sus ainabili y
A icle
Fuzzy Simila i y Used by Mic o-En e p ises in
Ma ke ing Communica ion o
Sus ainable De elopmen
Da id Schülle 1and Ka el Doub a ský2,*
1
Depa men o Managemen , Facul y o Business and Managemen , B no Uni e si y o Technology, Kolejni
2906/4, 61200 B no, Czech Republic; [email p o ec ed].cz
2Depa men o In o ma ics, Facul y o Business and Managemen , B no Uni e si y o Technology, Kolejni
2906/4, 61200 B no, Czech Republic
*Co espondence: [email p o ec ed].cz; Tel.: +420-54114-3723
Recei ed: 4 July 2019; Accep ed: 18 Sep embe 2019; Published: 30 Sep embe 2019

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Abs ac :
The pu pose o his pape is o p esen uzzy easoning as a o mal ool o de e mining he
di e ences in pe cep ion o indi idual communica ion channels by cus ome s. These di e ences in
cus ome pe cep ion a e impo an o mic o-en e p ises o de elop an e ec i e g een ad e ising
campaign. These kinds o en e p ises a e no able o conduc hei own ex ensi e ma ke ing esea ch
o use he se ice o ma ke ing agencies. Mic o-en e p ises a e he co ne s one o sus ainable local
economic g ow h whe e he communi y plays an i eplaceable ole o sus ainable de elopmen .
Ma ke ing communica ion is unique and complex because i ocuses on eelings, moods, and pe sonal
p e e ences. The main p oblem is he unce ain y o his inpu da a which makes i di icul o de elop
e ec i e g een ad e ising campaigns. Fuzzy se s and uzzy easoning a e used o make e bal
desc ip ions sui able o compu e applica ions. A uzzy pai wise simila i y is used in his pape .
The case s udy has eigh ele an a iables/ma ke ing communica ion media, e.g., e-mailing, social
ne wo ks, web pages, ex messaging, newspape s, phone calls, pos e s and adio, and i e segmen s
o esponden s selec ed by age. Each segmen is p esen ed as a uzzy condi ional s a emen . A se o
uzzy pai wise simila i ies is gene a ed.
Keywo ds:
mic o-en e p ises; ma ke ing communica ion; g een ad e ising; sus ainable
de elopmen ; e bal desc ip ion; uzzy simila i y
1. In oduc ion
Sus ainabili y is a c ucial opic con on ing a wide ange o businesses, p omp ing ma ke e s
and academics o se no el and ele an a ge s [
1
]. Me hods o de eloping sus ainable p ocesses,
p oduc s, and se ices became a key opic challenge o ma ke ing p o essionals and o he en i ies like
go e nmen s. Sus ainable ma ke ing is based on he heo y o sus ainabili y and co e s he same h ee
dimensions—en i onmen al, economic, and social. Sus ainable ma ke ing ocuses on he u u e o
mu ual ela ionship and communica ion be ween en e p ises and hei cus ome s [
2
,
3
]. E en hough
bo h cus ome s and en e p ises ealize he impo ance o sus ainabili y, i is di icul o en e p ises o
d aw cus ome s’ a en ion ia sus ainable ma ke ing s a egies [
4
]. En e p ises need o communica e
hei sus ainable ma ke ing s a egies e ec i ely and ma ke ing communica ion has i s i eplaceable
ole in sus ainable de elopmen . Ma ke ing communica ion has he po en ial o clea ly communica e
new sus ainable kinds o business o consume s [5,6].
Ma ke ing communica ion is associa ed wi h g een ad e ising. Bane jee e al. [
7
] de ines he
g een ad e ising in hese h ee aspec s:
Sus ainabili y 2019,11, 5422; doi:10.3390/su11195422 www.mdpi.com/jou nal/sus ainabili y
Sus ainabili y 2019,11, 5422 2 o 15
1. Any ad e ha includes he ela ionship be ween a p oduc and biophysical en i onmen ;
2. Any ad e ha comp ises a g een li es yle wi h o wi hou highligh ing a p oduc ;
3. Any ad e ha p omo es a co po a e image o en i onmen al esponsibili y.
One o he mos well-known de ini ions o g een ad e ising is based on a wo- ie app oach.
