From Theory to Practice of Management

18 Pages·2017·0.52 MB·English

Pobrane z czasopisma International Journal of Synergy and Research http://ijsr.journals.umcs.pl
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DOI: 10.17951/ijsr.2017.6.5 5
Is Management a Science or an Art? Is Management
a Science
S
From Theory to Practice of Management or an Art?
From Theory
to Practice
Wiesław M. Grudzewski
C of Management
Associate member of the Polish Academy of Sciences (PAN)
Zoia Wilimowska
University of Applied ScienceMs in Nysa, Poland
[email protected]
Abstract
Purpose – The purpose of this article is to discuss and show that management is a science, not
just an art. Decision-making in tUhe enterprise requires talent and special skills supported by the
right qualiications. According to Tatarkiewicz, management can be considered as an art, which
can be interpreted as follows: “(...) man’s conscious creation is a work of art always when it
recreates reality, shapes forms, or expresses experience, yet it is able either to delight, or touch,
or shock” (Tatarkiewicz, 1972). On the other hand, the company management is understood
as a continuous process of making decisions based on reliable knowledge, observations and
experiences – it is, therefore, a science, and modern managers are not just passive consumers of
research knowledge, but also its creators. Contemporary theories focus attention on constructing
appropriate models, which support the decisions of managers allowing them to somehow “spy”
and observe the effects of their decisions. The aim of the paper is to show that in the modern
economy, design models to support the management of the enterprise is the science that uses
the achievements of other sciences, creative adaptation of these achievements in modeling
phenomena occurring in the world economy. The aim of this article is to show that management
sciences are increasingly exploiting modern knowledge to build models for developing practical
concepts of management systems.
Design/Methodology/Approach – The authors present the review of mathematical models,
computer models (used in situations where the analytical models cannot ind the best solution),
and in particular artiicial intelligence algorithms and selected models of dynamic system for
managing the organization and some examples of applications.
Findings – The results obtained show that in the management sciences, many models are used to
support managerial decisions. Of course, the achievements of other sciences are very often used,
management is of an application, but also of scientiic nature, because, in order to skillfully use
knowledge from other ields, decision-making models should be developed to solve problems in
management and allow to use the achievements of these other areas.
Research limitations/implications – The limitations of this paper result from the fact that only
selected models are presented in the article. The authors hope that these selected models will be
the argument that management science is becoming more and more science and not an art only.
Originality/Value – This paper presents the review of modern methods used in management
sciences to show that modern management is more a science than an art.
International Journal
of Synergy and Research
Keywords – management, models, artiicial intelligence, neural networks, agent, risk Vol. 6, 2017
pp. 5–21
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6
IJSR 1. Introduction
6 In the market economy, management of any enterprise is of particular importance
S
because its appropriate implementation ensures the proper growth and development
of an enterprise. The management process consists mainly of continuous decision-
making. Whether managerial decisions will ensure eficiency or improve the company’s
image, it is dificult to determine at the time when the decisions are made. The effects of
C
decisions are only observable in the future, sometimes very distant. Making decisions
determining the company’s future and goals accomplishment requires a thorough
knowledge in many areas (decision-making, inancial management, risk assessment,
forecasting, etc.) and experience as well as creative capabilities of decision-makers.
Then, is management art oMr science?
According to the Polish Language Dictionary [II], art “is an area of artistic activity
distinguished for its aesthetic values; also a product/creation or products of such
activities, but also the ability requiring talent, skill or special qualiications”. The creator
is any person [III] “who creates something, especially in the ield of art, or a person who
is the cause of something”.
Decision-making in the enterprise requires talent and special skills supported by
U
the accurate qualiications. In this context, management is an art that can be interpreted
as (Tatarkiewicz, 1972) “the conscious work of a human being [which] is considered
a work of art always and only when it recreates reality, shapes forms, or expresses
experience, and, at the same time, is fascinating, emotional, or even shocking”.
The Polish dictionary by PWN deines science as [IV] “All human knowledge
arranged in the system of issues; also: the discipline of research relating to a certain
ield of reality” or “A set of views that constitute a systematized and consistent whole
and are part of a particular discipline of research”.
In this context, the company’s management understood as a continuous decision-
making process based on sound knowledge, observation and experience is science, and
modern managers are not just passive consumers of research knowledge but also its
creators.
These theories include, among others, the quantiied theory of a production function
and the ways it is created in national economies and particular branches of production.
There is also the theory of strategic and operational management, organisational
balance, assessment stimulation and measurement of a function of demand and
supply, trust management, management of enterprises under conditions of uncertainty,
knowledge management, measurement of technological and technical gaps in national
economies and economic sectors, and other well-known theories such as the application
of Danzig’s programming and linear algorithm to solve transport problems, network
planning for programming and implementing projects in construction services and
restoration of facilities, sustainability in business (Grudzewski et al., 2013), crisis
management, creation of a company in the future, dynamic programming applied to
create decision-making systems in processes and management systems, probability
calculus/theory in mass/multiple service management such as telephone exchanges
or rental of apparatus, devices and measuring tools in scientiic research, conducting
experiments and designing projects applied in business practice. The number of these
theories is growing, and their practical use becomes the basis for the improvement
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of strategic and operational management systems in economics. On the basis of these Is Management
theories, organizational and process structures as well as IT networks are developed to a Science
process information in systems that use a large number of algorithms to enaSble practical
or an Art?
problem-solving. Various models are available for this purpose such as mathematical,
From Theory
static, and dynamic models: deterministic, stochastic, fuzzy, network, cybernetic, IT,
to Practice
iconographic, etc.
C of Management
2. Models in management systems
Uncertainty in the decision-making process depends on the dynamics of changes in the
business environment as well as the degree of conidence in the opinions, ideas, solutions
M
that the decision-maker makes, etc. It is dificult, costly, and often even impossible to
undertake experiments and test the potential effects of decisions on a living organism,
just like an enterprise. Hence, contemporary theories focus on constructing appropriate
models that support managerial decisions, allowing them to “view/track” the effects
of their decisions. The main purpose of modelling is to understand how a company
operates as well as to analyse its performance and propose possible improvements.
U
The study of processes and systems can take place on real objects/assets or on
models. The investigated actual/current system is a fragment of the environment, while
the model is merely a simpliied representation of the examined part of reality containing
a certain number of its properties relevant for the research conducted.
Modelling supports and motivates mental imagery and knowledge about possible
future consequences, and, thus, facilitates inding a goal. It allows one to verify the
reliability and feasibility of the system’s objectives with respect to the values and
expectations of the environment, as well as evaluate the technical usability in particular
aspects of: structure, functionality, time, society and economics.
Taking into account the complexity of enterprise management, the rationality of
managerial decisions requires a prior analysis of the potential impact of decisions, thus,
requires modelling of decision-making processes.
One of the most important tasks implemented by modelling phenomena and
processes is to ind the best solutions in complex reality.
3. Mathematical models
Finding the best solutions to speciic problems is as old as the history of civilization.
This inds its justiication in the pursuit of man to perfection. In the history of Carthage,
in the Aeneid by Virgil [70–19 BC], there is the phrase “ind a curve closed on a plane
of a given length, which contains the maximum surface”.
Over more than 300 years, people have sought some formalized methods to ind the
best solutions. At the end of the 17th century, Johann Bernoulli announced a competition
to solve the following problem: “Given two points A and B in a vertical plane, what is
the curve traced out by a point acted on only by gravity, which starts at A and reaches
B in the shortest time.” There were several solutions provided by famous mathematicians.
Thus, the period of development of the mathematical analysis and the search for optimal
analytical solutions that require strictly mathematical models began.
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The advantage of mathematical models is their abstract character; an identical mathematical
Data: 22/01/2023 02:12:30
model may have systems and processes of different physical nature, and this particular feature
8 of mathematical models is of particular interest. Searching for optimal solutions using
mathematical models requires precise formulation of the model.
An enterprise is a complex system. In order to construct the best model for the type of
IJSR A mathematical model is a set of rules and relationships, based on which the course
6 doef cai smioodne-lmleadk pirnogce pssr ocacne sbse fionr eqsueeens t(iboyn w, ainy osfu cbajleccutl-arteiolna)t.e Tdh lei tmeraathtuemrea taicnadl mporadcelt ice, it is proposed
toof dtheec osmtudpioedse m thatee rsiayls/ttaenmgi.b le system will be called thSe system of equations whose
solutions are similar to the course of the modelled actual object size/dimension.

