Fuzzy interaction modeling for participants of innovation development: approaches and examples

• Author: Chernov V., Dorokhov O., Dorokhova L.
• Pages: 319-340

Bulletin of the Transilvania University of Braşov

Series V: Economic Sciences • Vol. 10 (59) No. 2 – 2017

Fuzzy interaction modelling for participants

in innovation development: approaches and examples

Vladimir CHERNOV1, Oleksandr DOROKHOV2, Liudmyla DOROKHOVA3

Abstract: The article considers the interaction problems of the participants in innovative

development at the regional level. Mathematical approaches and formulations for modelling,

such as the interaction on the basis of game approaches and the theory of fuzzy sets, have

been proposed. In particular, the interaction model of innovative participants in the region,

considered as a fuzzy coalition game, is presented. Its theoretical justification and an

example of practical calculations are given. Further, the methodology of interaction

modelling is considered, taking into account the motives of the participants in innovative

development when forming fuzzy coalitions. An example of the corresponding calculations is

also given. Also, the interaction model of "state-regions" in the interpretation of the fuzzy

hierarchical game is proposed and described. The features of its solution are described and

an example of calculations is presented.

Key-words: innovative development, fuzzy sets applying, interaction modelling, fuzzy games

1. Introduction

Issues of innovative development are extremely important for the market

transformation and modernization in post-Soviet and post-communist economies, in

particular, such as Russia and Ukraine ( Kolosok and Trusova, 2015; Untura, 2015;

Kovalenko, 2015; Dnishev et al, 2015; Bezkorovainyi and Jarzębowski, 2016;

Shatkovskaya et al, 2017).

At the same time, it is necessary to take into account the significant role of the

state and local administrations, the presence of other various external and internal

participants in this process (Przygoda, 2015; Iurchenko, 2015; Fundeanu, 2015;

Simba, 2015; Makarov et al, 2016; Yordanova and Blagoev, 2016).

In such conditions, mathematically adequate modelling of all subjects of

innovative development of regions becomes an important and urgent task. It is

extremely necessary to use modern, adequate methods of mathematical modelling,

1 Vladimir State University, Russia, chernov.vladimir44@gmail.com

2 Simon Kuznets Kharkiv National University of Economics, Ukraine, aleks.dorokhov@meta.ua

3 National Pharmaceutical University, Ukrain e, liudmyladorokhova@gmail.com

Bulletin of the Transilvania University of Braşov - Vol. 10 (59), No. 2 - 2017 • Series V

320

appropriate models and decision-making methods based on sufficiently reasoned

calculations ( Gureev, 2015; Golova et al, 2017).

At the same time, despite the definite availability of scientific literature on

specific issues of mathematical and economic modelling of certain aspects of

innovative development at the state or regional level, the development of new

approaches to resolving these issues remains highly relevant ( Pashkus, 2016).

This is especially true for the interaction of participants in the investment

development, which in practice occurs in the context of significant uncertainties of

different origins (Lipieta and Malawski, 2016; Maltseva, 2016; Maltsevaet al, 2016).

As it is already known, for the innovative development of the region, one of

the most important conditions is the favourable innovative environment. It is, among

other things, determined by the narrow, transparent, and flexible relationships

between key participants in the innovative activity.

Consequently, the regional innovation system is characterised by synergies,

because the maximum effect can be achieved only in the case of maximizing the

effectiveness of the collaborative operation of its elements. At this level, the

innovation development of the region's economy depends not so much on the

effective functioning of the individual economic agents, but on the interaction

between all subjects in the innovative activity.

2. The interaction model of innovative participants in the region as a fuzzy

coalition game

It is obvious that participants in the innovation process may have an insufficiently

clear understanding of the expected results of cooperation, manifested in the form of

an open, dynamic system. In doing so, they can form vague coalitions which are

justified also by the fact that they make it possible for various innovative players to

participate in different coalitions.

Proceeding from the facts above, the cooperation of the innovative

participants at various levels of the region can be represented by fuzzy cooperative

games, where players will consider partnership as a function of usefulness, which

enables them to achieve the maximum individual effect (Lekeas and Stamatopoulos,

2016).

Suppose that for the implementation of the innovative program

IP

, consisting

of several projects

),1,( LlPP l==

, participants form coalitions.

Then we have a fuzzy cooperative game, which is defined by a pair

)

~

,( vI

,

where

v

~

— characteristic function of a cooperative game (satisfaction function),

}...2,1{ mI =

the finite and non-empty set of innovative players of the region

(scientific and research centres, universities, companies, government agencies etc.),

which consists of fuzzy coalitions

KI⊆

.