The i s ie comp ises and signi ies he echnical pe spec i e a i ude and he second ie highligh s he
wide concep s o sus ainabili y [
8
]. This de ini ion poin s ou he in e connec ion be ween echnical
aspec s o ad e ising and sus ainabili y. The e o e, i is c ucial o he pu poses o he a icle and
p esen ed case s udy. Many o he au ho s ocus on he concep o g een ad e ising a di e en
le els [
9
–
11
]. McDonald and Oa es [
11
] a gue ha g een consume s y o apply hei sus ainable
alues in o pu chasing c i e ia such as ene gy e iciency o local sou cing. The au ho s also emphasize
ha i is easie o encou age sus ainable buying beha io in as -mo ing goods like ood han in
occasional pu chase o la ge p oduc s such as a idge o mo o ca . These au ho s add in hei la e
esea ch ha demog aphics and g een beha io o consume s a e o en aken in o conside a ion so
ha ele an a ge g oups o consume s could be iden i ied wi h mo e e ec i eness [12].
A mic o-en e p ise used in he case s udy is ela ed o he McDonalds’ and Oa es’ esea ch mainly
in hese aspec s— ood indus y and local sou cing. The segmen s o consume s a e analyzed om he
pe spec i e o demog aphic segmen a ion (age) in he ield o ma ke ing communica ion.
Mic o-en e p ises a e de ined as i ms wi h ewe han i e employees [
13
]. Acco ding o he U.S.
Small Business Adminis a ion, mic o-en e p ise is de ined as an en e p ise ha has ewe han i e
employees [
14
]. On he con a y, The Wo ld Bank de ines mic o-en e p ise as a company ha has up o
10 employees and i s o al asse s o up o $10,000 and o al annual sales o up o $100,000 [
15
]. The
Eu opean Union de ini ion o mic o-en e p ises is ele an o he pu poses o his pape . The Eu opean
Commission de ines a mic o-en e p ise ha has up o 10 employees, a balance shee o al below EUR
wo million, and u no e also below EUR wo million [16].
I is impo an o see hese en i ies no only om he pe spec i e o sus ainable economic g ow h
bu also hei social, en i onmen al, and cul u al dimensions. Mic o-en e p ises a e communi y
based, which is c ucial supposi ion o b ing oge he all elemen s o sus ainable de elopmen .
Mic o-en e p ises os e sus ainable de elopmen only i hey a e also in eg a ed in o communi y
de elopmen [17].
Sus ainable en ep eneu ship b ings a signi ican change in business a ge s [
18
]. I is essen ial
o shi om p o i -cen e ed aims o sus ainable-cen e ed ones, see [
19
]. The in e ac ion be ween
mic o-en e p ises and cus ome s plays a key ole o each he sus ainable-cen e ed a ge s and bo h
subjec s ha e o be well-mo i a ed o suppo sus ainable en ep eneu ship. Solid in en is needed o
become a sus ainable en ep eneu who can suppo he whole communi y. This in en is an impo an
s imulan o becoming sus ainable en ep eneu [20].
Mic o-en e p ises a e closely in ol ed in communi ies and hey ha e a be e chance o being
ecognized when hey p o ide p oduc s o se ices. I is bene icial o mic o-en e p ises o ocus on
g een p ocesses as hey can easily a ac po en ial cus ome s. En ep eneu s p o iding se ices ough
o acqui e a dis inc ma ke , based on g een ac i i ies [21].
I is necessa y o companies o in o m he po en ial cus ome abou he sus ainable in en ions, o
aise awa eness, and y o in luence consume beha io owa ds sus ainable de elopmen [18].
Fo hese pu poses, en ep eneu s ha e o s i e o use e ec i e ma ke ing communica ion and
an op imal communica ion mix.
Nowadays ma ke e s ace a wide choice o media channels in communica ion wi h hei cus ome s.
I is necessa y o manage ma ke ing communica ions ca e ully and e ec i ely. Apa om adi ional
ma ke ing channels, online media is inc easingly signi ican in he communica ion mix. Online
ma ke ing communica ion con ains a ious kinds o media such as social media, sea ch engine
ma ke ing, email ma ke ing, display ad e ising, o mobile ad e ising. The in e ne has become an
e e yday pa o he li es o millions o people a ound he wo ld [22].
Sus ainabili y 2019,11, 5422 3 o 15
Today, ma ke ing communica ion includes c ea ing and main aining online communi ies.
In e ac ion and collabo a ion wi h cus ome s allows en e p ises o ge a be e unde s anding o
hei wishes and needs [23].
Good coo dina ion o a ious communica ion channels is he key in in eg a ed ma ke ing
communica ion. En e p ises can deli e he message o he cus ome wi h a highe impac by
using mo e communica ion channels. This impac is a esul o he ac ha a cus ome ecei es a
consis en message om mo e ma ke ing channels, see [
24
], which is mo e e ec i e han using only
one communica ion medium.