The advantage of mathematical models is their abstract character; an identical
mathematical model may have systems and processes of different physical nature, and
3.1. The examples of company risk evCaluation
this particular feature of mathematical models is of particular interest. Searching for
Tohpteim oarlg saonluiztiaotnios nusailn ge nmvaitrhoenmmateicnatl ims obdeeclso mreqinuigr ems porreec idsey nfoarmmuicla atinodn oufn tphere mdoicdteal.b le, and, therefore,
orgaAninz eantiteornpsri saer eis r ae qcoumirpelde xt osy msteomni. tIonr o trhdeeirr t oe ncvonirsotrnumct ethnet bceosnt tminoudaell lfyo ra tnhde taydpaep t to it.
of decision-making process in question, in subject-related literature and practice, it is
Many social groups are interested in the effects of company’s operation. And each
proposed to decompose the system.
group is interested in varioMus types of risk of organization activity. There is no profit without
risk. Generally speaking, risk is a concept that denotes a potential negative impact that may
a3ri.s1e. fTrohme ae fxuatmurpe leevse notf, cesopmecpiaalnlyy ar itsokta el voar lpuaarttiiaoln loss of invested resources.
The organizational environment is becoming more dynamic and unpredictable, and,
Risk can be understood as a possibility that actual cash flows generated by the
therefore, organizations are required to monitor their environment continually and
company will be less than forecasted cash flows – actual rate of return will be less than
adapt to it.
expeMctaendy sroeUcqiuail rgerdo urpest uarren inbteecreasutesde ino ft hve aerfifaebctisl iotyf caonmdp aunnyp’sr eodpeicratatibonil.i tAyn do fe atchhe cash flow levels
CgrFou ipn i sf uintuterree sttiemd ein pvearriiooudss t(yFpiegs uorfe r i1s)k (oWf oirlgimanoizwatsikona ,a Wctiviliitmy. oTwhesrkei ,i s2 n0o0 p2r)o. iItf required level of
i
without risk. Generally speaking, risk is a concept that denotes a potential negative
cash flow is a linear function of time CF(t) (then the risk connected with variability of cash
impact that may arise from a future event, especially a total or partial loss of invested
flow is zero, and growing level of cash flow increases investment profitability), then for
resources.
inveRstimske cnatn A b ev aurniadberisltiotyo do fa sC aF po(ts)s iibsi lgitrye athteatr ,a scotu tahl ec arsishk l iosw gsr egaetneerr.a tFeodr biyn vthees tment B cash flow
A
CcoFm(pta)n iys wthiell lbeea slet ssst athbalen –fo irte ccaasutesde sc athshe lgorewast e–s ta critsukal. rate of return will be less
B
than expected required return because of variability and unpredictability of the cash

CF (t)
Cash flow B CF(t)
CF(t)
CF (t)
A
Figure 1.
Variability of cash Timet
lows for A and B
irms 0 1 2 3 . . . n

Source: Wilimowska and Wilimowski (2002).
Figure 1. Variability of cash flows for A and B firms
Source: Wilimowska and Wilimowski (2002).

4
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9

low levTelhse C Ff ainc tfourtsu re tthimate pdereitoedrsm (Finigeu rec 1o)m (Wpailnimy’osw skvaa, lWueil imwohwisckhi, 2e0x02is).t sI f in Isd Mynaanmagiceamllye ntc hanging
i
requirede nlevvierlo onfm caesnht laonwd iisn af lluineenacr ifnugn ctthioen foofr teicmaes tCeFd( tc) a(sthhe nf ltohwe rlisekv ecol nanreec tneod t determinai sStcicie. nTchee y follow
with variability of cash low is zero, and growing level of cash low increaseSs investment
the unpredicted environment changes and internal changes of the compaonry .a nS oA rtth?e factors
proitability), then for investment A variability of CF (t) is greater, so the risk is greater.
should have non-deterministic characAter in valuation process. From Theory
For investment B cash low CF (t) is the least stable – it causes the greatest risk.
B to Practice
The factors that determine company’s value which exists in dynamically changing
environm3.e2n.tD ainsdc irneltuee nmcientgh tohde foofre rciasskte de vcaaslhu laotwio nle vel areC not deterministic. They of Management
follow tAhes uwnparse dmicetendt ieonnveirdo nbmeefnotr ech, atnhgeerse ainsd n iont eprrnoafl icth wanigtheso ouft trhies kc.o mGpeanneyr. aSloly speaking, risk is a concept
the factors should have non-deterministic character in valuation process.
that denotes a potential negative impact that may arise from a future event, especially a total
or partial loss of invested resources.
M
3.2.DiscreteT mhee trhisokd o of ft hreis kco emvaplaunayt ieovnaluation problem can be defined as follows (Wilimowska,
As was 2m0e0n4ti)o:n etod bcelfaosres,i ftyh erae icso nmo pparoniyt wtoit hoonute rioskf . MGe nreirsakll yc slapesaskeisn g–, ri1s,k 2is, ..., M using some factors
a concept that denotes a potential negative impact that may arise from a future event,
describing it. Depending on the type and quantity of input information, two tasks are
especially a total or partial loss of invested resources.
considered:
The risk of the company evaluation problem can be deined as follows (Wilimowska,
2004): to classify a company to one of M risk classes – 1, 2, ..., M using some factors
 number of Urisk classes is known,
describing it. Depending on the type and quantity of input information, two tasks are
considered: number of risk classes is unknown.
• number of risk classes is known,
• number Tofh reis kt calsakssse s cisa unn kbnoew nr.esolved using cluster analysis and pattern recognition theory,
The tasks can be resolved using cluster analysis and pattern recognition theory,
respectively. In the risk classification task, points of the feature space are firms described in
respectively. In the risk classiication task, points of the feature space are irms described
in vectovrse ocft oferast uorfe sf teearmtusr.e Psr otecermss so.f Pdirsocrceetes si noafn dciiaslc rrieskte m feiansaunricniga slh roiwsks Fmigeuarseu 2r.ing shows Figure 2.
Figure 2.
Scheme of risk
classiication

