Decisions in uncertainty based on entropy

• Author: Chernov V., Dorokhov O., Dorokhova L.
• Pages: 231-246

Bulletin of the Transilvania University of Braşov

Series V: Economic Sciences • Vol. 10 (59) No. 1 - 2017

Decisions in uncertainty based on entropy

Vladimir CHERNOV1, Oleksandr DOROKHOV 2, Liudmyla DOROKHOVA3

Abstract: At present, the choice of the best solutions out of many possible under conditions

of uncertainty is the actual economic task, arising and to be solved in many economic

situations. Famous classical approaches to its solution are based on various assessments of

decision-making practical situations. However, they often give insufficiently accurate or

incorrect results, and do not satisfy sustainability requirements, when the only invariant

calculation result relative to calculation methodo logy is a reliable one and a corresponding

to the reality resu lt. This article describes an alternative approach to th e justification of

decisions under conditions of uncertainty without the construction and use of assumptions

about the decision-making situation and in conformity with the approaches of the stability

theory. The problem of multi-criteria decision-making in conditions of complete uncertainty,

wherein structuring of alternatives is performed using the fuzzy entropy, has been formulated

and conceptually investigated. The idea of the described method assumes that the criterial

conformity is estimated by fuzzy numbers and (or) linguistic allegations, i.e. formalizes by

tools of fuzzy set theory. In opposition to classical approaches, this approach does not

require the construction of hypotheses about the possible circumstances of decision-making

and meets the requirements of stability theory. As a confirmation, it has been shown that the

calculation of the fuzzy ent ropy by various methods does not lead to contradictory results. In

this work appropriateness and practicality of using fuzzy entropy criterion for ordering sets

of alternatives in fuzzy conditions of decision making has been is substantiated. The method

for calculating the fuzzy entropy when evaluating criteria in linguistic form has been

grounded. The paper presents numerical examples for which the fuzzy entropy calculation

allows generating grounded clear recommendations and choose the best solution, which

does not provide, under the given concrete numeric data, classical methods. The proposed

approach for ordering and search of alternative solutions with a strong uncertainty using

fuzzy entropy makes it possible to significantly enhan ce the validity of the required multi-

criteria decision through the achievement of the invariance of the calculation results

regarding the models and methods of processing fuzzy input data.

Key-words: multi-criteria decisions, fuzzy sets applying, fuzzy entropy, alternatives fuzzy

ordering, fuzzy 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. 1 - 2017 • Series V

232

1. Introduction

The situations of the necessity of multicriteria decisions are quite frequent in various

areas of economics: management and business, financial, investment and banking,

economic, industrial and trade activities (Balke and Nigel, 2014; Hudec et al, 2014;

Janssen et al, 2017; Kostenko et al, 2014; Mastorakis and Siskos, 2016).

At the same time, in the context of globalization and competitive market

relations, there is (and requires an objective assessment and reasonable choice) a

sufficiently large number of diverse opportunities, options, alternatives (in any of

the above-mentioned spheres of economic activity).Meanwhile, as a rule, the

baseline information (according to which solutions must be built) is often

insufficiently reliable, incomplete, poorly formalized and difficult to apply to

traditional economic methods of classic statistical analysis (Diday et al, 1994;

Malugin et al, 2014; Saaty and Ergu, 2015; Tomer, 2015; Zamani-Sabzi et al, 2016;

Žmuk, 2017). Considering the aforementioned facts, it is highly desirable and

necessary to implement and appropriately adapt various methods of the classical

decision-making theory and tools to the economic tasks and problems nowadays.

In particular, such its use in the field of business are devoted publications

(Canco, 2016; Kanagal, 2016; Kościelniak et al, 2015; Podviezko, 2015).

The applications in production activity was considered in research

(Barbacioru, 2014; Rojas-Zerpa and Yusta, 2015).

The adaptation to management tasks was carried out in works (Puseljic et al.,

2015; Sacheti et al., 2016).

The problems of multi-criteria decision-making for business in terms of the

sets of alternatives was given in the articles (Gawlik, 2016; Iuan-Yuan Lu et al,

2016; Kitsios et al, 2015; Rezaei, 2015).

The corresponding approaches to solving logistical problems was described in

studies (Aguezzoul, 2014; Dieaconescu et al, 2016; Erodlu, 2016; Olariu, 2014).

The possibilities for applying mentioned approaches in financial or banking

sector was shown in papers (Forbes et al, 2015; Johnston et al, 2016; Karimi, 2014;

Spãtãrelu and Petec, 2016).

In all these cases and tasks, the situations of full uncertainty occupy a special

place, and the best mathematical tools for formalization, comprehensive review and

consideration, and final effective solutions are represented by approaches based on

the theory of fuzzy sets and fuzzy logic.

In the theory and practice of decision-making into a separate group, criteria

for decision-making under conditions of total uncertainty stand out, when the

decision maker faces a complete lack of information about the probabilities of states

of the environment (nature), or this information cannot be considered as credible.

The uncertainty of such kind is called „hopeless” or „stupid” (Carrigan, 2010;

Schjaer-Jacobsen, 2004; Sinn, 2012). The known methods of the structuring of