En e p ises ha e o ge o know how cus ome s pe cei e he impo ance o indi idual
communica ion channels o p o ide a consis en message wi h a high syne gy e ec . Se e al s udies
ocused on syne gy in adi ional ma ke ing channels [
25
], bu also be ween adi ional and online
media [26,27].
Real-wo ld modeling and op imiza ion o ma ke ing communica ions (MC) is based on unce ain
inpu s, such as he pe sonal knowledge. This unce ain y o he inpu in o ma ion o en excludes
s a is ical me hods, see [
28
,
29
]. The no mali y and he minimum numbe o da a se s a e he essen ial
equi emen s o he co ec applica ions o s a is ical me hods; o de ails see, e.g., [30,31].
Realis ic MC p oblems a e unique and usually di icul o measu e and quan i y. This uniqueness
may make i impossible o isola e hem wi hou signi ican ly dis o ing he inpu in o ma ion which
has a signi ican impac on he accu acy o he p oblem. This is he main eason o being unable o use
s a is ical me hods o eal MC- ela ed asks.
The objec i e way o e alua e he p obabili y o an e en is o epea he measu emen /obse a ion
o he ou come o he e en many imes unde he same condi ions. This is p ac ically impossible. This
is he main eason why new o mal ools a e necessa y o he s udy o ma ke ing communica ion asks
when he model mus be nei he oo simpli ied no oo speci ic. This pape p esen s a new app oach
how o use uzzy logic o in eg a e shallow MC knowledge i ems in o a o mal model using small da a
se s and o ob ain a ela ionship be ween he moni o ed a iables.
MC indica o s ha e been p oduced o a ious pu poses by a wide spec um o ins i u ions
leading o di e se indica o s. Howe e , using an adequa e and consis en se o indica o s o measu e
ma ke ing communica ion o a company o cus ome is no easy. The e a e wo app oaches o sol ing
MC ealis ic p oblems:
•Common sense app oach based on eelings, expe iences, analogies;
•Fo mal app oach based on ma hema ical models.
Fuzzy se s a e ools ha allow o in eg a e bo h o he abo e app oaches.
The a icle con ains he ollowing sec ions: Ma e ials and Me hods, Case S udy, Discussion and
Conclusion. The ma hema ical amewo k o uzzy easoning is explained in he sec ion Ma e ials and
Me hods. The au ho s delibe a ely chose a con ec ione y mic o-business o he case s udy because
cus ome s in his sec o a e mo e sensi i e o sus ainable buying beha io [
11
]. The owne o he
chosen mic o-en e p ise ies o lead he company wi h he p inciples o sus ainable de elopmen ,
mainly by using local bio- aw ma e ials, using pape packaging ins ead o plas ic. The owne plans
o o ganize baking cou ses o cus ome s as a new ac i i y o he mic o-en e p ise which p oduces
con ec iona y p oduc s. Wi hin hese cou ses, she in ends o p omo e he idea o he ecology o
sus ainabili y, especially in he a ea o using local esou ces, eco- iendly packaging, and o elimina e
semi- inished p oduc s. Baking cou ses also ha e a social o e lap as hey a e also a ge ed a he local
communi y, which will ha e a posi i e impac on s eng hening local people’s ela ionships. On he
basis o hese ac s he ollowing esea ch ques ion is o mula ed.
Wha a e he di e ences in pe cep ion o communica ion channels by cus ome s based on hei
age? Fuzzy easoning will be used o his pu pose.
Sus ainabili y 2019,11, 5422 4 o 15
2. Ma e ials and Me hods
2.1. Fuzzy Reasoning
A uzzy se heo y is based on he p emise ha he key elemen s o human hinking a e no
numbe s bu wo ds, see, e.g., [32–34].
In he case o la ge amoun s o inpu da a, he key ea u e o human hinking is he ex ac ion o
only expe iences ha is ele an o he p oblem, see, e.g., [
35
–
37
]. Fuzzy easoning is based on a e y
simila p inciple.
The e a e many di e en uzzy hinking algo i hms wi h di e en le els o sophis ica ion, see,
e.g., [
38
,
39
]. Howe e , many o hese algo i hms a e oo complex and di icul o unde s and o widely
use. MC expe s will be willing o accep uzzy easoning algo i hms only i hese algo i hms a e no
disp opo iona ely heo e ically demanding. The e o e, he ollowing p esen a ion o uzzy easoning
is based on an easy o unde s and algo i hm, o de ails see [33,40,41].