Source: Wilimowska and Wilimowski (2002).
Figure 2. Scheme of risk classification
The main problem of right classiication is to ind the proper function of H(x)
transforSmoiunrgc et:h We fieliamtuowres vkae catnodr Wini ali mpaorwtisckui l(a2r0 c0l2a)s. si. There are many methods of pattern
0
recognition and classiication theory. The methods depend on the type of information
that is known befTohree. main problem of right classification is to find the proper function of
Let us assume that objects in each M classes are random variables and p(x/i) i = 1,
H(x)transforming the feature vector in a particular classi . There are many methods of pattern
..., M are their a priori conditional probability functions. Let us assume that 0p, i = 1, ...,
recognition and classification theory. The methods depenid on the type of information that is
M are a priori probabilities of class i respectively. If probability distributions p(x/i) and
p, i = 1,k .n..,o Mw enx biset faonrde a.r e known, than full probabilistic information about objects and
i
classes is known.
Let us assume that objects in each M classes are random variables and p(x/i) i = 1, ...,
Using a statistical theory of decision making there is possible loss functions deining
M are their a priori conditional probability functions. Let us assume that p, i = 1, ..., M are a
λ(i/j) i, j = 1, ..., M, which represent losses of incorrect classifying of object i to i
wrong cplarsiso jr. i probabilities of class i respectively. If probability distributions p(x/i) and p, i = 1, ..., M
i
exist and are known, than full probabilistic information about objects and classes is known.
Using a statistical theory of decision making there is possible loss functions defining
(i/j) i, j = 1, ..., M, which represent losses of incorrect classifying of object i to wrong class j.
Let us describe p(j/x) as a posteriori probability that x belongs to class j. Then
M
L (i)(i/j)p(j/x)
x
j1
5
The factors that determine company’s value which exists in dynamically changing
environment and influencing the forecasted cash flow level are not deterministic. They follow
the unpredicted environment changes and internal changes of the company. So the factors
should have non-deterministic character in valuation process.
3.2.Discrete method of risk evaluation
As was mentioned before, there is no profit without risk. Generally speaking, risk is a concept
that denotes a potential negative impact that may arise from a future event, especially a total
or partial loss of invested resources.
The risk of the company evaluation problem can be defined as follows (Wilimowska,
2004): to classify a company to one of M risk classes – 1, 2, ..., M using some factors
describing it. Depending on the type and quantity of input information, two tasks are
considered:
 number of risk classes is known,
 number of risk classes is unknown.
The tasks can be resolved using cluster analysis and pattern recognition theory,
respectively. In the risk classification task, points of the feature space are firms described in
vectors of features terms. Process of discrete financial risk measuring shows Figure 2.

