the critical value of

sustainability has been identified for an individual

node of the organization. Then the overall level of

sustainability can be adjusted and compensated for by

the rest elements of the network enterprise.

Special attention should be paid to the situation

when the value of the sustainability integral indicator

for the network enterprise turned out to be equal to

0.5. In this case, a complete analysis of all nodes of

the organization should be carried out in order to

identify the "weak spot" and plan measures to

improve the functioning efficiency of this element,

which, in turn, will lead to an increase in its

sustainability level.

To determine the sustainability degree of the

enterprise in the work, a three-level fuzzy classifier

was used. However, in some cases, three levels may

not be enough; a more accurate assessment of

indicators is required. Then it makes sense to increase

the number of levels and go, for example, to a five-

level classifier. The linguistic variable terms can be

roughly as follows:

 absolutelyunstable;

 critical;

 borderline state;

 acceptable;

 high.

A further increase in the number of fuzzy

classifier levels is impractical, as it will lead to

"blurring" of the indicators assessment accuracy.

5 CONCLUSIONS

Summing up the general results of the work, it should

be noted that the mechanism of the functioning and

development of business networks has not yet been

sufficiently studied, the paradigm for managing

network structures has not been finally formulated.

Therefore, these questions require further research.

The organizational environment is dynamically

changing due to many factors to which the network

must respond. Otherwise, it is impossible to ensure

the economic sustainability of the network and

maintain or accelerate the pace of its development.

The problem of ensuring the economic

sustainability of enterprises is especially relevant for

enterprises in the small and medium-sized enterprise

sector, where today there is the greatest concentration

of networks. The methodology for assessing network

economic structures is in its infancy. This indicates

the advisability of continuing research in this

direction.

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