A e bal alue is a “ alue” ha is gi en by wo ds, e.g., e y low, low, medium, high, a ound 5
deg ees Celsius, e c. A e bal alue o a moni o ed a iable is ans o med in o a uzzy se by he
speci ica ion o a g ade o membe ship. Fo example, a e bal alue a ound 5 deg ees Celsius o
he a iable emp is ans o med in o a uzzy using he membe ship unc ion
µ
, see Figu e 1. The
membe ship unc ion exp esses whe he a alue belongs o a uzzy se ; o de ails see [
42
,
43
]. A ypical
uzzy se 5co he e bal alue a ound 5 deg ees Celsius o he a iable emp is
b< emp <c, (1)
whe e (see Figu e 1)
µ5C( emp); emp ∈[0,∞] (2)
is he g ade o membe ship o he nume ical alue o he a iable empe a u e o he uzzy se 5c.
The e a e wo uzzy in e als, namely, see Figu e 1:
a< emp <b,c< emp <d(3)
Sus ainabili y 2018, 10, x FOR PEER REVIEW 4 o 15
2. Ma e ials and Me hods
2.1. Fuzzy Reasoning
A uzzy se heo y is based on he p emise ha he key elemen s o human hinking a e no
numbe s bu wo ds, see, e.g., [32–34].
In he case o la ge amoun s o inpu da a, he key ea u e o human hinking is he ex ac ion o
only expe iences ha is ele an o he p oblem, see, e.g., [35–37]. Fuzzy easoning is based on a e y
simila p inciple.
The e a e many di e en uzzy hinking algo i hms wi h di e en le els o sophis ica ion, see,
e.g., [38,39]. Howe e , many o hese algo i hms a e oo complex and di icul o unde s and o
widely use. MC expe s will be willing o accep uzzy easoning algo i hms only i hese algo i hms
a e no disp opo iona ely heo e ically demanding. The e o e, he ollowing p esen a ion o uzzy
easoning is based on an easy o unde s and algo i hm, o de ails see [33,40,41].
A e bal alue is a “ alue” ha is gi en by wo ds, e.g., e y low, low, medium, high, a ound 5
deg ees Celsius, e c. A e bal alue o a moni o ed a iable is ans o med in o a uzzy se by he
speci ica ion o a g ade o membe ship. Fo example, a e bal alue a ound 5 deg ees Celsius o he
a iable emp is ans o med in o a uzzy using he membe ship unc ion 𝜇, see Figu e 1. The
membe ship unc ion exp esses whe he a alue belongs o a uzzy se ; o de ails see [42,43]. A
ypical uzzy se 5c o he e bal alue a ound 5 deg ees Celsius o he a iable emp is
b < emp < c, (1)
whe e (see Figu e 1)
Figu e 1. The membe ship unc ion.
μ5C( emp); emp ∈ [0,∞] (2)
is he g ade o membe ship o he nume ical alue o he a iable empe a u e o he uzzy se 5c.
The e a e wo uzzy in e als, namely, see Figu e 1:
a < emp < b, c < emp < d (3)
The e a e wo in e als o nume ical alues o he a iable emp which belong o he uzzy se
5c wi h he ze o g ade o membe ship:
[0,a],[d, ∞] (4)
A basic uzzy model is a se o m n-dimensional condi ional s a emen s; see, e.g., [33,44]:
i A1,1 and A1,2 and … and A1,n hen B1 o
i A2,1 and A2,2 and … and A2,n hen B2 o
⁝
i Am,1 and Am,2 and … and Am,n hen Bm,
(5)
whe e uzzy se s:
Figu e 1. The membe ship unc ion.
The e a e wo in e als o nume ical alues o he a iable emp which belong o he uzzy se 5c
wi h he ze o g ade o membe ship:
[0,a],[d,∞] (4)
Sus ainabili y 2019,11, 5422 5 o 15
A basic uzzy model is a se o m n-dimensional condi ional s a emen s; see, e.g., [33,44]:
i A1,1 and A1,2 and . . . and A1,n hen B1o
i A2,1 and A2,2 and . . . and A2,n hen B2o
.
.
.
i Am,1 and Am,2 and . . . and Am,n hen Bm,
(5)
whe e uzzy se s:
Ai,j,Bi o i=1, 2, . . . ,mand j=1, 2, . . . ,n(6)
a e one-dimensional uzzy se s and can be easily speci ied o /and modi ied using poin s a,b,c,do a
a iable Xj(see Figu e 1).