Figure 2. Scheme of risk classification
Source: Wilimowska and Wilimowski (2002).
The main problem of right classification is to find the proper function of
H(x)transforming the feature vector in a particular classi . There are many methods of pattern
0
recognition and classification theory. The methods depend on the type of information that is
known before.
Let us assume that objects in each M classes are random variables and p(x/i) i = 1, ...,
M are their a priori conditional probability functions. Let us assume that p, i = 1, ..., M are a
i
priori probabilities of class i respectively. If probability distributions p(x/i) and p, i = 1, ..., M
Pobrane z czasopisma International J ournal of Synergy and Research http://ijsr.journals.umcs.pl i
exist and are known, than full probabilistic information about objects and classes is known.
Data: 22/01/2023 02:12:30
Using a statistical theory of decision making there is possible loss functions defining
is an average conditional loss.
10
is( ia/nj) aiv, ejO r=ab g1jee, c.c.t.o ,b nMedli,o twnioghnsia ctlho l orceslpsa.rs ess ien, tw lohsiscehs mofi ninimcoizrriencgt vcalalsusei fLyi(nig). oTf hoeb jsecchte im toe wofr othneg acllgasosr ijt.h m
0 x
isis a: n av erage conditional loss.
LOebtj eucst d beeslcornibges pto(j /cxl)a asss ai0 ,p woshteicrhio mri ipnriombiazbinilgit yv athluaet xL bx(eil)o. nTghse t osc chleamsse j .o Tf hthene algorithm
I6JSR iiLss1 e:.a t Dn u eassv dcOereMribsabjcgeere cio btc beboj eneplcd(otji n/txxigo.) s na atsol a lco lpsaoss.ss t ei0r,i owrhi ipcrho bmaibniilmityiz itnhga tv xa lbueel oLnxg(is) .t oT hcela sscs hje. mThee onf the algorithm
i1sL.: x D (ie)scribe o(ib/jje)pct( jx/.x ) S
is 1a2n. . D aCveoesucraOrnjigtbb 1eeji e co1co,b2tn ,j.b.de.,eicMtltio oLxnn.xg a(sil) tl oo scsl.a ss i0 , whi ch mini mizing value L x(i). Th e schem e of th e algorithm
i2iss .: aC no uavnet rage condLixt(iio)n al loss .
Objeict1 ,2b,e...l,oMngs to class i , which minimizing value L(i). The scheme of the algorithm
is:21 O 3.. b.CD jMeoecsuatcnk 5 rtebi b eidele1o ,oc2nib,.sg.j.i,seoM cnttL otxxh .( aci)tl a xs sb eil0o,n 0gwsh tioc hc l amssi niCi0m {iz1i,n 2g, .v. .a, lMue} ,L fx xo(ri )w. hTihc he sche me of the
algo rithm is :
1. 1. 23DD..L eeCMxss(ccoia0rrukii)nbbe tee d iooembbc1,ijij2nese,.ic.c.o,ttLM n xxx .(Lt. hix)a.(ti )x belong s to cla ss i0{ 1, 2, ... , M}, fo r which
32.. 2 . 3 3AM CCLLA..xo x oavMM ((uuvkiie00nneaaer ))rttykk yd eei s e isiidd1cimimm,11meei2,,1s..,pcc.i.i,....i.n,np,.ii.l.oMM,,sselMMneii LooLa Latxnnxlhglx(( giiatto())hhiotr..) aari xt itt ht b xxh m e mbbl oeec cllanooaM ngnnn sbgg betssoe utt ooucs sle ccaedllsdaa si ssf issif t ∈hiit00he  {e l1 {{ol,o11 s2s,,s s, 22 f .,,fu. u...n,..n ..cM,,ct iMMto}ion,}} n f,,i osffisroo “ rrw“ 0 0ww-h-1hhi1”cii ” hccf hh fuu n nc ctitoi onn. .
Let us define for i, j = 1, ..., M 0
3. ALMLe xvat( kieu0res)y dd seeiicmfm1ii,sn.p.i.in,eloMe nf oLa trxlhg (iaio,) tr.j x i =t hb m1e ,l o.c.na.,gn Ms b t eo ucslaesds i if0 th{e1 l,o 2ss, .f.u.,n Mct}io, nf oirs w“0h-i1c”h f unction.
0 fori j
LxLAAL(iee 0vvt(t) ieeuu/rrssyjy )d dmsseeiiimfmini0n1nppeeflLlfo e eoxff r or(aoaiirlri)l g. gii o,o, rjjrj ij i=t.=th h 1m1 m,, . c..c.a.a., n, n M Mb b ee u usseedd i fi ft hthee l olosss sf ufunncctitoionn i si s“ 0“-01-”1 ”f ufnucntciotino.n .
(i/j)i1,...,M
A Lvteeh(rtie y/nu j ss) idmUepf1il0nef efoao lfrrgoioir rii,t hjjj. m= 1c,a .n.. ,b Me u sed if the loss function is “0-1” function.
1fori j.
then
thLenetth lux(ei(sn/i )dj)efMiMne10p f(fofoxorr/r jii),i pj j=jj .1 p, (.x..), Mp (x /i)pi.
(tllihxx/e((jiin))) jjM10jj1i1ifppfoo((rxrx//iijj))ppjjjj. pp((xx))pp ((xx//ii))ppii..
theIlnpnx( ( itx)h/iios) jjsMIpniI1iitn upt h(tahxitsii/mos js )nsaipt,ix utjtuahpateit(p oixoo(n/bxni,)) j, te phtchie.pte (ox xo b/ibi js)ej pecciclt.a t x sx si isii s c ecldala stssosi f icfi eileadds ts ot oi oc ∈cl al as{ss1s i, oi2o, .{ .{.1,1, M,2 2,} ,. , .. ..f,.o ,M rM w}},h ,f ifocorhr w whhicichh
Tol xc(plia()sxs/ieoMs) pojjIpifnTo1(i o rxoti/h sicjiki)msl1p a ,1d.sa.s,j..,ie.xs.Mt,ieuMspnap t(i(oinxxof/g) nir),i, s tptpkhhi(. ee dx /aeoig)fbip gnjiel.ionc mtg ,x e trih sae tc iaolagnsg smliof eimethdeo rtadot ioco lfna c smlsu eisotthe or { da1 no, af2 lcy, l.su.i.ss, t Mecra} na, n bfaoelr yu wssiesh dicc.a hn be used.
p(x/iojj)1ipITinoo t hcilimas1 s,.sa.s.,ixeMtus paot(fixo /rnii)s, kpt hid.e e foibn jiencgt, xt hi es calgagslsoif mieedr attoi oc nla msse itoho d { 1o,f 2c,l u..s.t,e Mr a}n, afolyrs wish ciacnh b e used.
The example
TThhee pTo Te(bhxhxje/eeai o cemI)otnxipbp avTtijomhleeoe ic ospct ifillsv maei1tes th,.au.s .e,xoeaM srtfi e poots(hnfexe ,a/r iitrr)shce kpehs ie d.oi asebr fjtcieonh c i ctni lsxga ,sti ossthi cfc eyll aa asssgessgilifelfiocyem t des deetolr eca ccotiltmoae nsdps am cinooeimteh sp{o ta1don, ois2eof,s mc. .tl.oeu , sMcstleo}arm,s asfeneo sarc llowyafssh isriseic sschk a o naf t b reis ku saetd .t h e
base of 4 characteristics (four financial ratios) (Wilimowska et al., 2016).
thpe (bxTTa/hihsoeee) pooeixbf ajT4eFm occot mphcirv allaeaerxt sa hsocipesftse ( tx rhop/iisefu) t r rirppicesios.sk se( edfa,ore cufthirhn eiiins n gaat,ogn t gchclieloaa lmas gsreaigfrt lyaioot imssoe)ne l(er Wacmtt ieioledintm h cmooodwme tshpwkoaaindl li e eotsf ba cetlol .u, uss2ost0eem1rd 6 ea ) nfc.oallary sssniesus mc oabfne rrbi seko u fas etc dtlh.a se s
TbFahosere otohbofi js4e c icpthi1uv,.a.r.e,rpM aoocsfte et,rh isetht irece ss ae(gfaogrculohr m fiisen rataont cicoilanal s rsmaifteiyot hsso)e dl(eW cwtielidilml cobowem spukasaen ediet saf olt.or, 2sn0ou1mm6e)b .e crl asosfe sc loafs sr isk at the
definition. The result of this method is the tree of connections, the so-called dendrogram.
deinTbiathisoee n eo.x fT aF4hmo ecrp h rlaetehrs auiscl tt eoprfiu strthpiciosss me(f, eotuthhroe fd in aiasg ngthclioea mtlr reeareta iotoifos )cn o( Wnmnieeltichmtiooodwn ssw,k tiahl lee tsb oael- .c, au2ls0lee1dd6 d)f.e onr drnougmrabmer. of class
UsinTgo t chlea smseest hoof dr isokf daegfginloinmge, rtahteio ang, gtlhoem ererasetiaornc hmere thsuobdj eocft civlueslyte rd aentearlmysiinse cs atnh eb en uusmedb.e r of
UsinTdgeh fteih neoi tbmijoFeenoct.rth i oTvtdehh eioos ff r eapthsguuegrl pltro oeomssfee e,a trrhactithhsieo i mnsa, e tgtothgh eloco ldrmae ssiesseri afatyrthic eosh neetl rree mcsetu eebotdhjf e occcodtom ivnwpenlaieylncl tidieobesnet et sor,um ssthoienemde sesf otoch-rlcea a snnlsluueemdsm obbdefee rrnr idsorkfo gactr laatmhses.
ofT chlbdUaecaess lsfseaiienexsn ssgaoi et m(fist coh4 pl(nu eclc. sel humtT eashrretaseeth)cr storse)ede rsst iutesoittlnftit ic gnaos gt gf(h gftetohlh oueliim srnl ifeenmi rneoaea ftotni hoifcno niitdna,e l tr teirshsrae setcet ihtocrieestoi s)no et( rnaWoe rofec i fthl ohitemhfer e otcs rwtouerneebsne.kj e.ea cc ettiitvo aenlls.y,, 2dt0he1ete6 sr)mo. -icnaelsle dth ed ennudmrobgerra mof.
ThUcIenl sa oistnbhsgejee s c teF(htIxcioenvlar u e mmst htotpheeefltri ehsste, h)o xedpsda e uermtonretpfisdpn oerlagaesog er,gt cg,hr dhlaeoe t mhimlnsied n e wtrerooa aa oggtcsifrgl o aailcnnmoso,tsm ne itfrswehystreer aau scstercit eoiltcoesenocned nta eomrsudcfts re htiucthnehocergotm e tdstrdpu he abeewunj. e siim elcilnst ei gtvtbh oeeot l hsydeou mdosmeefed te eW ctrhlfmaaoorsirddns eenaossnu f o mdthfW betrhe iasenrrk du o mafat b ntecdhrl e at oshsfe
EucliEdueacnli ddeiasnta dnicseta, nwceh,i cwhh iwche rwe eures euds etdo tod edteetremrminien et hthe ec clulusstteerr ffoorr sseelleecctteedd fiinnaanncciaial lr atios. The
badcselea fosinsfe i4tsi ocI(ncnhl .au trTshateche terese r)xri esastsemiutctlpsitn l (egof,o ft udhtreeh n filsidin nrameon geocrtfiaha imoln drt ae wtriissao esstc h)t cei(oo Wntnr sieolteifrm utohcoftew e cdtsro kenueans. eei ntc gati lo.t,nh 2se0, 1tmh6ee). t hsood-c aolfle dW daerdn darongdr atmhe.
ratiosr.e Tsuhlets r oefs uthltes colfu tshteer calnuasltyesr iasn aarley sshiso awrne isnh oFwignu rien 3F.i gure 3.
UEusicnligFd oetIahrn ne tdthmhiiseset tahepnoxucdaremp , oowpfsl heea,i, cg hgtdh lewoen medrareegor gagutlrsioaeommdn ,e t orwta hdtaeieso tnrece rosmmenaisenrttcrehuh otcehdtree dscw uluubilsjsle tiencbrtg ie fv otehrul eysse eddmle ecetftetoehrrdmo dfin innuoeamsfn bctWheiarea l rnrodauf t miaocnbslda.e srTs thh oeef
So, ive classes were deined. The irst class consists of the companies that have a good
decErfeilunascisutlsliietodssne o.(a cfnT lt uhdhseiets etcrralesuns)sc ustelee,tr t w toainfhn giatc lhthyhis sewi slme iarnereeet hu ososfhed oid nw ittseon r tsdihneeec t Ftetiirrogmenue ir oneofe f 3 t th.hc eoe ntcrnelueecs. tt eior nfso,r tsheele csote-dc aflilneadn cdieanl drraotigorsa.m T.h e
inancial condition – small level of risk. The second class is composed of the companies that
areU csrhienasgrua lctthste eoIr nifmz tehtedhet he bc oyledu xa s aotsemfur f paailgncegai,e lloyndmste iinse dnraaarrotneigc osrinhaa,lom wcth onewn diarniset isFoecinaog.rnu cIsrnhetr e cu3ro c. nsteutrdba jseutc,s ttiihnvege lcytoh med epmtaenreimtehsio nwde hs oictfhh e Wh anavuremd baenrd otfh e
a fcrlaaEislu siecnsli ad(nceclauinas lt decirosstn)a dsniecttietoi,nn w ga hrteihc eihn l iwtnheeer oeth fu iirsndet dec rltsaoes csd.te iOotennr m othfi ent heoe tt hhtreeer e ch.l ua nstde,r tfhoer fsoeulretcht ecdla fsisn aconncisaisl trsa tios. The
of cormespualtnIsni eo sft h wtehi ethe c xalau vmsetperyrle ab, nadadle yinsndiasro nagcrireaa lsm hc oownwdanist ii oncn oF n–igs hturirugech t3 el.ed v eul soinf gri stkh.e T hmee ltahsot dc laosfs , Wifathrd, isa nd the
coEmupcolisdeeda onf dciosmtanpcane,i ews hwicithh wa ecrreit iucsael di ntoa ndceitaelr cmoinndei ttihoen c–l uthsete hr ifgohre sste lleecvteeld o ff irniaskn.cial ratios. The
6
results of the cluster analysis are shown in Figure 3.
6

6

6

6
Pobrane z czasopisma International Journal of Synergy and Research http://ijsr.journals.umcs.pl
Data: 22/01/2023 02:12:30
11
Is Management
a Science
S
or an Art?
From Theory
to Practice
C of Management

Figure 3. Cluster analysis using the methods of agglomeration
Source: Wilimowska et al.F (i2g0u1re6 )3. . Cluster analysis using the methods of agglomeration
Source: Wilimowska et al. (2016). M

So, five classes were defined. The first class consists of the companies that have a
So, five classes were defined. The first class consists of the companies that have a
good financial condition – small level of risk. The second class is composed of the companies
good financial condition – small level of risk. The second class is composed of the companies
that are characterized by a sufficient financial condition. In contrast, the companies which
that are characterized by a sufficient financial condition. In contrast, the companies which
have a frail financial condition are in the third class. On the other hand, the fourth class
have a frail financial condition are in the third class. On the other hand, the fourth class
U Figure 3.
ccoonnssiissttss oof fc coommpapnaineise ws iwthi tah vae rvye bryad b faidna fnicniaanl ccioanld citoionnd i–ti ohing h– lhevigehl olfe vrieslk .o Tf hries kla.s tT chlea slsa, st class,
Cluster analysis
ffiifftthh,, iiss c coommppoosesde do fo cfo cmopmanpiaensi wesi twh iat hc rait iccrailt ifcinaal nfciniaaln ccoinadl ictioonnd –it tihoen h–ig thhees th liegvheel sot fl erivske.l of risk.
using the methods of
AA ppriroiorir i prporboabbailbitiileitsi efso r fo5r c5la scsleass saerse acraelc uclaatlecdu labtaesde d boanse dth eo np erthceen tapgeer caeogngf tloamgeer atoiof n
aannnnoouunncceedd b banaknrkurputpcytc yo f oefc oencoomnoicm einct ietinetsi tiine sr eilna tiroenla ttoio nth et ot otthael dteolteatle dd ecloemtepda ncioesm fproanmi es from
Source: Wilimowska et al. (2016).
RREEGGOONN r ereggisitsetre. rT. hTehreefroerfeo,r teh,e t hae p ari oprrii oprroi bparboibliatyb iolfi tcyl aosfs c1l,a 2s,s 31 i,s 2 0, .331 i sa n0d.3 f1o ra cnldas fso 4r acnlads s 4 and
class 5 it is 0.035.
class 5 it is 0.035.
A priori probabilities for 5 classes are calculated based on the percentage of
Results of the Kolmogorov–Smirnov test and histogram figures of numerous layouts
announced bRaneksurulptst coyf o tfh eec oKnoolmmico geontriotive–s Sinm rierlnaotivon t etos t thaen dto thails dtoeglertaemd cfoimgupraensi eos f numerous layouts
of tested ratios in the class were calculated by computer program STATISTICA. The tests for
fromo Rf EteGstOedN rraetgiiosste ri.n T thheer ecfloarses, twhee rae p craiolrciu plarotebdab bilyit yc oomf cplaustse 1r ,p 2r,o 3g irsa m0.3 S1 TaAndT fIoSr TICA. The tests for
features for bad and good financial condition of companies, showed that probability density
class 4 and class 5 it is 0.035.
features for bad and good financial condition of companies, showed that probability density
fRuenscutlitosn so fa reth neo rKmoallm. ogorov–Smirnov test and histogram igures of numerous
functions are normal.
layouts of teUstseidn gra tthioes fionr mtheu lcal afsosr wneorrem caall cpurloabteadb ibliyt yc odmenpsuitteyr fpurnocgtriaomn SanTdA TcIaSlcTuIlCatAed. parameters,
The ftoers tesa fcohrU ffeseaianttuugrr eet shh efeo rfero ,b rcamodn uadlniatd io fgonora oln dpo riromnbaaanblc iilpaitrly oc bdoaenbndsiitliiitotyyn f udonfe cnctosioimtnyp wafnuaisne scc,ta islochnuol waateneddd thcaatl cula, twedh eprae ria meters,
probf=ao b1ri ,l2eit,ay3c ,dh4e (nfnesuiatmtyu bfrueenr hcotefir ofene,sa ctauorrene sdn)io;t rijmo =na al1.l, 2p,r o3,b 4a,b 5il i(tnyu mdebnesr iotyf cfluansscetsio).n was calculated , where i
Using the formula for normal probability density function and calculated parameter(s, |)
= 1,2,3U,4n (dneur mthbee ra ossfu fmeapttuiorne s)th; aj t= f 1ea, t2u,r e3s, 4a,r e5 i(nnduempebnedre onft, cltoastasle sc)o. nditional probability
for each feature here, conditional probability density function was calculated , where i = (|)
density fUunncdteior n tihse: assumption that features are independent, total conditional probability
1, 2, 3, 4 (number of features); j = 1, 2, 3, 4, 5 (number of classes).
dUenndseirt yt h feu nascstuiomnp itiso: n that features are independent, total conditional probability
densiftyx fu|njct ionf ixs:| j* fx | j* fx | j* fx | j, j = 1, 2, 3, 4, 5.
1 2 3 4
fx| j fx | j* fx | j* fx | j* fx | j, j = 1, 2, 3, 4, 5.
That means: 1 2 3 4
That means:
That mean4s: 1 x x 2
fx| j exp i ij , j = 1, 2, 3, 4, 5.
i14 21i2j  2xi2jx2
fx| j exp i ij , j = 1, 2, 3, 4, 5.
i1 2i2j  2i2j 
7

7
Where:
W– hsetaren:d ard deviation of i-feature of j-class;
Pobrane z czasopisma Int e–r en–xa spttieaocnntdeaadlr vdJa odluuevern ioaaftli o io-nffe oaSft yui-rnfeee oargftu yjr- eca lonafsd sj ;-R cleasses;a rch http://ijsr.journals.umcs.pl
Data: 22/01/2023 02:12:30