The model (5) ep esen s a unc ion
Bi= i(Aj), (7)
whe e A
j
is he j- h independen a iable and B
i
is he dependen a iable. Howe e , a dependen
a iable Biis no conside ed in his p oblem and pape :
0= i(Aj) (8)
The e o e, he model (5) is eplaced by he ollowing ma ix (m×n):
A1,1 . . . A1,n
A2,1 . . . A2,n
.
.
.
Am,1 . . . Am,n
(9)
2.2. Fuzzy Simila i y and Simila i y G aphs
A simila i y so wo n-dimensional uzzy se s V,Wis:
s(n,V,W)=min(max(min(µV(xj), µW(xj)))), (10)
whe e j=1, 2, . . . ,nand xjis a conc e e alue o a moni o ed a iable Xj.
The simila i y s
∈
[0;1], s=0 means he e is no simila i y o he uzzy se s VaW,s=1 means he e
is 100% simila i y, i.e., he uzzy se s Vand Wa e iden ical.
A simila i y g aph is he di ec ed g aph. This g aph consis s nodes and edges. All s a emen s
a e ep esen ed by nodes, see (5), (9), and all non-ze o simila i ies sa e ep esen ed by edges. The
de e mina ion o a uzzy simila i y and a simila i y g aph is shown in he ollowing illus a i e example.
In his example, le us conside an obse ed a iable Xand ou s a emen s; see Table 1. The
conside ed model (9) has n=1, m=4.
Table 1. S a emen s.
S a emen Va iable X
1 High (H)
2 Medium (M)
3 Medium (M)
4 Small (S)

Sus ainabili y 2019,11, 5422 6 o 15
Ve bal e alua ion (small, medium, high) is quan i ied using uzzy se s. The uzzy se s, see Table 2,
a e dic iona ies o he a iable Xin Table 1. Thei g aphical ep esen a ion is shown in Figu e 2.
Table 2. Dic iona ies o he a iable X.
X a b c d
Small (S) 0 0 10 20
Medium (M) 10 20 20 30
High (H) 20 30 50 90
Sus ainabili y 2018, 10, x FOR PEER REVIEW 6 o 15
Figu e 2. G ade o membe ship o X, see Table 2.
Le us conside a que y Q quan i ied using he uzzy se (11).
a b c d
25 30 30 35 (11)
The g aphical ep esen a ion o he que y (Q) is shown in Figu e 3.
Figu e 3. G ade o membe ship o Q, see (11).
The uzzy simila i ies o he que y Q (11) wi h he s a emen s, see Table 1 can be de e mined by
(10) o n = 1. A g aphical backg ound o he uzzy simila i y is shown in Figu es 4–6.
Figu e 4. The uzzy simila i y be ween Q and he i s s a emen .
Figu e 2. G ade o membe ship o X, see Table 2.
Le us conside a que y Qquan i ied using he uzzy se (11).
abcd
25 30 30 35 (11)
The g aphical ep esen a ion o he que y (Q) is shown in Figu e 3.
Sus ainabili y 2018, 10, x FOR PEER REVIEW 6 o 15
Figu e 2. G ade o membe ship o X, see Table 2.
Le us conside a que y Q quan i ied using he uzzy se (11).
a b c d
25 30 30 35 (11)
The g aphical ep esen a ion o he que y (Q) is shown in Figu e 3.
Figu e 3. G ade o membe ship o Q, see (11).
The uzzy simila i ies o he que y Q (11) wi h he s a emen s, see Table 1 can be de e mined by
(10) o n = 1. A g aphical backg ound o he uzzy simila i y is shown in Figu es 4–6.
Figu e 4. The uzzy simila i y be ween Q and he i s s a emen .
Figu e 3. G ade o membe ship o Q, see (11).
The uzzy simila i ies o he que y Q(11) wi h he s a emen s, see Table 1can be de e mined by
(10) o n=1. A g aphical backg ound o he uzzy simila i y is shown in Figu es 4–6.
Sus ainabili y 2018, 10, x FOR PEER REVIEW 6 o 15
Figu e 2. G ade o membe ship o X, see Table 2.
Le us conside a que y Q quan i ied using he uzzy se (11).
a b c d
25 30 30 35 (11)
The g aphical ep esen a ion o he que y (Q) is shown in Figu e 3.
Figu e 3. G ade o membe ship o Q, see (11).
The uzzy simila i ies o he que y Q (11) wi h he s a emen s, see Table 1 can be de e mined by
(10) o n = 1. A g aphical backg ound o he uzzy simila i y is shown in Figu es 4–6.