– i- –fe eaxtup reec otefd c lvaaslsuiefi eodf io-bfejeactut.r e of j-class;
12

Where:
W– h ieR-rfeee:ma tuermeb oefr icnlgas tshifaite dB oaybejesc’ t.a lgorithm needs a value ofpjf(x/ j), calculation for each
Where:
class a–n ds tcahnodoasrdin dge tvhiea tmioanx oimf iu-mfe avtuarlue eo of fj -tchlaats sa; posteriori probability of class, the results of
IJSR –W stRhaenermdea:ermd bdeerviinagti othna ot fB i-afyeeast’u rael goofr ji-tchlmas sn;e eds a value ofp f(x/ j), calculation for each
classification shows Table 1. j
6 ––– s etxsatpnaedncadtreaddr d dv edaveluivaeit aiootfino i n-of feo iaf-t fiue-rfaeet uaotrfue jr -oecf lo ajf-s csjl-;ac slsa;s s;
ccllaass–– ss–– i –iifa -- eeifnfcxxeeedaappxa ttteepciuuoccherrnttoceeee to sddeoohs dffvvio n aaccvwgllllauuaa sltss eeuhTss Teeooiiaafi ffboibm eeliilfe--ddea ffi 1 x-ee1oo.fiaa .bbTme ttjajuuheeuterrcucm eeettr .x.ooe av ffmo ajjfpl--u ccljeell-saac oosslassff ;;sc tslha;sasti faic aptoiosnt ebryi oBraSiy epsr’o mboadbeill ity of class, the results of
– i-feature of classified object.R esult Result Result Result Result
– Ri-efemRateeummrebe meorfbi ncelgrai nstshgia fttiTh eBaadbt al RoeyB be1eaaj.sle y T’c ehtas.eol ’ fge xoacallragmistosph rlmeiotshf o nmcfe lc aelnsadses sse iodaffis c v acatlaia losvunsae bl ouyof e fB caoplayfsesspf ’ mo(ffxo (cdx/lea/ljs sj) ),, C cclaaasllscc uullaattiioonn ffoorr each
Coemcalpa cashns y c alnaRRdssee c mmahneeodmmo scbbiheenorrgiio nntsgghin ettg hhm aathtta CxeBBl iammaasyysau eexmss1i’’m vRaaualleggmlsuoou elrrvt ii 2attohh lfumm Rtehe snnoaCuteefl teeat 3hdd passR to aaesa st vveupaalrotill 4souu treeeRi r ooepiffosrjuorpplitb jj5paff rb((oRixxlbei//stayubjjl ))tio l,,i ftcc ycaa llloaccsfuu scll,aal attthiisooesnn , r teffhooseurr leetsaa ccohhf
rcelsausslt sa nodf cclhaososisiincga ttihoen mshaoxwiRmse uTalma b vloeaf l1cul.eas so f otfh aclta sas poofs tcelarsiso roi fp crloabsjsa boilfi tcyla ossf cCllaassss , the results of
Cocplaals sification shows Table1 1–.3 0.996 0.004 0.000 0.000 0.000 1
Ccloamspsa anny d choosing the maxiCmlausms v1a lue of 2t hat a p3o sterior4i probab5il ity of class, the results of
classification shows Table 1.
AnCdcrlooapismsaiplf eixc ation shows TabTlaeb1 l1–e3.R 11 e–.a T3l h 0e.0 e00Rx.1e9a sm9u6pltl 0 eo.sf5 0o4f.2R 0 ce0lsa4usl s0ti .fo4if0c5 a.70t Ri0oen0s u 0bl.ty0 o00Bf.0 a0 y0Re0ess’ 0 um.l0t0o0 od.0f0e l0 R0e 2s ul1t of
Azomet Sp. z Coo.om. pany TTaabb4ll–eeC5 11l a.. sTTMshh0ee.0 ee0xxR0caae lmmassuppslll t01ee .ss0 oo0Rff0 e cccslllaaausssltsss0 ii2.ff0iicc0Raa0tte iisoocunnlal ts1bb s.yy 03 0BBR0aae yyseeucssll’’ta0 smm.s0 oo04Rdd0eee lls ulct4l a ss 5 Class
Androimpex 1–3 0.001 0.542 0.457 0.000 0.000 2
Copal 1R–3eal Rofe0 s.c9ul9al6ts s Rofe s0cu.l0al0ts 4s Rofe scu0l.al0ts 0s0 Rofe scul0alt.s 0s0 0Rofe sculalt0s .s0 00Class 1
B.P.C Porminpt aSnpy. z o.o. 4–5 RCelaas0ls . 00Ro10f e sculalt0s s.0 0Ro20f e sculalt0s s.0 0Ro30f e sculalt1s s.0 0Ro40f e sculalt0s s.0 0Ro50f e sculalt4s s Class
AAznodmroiemt pSepx. z o.o. 41––53 0.000.000 1 0.0000.5 42 0.0000 .4571.000 0.0000.000 0.0040 2
Company RCelaasls o1f class o2f class o3f class o4f class o5f class Class
… ACCzooommpepatal S npy. z o.o. 4–54 C1–5–la3s0s . 00010 .0 9.090600 .00020 . 000.04000 .00032 . 000.0000 .099048 . 00100.0 .0000050 . 00004 . 0001 4
B.P. Print Sp. z o.o. 4–5 0.000 0.000 0.000 1.000 0.000 4
Copal 1–3 0.996 0.004 0.000 0.000 0.000 1
Table 1. B.P. Print Sp. z o.o. 4–5 0.000 0.000 0.000 1.000 0.000 4
The examples of Beł…cCAh naodtporawolism kpiee x Zakłady 411––5–3 3 000.0..0090091 6 000.0..5004002 4 000.0..4005207 0 000.9..0900800 0 000.0..0000000 0 412
Prze…Amnydsrłoui mBpaewxe łUnianego Sp. z 41––53 0.00.00010 0.504.020 0 0.4507.0 02 0.0000 .9980.000 05. 0002 4
classiication by
o.oB.B AAeełznłccodhhmraaotteoiomwtw Sspkspeike.x i zZe a okł.aod. y PrzemZyaskłuła dy4 –5 14––350 .00000.. 000010 0.00000.. 504020 0.00000.. 405070 0.00010.. 000000 1.00000.. 000000 24
Bayes’ model Azomet Sp. z o.o. 44––55 0.00.00000 0.000.000 0 0.0000.0 00 1.0000 .0000.000 1.0004 5
PBrazwemełnyisałnue gBo aSpw. ez łon.oia.nego Sp. z 5
SourcABe:.z PWo.m Pileirmitn Sotw pS.s pkz.a o ze. too a.. ol.. ( 2016). 44––55 00..000000 00..000000 00..000000 11..000000 00..000000 44
o.o. 4–5 0.000 0.000 0.000 0.000 1.000
SBou.Prc. eP:r Winti lSimp.o zw osk.oa. et al. (2016). 4–5 0.000 0.000 0.000 1.000 0.000 4
3.3. B…F.Pr .a Pcrtianlt Smp.o zd oe.lo .i n risk mode44l––li55n g 00..000000 00..000000 00..000020 01..909080 00..000000 44
Source: Wilimowska et al. (2016).
The… f ractal dimension was def4i–n5e d 0b.y00 0M an0d.0e0lb0 rot 0d.0u0r2i ng 0t.h99e8 stu0d.y0 00o f G4 reat Britain’s
coa33s.B…3t.le.3i łnFc.her a.Fa tTocrwthaasaklcn imetk aso ltd ome tlh ioinsdZ rraeeiksslłkea ida mnyrc ohr4d,–i es5hl keli nnm0og.t 0 oe0d0d tehall0ti .t0nh0ge0 coa0s.0tl0i2n e is0 n.9o9t8 an o0b.0j0e0c t Eu4 clidean, so its
BPrezłecmhaytsołwu skBiaew ełnianegZo aSkłpa.d yz 5
dimTTBPoheh.nreeozeł s.ec imfhforranyaatsoc cłwctutaaa slknlB inadedwo iimtme łnbeeienna nssdeiioogeZonns ac Skwrwłipaba.da esysz d d d4eb–eiy5fn ianende d0 ib. n0yb0te 0yMg eMar n0oad.0nfe 0dl20be rl(boMrt o0ad.t0n u0ddr0ieu nlrbgirn o0tgh.t0 ,e 0t 10hs 9etu6 d7s1y)t.u. 0 od0Tf0yh Geo rfee5 na Gtti rrBee arcitt oaaBinsrt’ilstia nien ’s
wacscoPo oac.raozso.set vltmileniyrneseeł.du .T TwBhhaaiwtanhnek łkNsns iat otncoe itr ghtcohil sieSs srp re.he szase evaai4rncr–cgh5h , t,hh hee0e .n 0sno0ao0mte teded tr 0htah.ad0at0i tu0t h tsh e–e c 0cor.o0.a 0asT0stlh tileninsee0e i . 0smis 0n 0eno aots tua a1rne.n 0mo 0ob0ebj nejetcsct 5 tEw Eueucrcelil dirdeeeapanen,a ,ts eod i ts
reddsuSiooomc.u oiirne.tc snge :s daWioinminldim e cinonawscnisronkeanoa e tstc iabanlen.g ( n 2dt0ohe1tes6 bc)r. reai dbdieeu4dss– c.5b r Iiytb teau0dn.r0 n b0ie0nyd t eaognue0 itr.n 0 t0tohe0fag te2 er v (0oMe.0fr 0ya20 n t(diMmele0ab .nr0iotd0 t0ew, l ab1sr9 o16ot.7b0, 0)t1a.0 9i Tn6eh7de). teThneht eifr oeel nlcotoiwraeis ntlgi ne
Source: Wilimowska et al. (2016).
equwcioavsaa slcetolnivnceeer rewedla aswt icoitonhv: eNr ecdi rwclietsh hNa vciinrgcl eths eh asavmineg rtahdei ussa m– er .r aTdhiuess e– m r.e aTshuerseem menetass wureerme ernetpse ated
S3o.3ur.c Fe: rWaiclitmaolw mskoa dete all . i(n20 r1i6s).k modelling
rwe3Td.he3ure.ce Fi fnrrregaap ccaettnaaadltl e middn icomrerdeedeanuls sciiinniong nrg it shawkena dmrsa iodnddiceuerfseli.ln aiIenstdi gnt u g br nythe deM oraaundt dituehslab.t r Ieot vtt eudrryun retiidnm goe u titht etwh aasstt ueodvbyet ariyon fet idmG trehe eai ttf owBlalorsiw taiinng’s
eo3Tqb.uh3tiea.v iFanflrreeaadncc ctttaheal el r emfdloaiomltldiooeewnnl s:ii innog nr eisqwkua imsv aodldeeenfliclneien rdge l abtyi onM:andelbrot during the study of Great Britain’s
coastline. Thanks to this research, he noted that the coastline is not an object Euclidean, so its
WhcTeorheae:s tNlfirn a–ec .nt aTulm hadbniemkrs eo ntfos c itoihrnci sle wrse,as rse a–dr rceahfdi,n ihueesd no(obf2 tyce∗ idrMc tl)heaasn,t=d Dtehl1 eb– r cfoor taa csdttaulilrn ideni gmis etnnhoseti oasnnt.u odbyj eoctf EGurceliadt eaBnr,i tsaoin i’tss
dimension cannot be described by an integer of 2 (Mandelbrot, 1967). The entire coastline
Wdcoimhaesetrnleisn:i eNo.n T– c hnaaunnmnkosbt e tobr eot hfd icse isrrcecrslieebsae,rd cr h b–,y hr aead nni uoisnte todefg tcehirar tco ltfeh se2, cD(oM a–sa tfnlrdianeceltb airslo dnt,io mt1 e9ann6s 7oi)ob. njTe.chte E eunctliirdee acno,a sstol iintes
SoW,dw tihhamees r efecnr:oas Ncviotea nr–le dcndaiu mwnmneibtonhets riNb ooen f c dciisrie:rcs clcelresis b,h erad v– ib nryag d atihunes i ons(fta2e mcg∗ieercr rl)eoasdf, i= 2uD s1 ( –M– farra.n cdTteahlleb dsreoim tm, e1ne9asis6ou7nr)e.. mTehnet se nwtierree croepasetaltiende
Swoa,s t hceo vfrearecdta lw diitmh eNn sciiornc liess: having the same radius – r. These measurements were repeated
reducing and increasing the radius. It turned out that every time it was obtained the following
was covered with N circles having the same radius – r. These measurements were repeated
Seroeq,du tuihvceia nlfegran accntead lr edinliamctrieeonanss:ii nogn tihs:e radius. It turned out th at every time it was obtained the following
ereqduuivcian legn acned r einlactrieoans:i ng the radius. It turned out that every time it was obtained the following
log
equivalence relation:
= 1
WheTrehT:e hN me –om nreou rmteh bete hro eob fjo ecbcijtre ccwlet isl,wl rib l–le rbafreda iyufesrad oy( fe2a cdn∗i dr(a crnl2)eadsg) ,g= rDeadg1 –,g eftrhdae,c ttmahleo d riemm otehrnees ifotrhnae.c tafrla cdtiaml ednismioenn sion
aaWpppphroreoareac:ch hN w w –ili lnl lbu bem ecb lceolros eso eft oct oitrh ctehl eevs av, laru l–eu eora fod 2fi u.2 s. o(=f2 c∗irlcol)ges,1= D1 – fractal dimension.
SWoh, etHhreeuH: r fNsurtar sc–ettx anpelu xodmpnimoebnneetern, n osatif,so canais r i cssatl:ae tssi,ts atrit ci–sa trlia cmdaileu amss oue(far2 esc u∗iurrcseel) ed(us 2s,f= eoD)dr 1 –fdo efrrt eadrcmetatieln rdimsimtiincei nsftrsiaicoc ntfar.l a,c itsa ld, eipse dnedpeennt dent
oSnol,y t8 ho en fthraec vtaall udeim ofe nthseio cno risre: lation coeficient C between the pair tested parameters, which
only on the value of the correlation coefficient C between the pair tested parameters, which
So, the fractal dimension is:
can be stored in the form (Kiłyk, Wilimowska, 2010; Czarnecka, Wilimowska, 2018):
can be stored in the form (Kiłyk, Wilimowska, 2010; C zarnecka, Wilimowska, 2018):
8
log
= log1
W here: C – correlation coeficient, H –=( H2 ul−or1sg)t( 2e1x)ponent.
Where: C – correlation coefficient, H – H=ur2st expon−en1t.
=(21)
(2)
So,
8
8
8

1
= (1+ )
The poss ible value of Hurst exponent can b2e betw een 20 and 1.
When the value H is below 0.5, one can say that the analysed signal is anti-persistent,
which means that there is a big probability that in the next step, it will be opposite to the
current step. It is worth mentioning here that if the size takes a value closer to zero the more
“jagged” signal (more unpredictable, more risky). For a value H equal to 0.5, the signal is
random and one can say that it is more like a Brownian motion.
The last interval for H is the value higher than 0.5. In this interval signal is persistent,
which means there is a bigger probability that in the next step, the signal will behave like in
the current step (trend will not be reversed). This means that the greater the value of H
assumed, the smoother the signal being analyzed (less unpredictable, less risky).
DMA method, as one of the few, is used for random fractals, which is difficult to define basic
parameters. The main objective of the DMA method is that the signal fluctuations scaled
accordingly with increasing scaling exponent (strongly dependent fractal dimension).
4. IT models
The concept of information system is found in subject-related literature quite often, however,
it proves to be a very difficult task to define the concept precisely. In many scientific
publications it is interpreted in an ambiguous way. Definitions of the information system
given by different authors often vary from each other, but the idea and the essence of the
information system remain rather unchanged. The variety of these definitions results from the
fact that their authors postulate them according to purposes which the system is supposed to
satisfy, and, above all, to the scientific disciplines they investigate. Studies dealing with the
research on information systems are an interdisciplinary field because it includes, among
others, IT issues, management sciences, sociology, and quantitative methods.
In Polish, the term “IT system” is quite misleading; another commonly used
expression is “EDP”, i.e. Electronic Data Processing. EDP concerns information processing
rather than IT. IT is closely related to the technology itself and not to what it serves. It is the
role of supporting business processes; IT itself is not a business process as some people think.

9
The more the object will be frayed and ragged, the more the fractal dimension
approach will be close to the value of 2.
Hurst exponent, as a statistical measure used for deterministic fractal, is dependent
Pobrane ozn clyz aosno pthies mvaal uIen toefr nthaeti oconrarle lJaotiuornn acol eofff iSciyennte rCg yb eatnwde eRn etsheea prcahir htetsttped:/ /pijasrarm.joetuerrsn, awlsh.iuchm cs.pl
Data: 22c/0an1 /b2e0 s2t3or 0ed2 :i1n 2th:3e0 form (Kiłyk, Wilimowska, 2010; Czarnecka, Wilimowska, 2018):

13
(2−1)
Where: C – correlation coefficient, H – H=ur2st expon−en1t.
So, So, Is Management
a Science
S
or an Art?
1
The possible value of Hurst expone=nt c(a1n +be betw)een 0 and 1. From Theory
The possible value of Hurst exponent can b2e between 20 and 1.
When the value H is below 0.5, one can say that the analysed signal is anti-persistent, to Practice
which Wmehaenns tthhea tv tahlueree H is ias bbiegl opwro 0b.a5b, iolintye tchaant isna yth teh ante xthte s taenpa,lC iyts wedil ls ibgen oalp ipso asnittei -tpoe trhsies tento, f Management
wcuhricrehn mt setaenps. Itth iast wthoerrteh ims ean tbiiogn ipnrgo bhaebreil itthya tt hiaf tt hine stihzee ntaekxet ss ate pv,a liut ew cillol sbeer toop zpeorsoit eth eto the
more “jagged” signal (more unpredictable, more risky). For a value H equal to 0.5, the
current step. It is worth mentioning here that if the size takes a value closer to zero the more
signal is random and one can say that it is more like a Brownian motion.
“jagged” signal (more unpredictable, more risky). For a value H equal to 0.5, the signal is
The last interval for H is the value higher than 0.5. In this interval signal is persistent,
random and one can say that it is more like a Brownian motion.
which means there is a bigger probability that inM the next step, the signal will behave
The last interval for H is the value higher than 0.5. In this interval signal is persistent,
like in the current step (trend will not be reversed). This means that the greater the value
which means there is a bigger probability that in the next step, the signal will behave like in
of H assumed, the smoother the signal being analyzed (less unpredictable, less risky).
the current step (trend will not be reversed). This means that the greater the value of H
DMA method, as one of the few, is used for random fractals, which is dificult
atsos udmeiende, tbhea ssimc opoatrhaemr ettheer ss.i gTnhael bmeaining aonbajelycztievde (olefs sth uen pDrMedAic tmabelteh, oleds sis r itshkayt )t.h e signal
DlMucAtu amtieothnos ds,c aasl eodn ea cocfo trhdei nfgewly, wis iuths eidn cforera rsainndgo smc aflriancgt aelsx,p wonheicnht i(ss tdriofnfigcluyl td teop deenfdineen tb asic
pfararacmtael tdeirms. eTnshieo nm).ain objectivUe of the DMA method is that the signal fluctuations scaled
accordingly with increasing scaling exponent (strongly dependent fractal dimension).
44. I.T I mTo dmelso dels
The concept of information system is found in subject-related literature quite often, however,
The concept of information system is found in subject-related literature quite often,
iht opwroevveesr, tiot bpero va esv etroy bdeif faic uvlet ryta sdki fitoc udlet fitnaesk thtoe cdoenicneep tt hper eccoisneclyep. tI np rmecainseyl ys. ciIenn tific
pmubanliyca sticoinens tiiit ci sp uinbtleircparteiotends iint ias ni natmerbpirgeuteodu si nw aany .a mDbefiginuiotiuosn sw oafy . thDee iinnfiotiromnast ioofn thsey stem
giinvfeonr mbayt idoinf fesryesntet mau tghiovresn obftye nd ivffaeryre nfrto mau tehaocrhs ootfhteenr, vbaurty t hfero imde ae aacnhd oththee re,s sbeuntc eth oe f the
iindfeoarm aantdio tnh es yesstseemn cree moaf itnh rea tihnefor rumnacthiaonng seyds. tTemhe rveamriaeitny roaft htheer sue ndcehfainnigtieodn.s T rheesu vltasr iferotym the
foafc t ththeaste thdeeiir naiutitohnosr sr epsouslttusl aftreo mth etmhe a cfaccotr dtihnagt ttoh epiru rapuotsheosr sw hpiocshtu tlhaete s ythsteemm aisc csourpdpinogse d to
staot ispfuyr,p aonsde,s awbhoivceh atlhl,e tosy tshtee msc iiesn stiufpicp odsisecdi ptloi nseast itshfeyy, ainnvde, satibgoavtee. aSltlu, dtoie st hdee aslciinegn twiiicth the
disciplines they investigate. Studies dealing with the research on information systems
research on information systems are an interdisciplinary field because it includes, among
are an interdisciplinary ield because it includes, among others, IT issues, management
others, IT issues, management sciences, sociology, and quantitative methods.
sciences, sociology, and quantitative methods.
In Polish, the term “IT system” is quite misleading; another commonly used
In Polish, the term “IT system” is quite misleading; another commonly used expres-
expression is “EDP”, i.e. Electronic Data Processing. EDP concerns information processing
sion is “EDP”, i.e. Electronic Data Processing. EDP concerns information processing
rather than IT. IT is closely related to the technology itself and not to what it serves. It is the
rather than IT. IT is closely related to the technology itself and not to what it serves.
role of supporting business processes; IT itself is not a business process as some people think.
It is the role of supporting business processes; IT itself is not a business process as some
people think.

4.1.Genetic Algorithms (GA)
A Genetic Algorithm is a kind of algorithm that searches the space for alternative
solutio9n s to a problem in order to ind the best solutions.
They are especially useful for inding optimal solutions in situations where many
extrem a occur (Figure 4).
Pobrane z czasopisma International Journal of Synergy and Research http://ijsr.journals.umcs.pl
Data: 22/01/2023 02:124:.310.Genetic Algorithms (GA)
A Genetic Algorithm is a kind of algorithm that searches the space for alternative solutions to
14
a problem in order to find the best solutions.
They are especially useful for finding optimal solutions in situations where many
extrema occur (Figure 4).
IJSR
6 global
S

local

C
Figure 4.
Example of local and
global extrema

Figure 4. Example of local and global extrema
Source: Based on Bryłka and ŚwiątkowsMki (2007).
Source: Based on Bryłka and Świątkowski (2007).

The idea of inding only approximate solutions is shown in Figure 5.
The idea of finding only approximate solutions is shown in Figure 5.
Almost there ...
I'm noUt at the top Almost there ...
I'm yneott. aBtu tt hI ee ntotepr ed
yet.t Bheu th Ii gehnetsetr…e d  I will reach the top
the highest…  I will reach the top
I'm not at the
I'm ntootp a yte tth. eB ut …

top yet. But …

Figure 5.
Finding solutions in
genetic algorithms

Source: Based on Bryłka and Świątkowski (2007).
Figure 5. Finding solutions in genetic algorithms
In the general scheme of applying genetic algorithms in solving real problems, two
Source: Based on Bryłka and Świątkowski (2007).
phases can be distinguished:

an initial phase, irstly to clarify the problem and adapt it to the terminology used in GA,
•I n thaen dg esneceroanld slyc,h teom ees toafb laisphp ltyhien gin igteianle ptiocp aullgaotiroitnh;ms in solving real problems, two
ph ases •c an bseea dricshti ngfouri shseodl:u tions, consisting in the evaluation of individuals, the
reproduction process and the application of genetic operators. The solution search
 pahna sine itiisa lc opmhapslee,t efidr swtlyh etno ac lasaritfiysf athceto pryro sbolelumti oann dh aads abpet eint tfoo uthned ,t eorrm ainno alolggoyr iuthsemd in
teGrAm,i naantdio sne ccoonnddlyit,i oton ehsatasb bliesehn t hree ainchiteiadl (peo.pgu. ltahteio ans; sumed number of generations
has been exceeded after reaching a certain number of steps, or when the solution
does not improve by the assumed number of steps).
10