Figu e 4. The uzzy simila i y be ween Q and he i s s a emen .
Figu e 4. The uzzy simila i y be ween Qand he i s s a emen .
Sus ainabili y 2019,11, 5422 7 o 15
Sus ainabili y 2018, 10, x FOR PEER REVIEW 7 o 15
Figu e 5. The uzzy simila i y be ween Q and he second and hi d s a emen .
Figu e 6. The uzzy simila i y be ween Q and he ou h s a emen .
The nume ical exp ession o uzzy simila i ies om Figu es 4–6 is seen in Table 3.
Table 3. Fuzzy simila i ies.
S a emen X Fuzzy Simila i y (s), See (10)
1 H 1
2 M 0.33
3 M 0.33
4 H 0
The g aphical ep esen a ion o he esul om Table 3 is shown in Figu e 7.
Figu e 7. Simila i y g aph, see Table 1 and (11).
Table 3 and Figu e 7 show ha he i s s a emen ( he uzzy simila i y equals 1) comple ely sui s
he que y. Fo he second and hi d s a emen , he uzzy simila i y is small. The ou h s a emen does
no sui he que y because he uzzy simila i y is ze o.
In his example, only one c i e ion/ a iable was aken. I is e y easy o ex end his issue o
se e al a iables. Mo eo e , his app oach may no only be used o selec ion, bu also o
compa ison, e.g., inding ou dependence be ween a iables, as shown in he ollowing case s udy.
Figu e 5. The uzzy simila i y be ween Qand he second and hi d s a emen .
Sus ainabili y 2018, 10, x FOR PEER REVIEW 7 o 15
Figu e 5. The uzzy simila i y be ween Q and he second and hi d s a emen .
Figu e 6. The uzzy simila i y be ween Q and he ou h s a emen .
The nume ical exp ession o uzzy simila i ies om Figu es 4–6 is seen in Table 3.
Table 3. Fuzzy simila i ies.
S a emen X Fuzzy Simila i y (s), See (10)
1 H 1
2 M 0.33
3 M 0.33
4 H 0
The g aphical ep esen a ion o he esul om Table 3 is shown in Figu e 7.
Figu e 7. Simila i y g aph, see Table 1 and (11).
Table 3 and Figu e 7 show ha he i s s a emen ( he uzzy simila i y equals 1) comple ely sui s
he que y. Fo he second and hi d s a emen , he uzzy simila i y is small. The ou h s a emen does
no sui he que y because he uzzy simila i y is ze o.
In his example, only one c i e ion/ a iable was aken. I is e y easy o ex end his issue o
se e al a iables. Mo eo e , his app oach may no only be used o selec ion, bu also o
compa ison, e.g., inding ou dependence be ween a iables, as shown in he ollowing case s udy.
Figu e 6. The uzzy simila i y be ween Qand he ou h s a emen .
The nume ical exp ession o uzzy simila i ies om Figu es 4–6is seen in Table 3.
Table 3. Fuzzy simila i ies.
S a emen XFuzzy Simila i y (s), See (10)
1 H 1
2 M 0.33
3 M 0.33
4 H 0
The g aphical ep esen a ion o he esul om Table 3is shown in Figu e 7.
Sus ainabili y 2018, 10, x FOR PEER REVIEW 7 o 15
Figu e 5. The uzzy simila i y be ween Q and he second and hi d s a emen .
Figu e 6. The uzzy simila i y be ween Q and he ou h s a emen .
The nume ical exp ession o uzzy simila i ies om Figu es 4–6 is seen in Table 3.
Table 3. Fuzzy simila i ies.
S a emen X Fuzzy Simila i y (s), See (10)
1 H 1
2 M 0.33
3 M 0.33
4 H 0
The g aphical ep esen a ion o he esul om Table 3 is shown in Figu e 7.
Figu e 7. Simila i y g aph, see Table 1 and (11).
Table 3 and Figu e 7 show ha he i s s a emen ( he uzzy simila i y equals 1) comple ely sui s
he que y. Fo he second and hi d s a emen , he uzzy simila i y is small. The ou h s a emen does
no sui he que y because he uzzy simila i y is ze o.
In his example, only one c i e ion/ a iable was aken. I is e y easy o ex end his issue o
se e al a iables. Mo eo e , his app oach may no only be used o selec ion, bu also o
compa ison, e.g., inding ou dependence be ween a iables, as shown in he ollowing case s udy.
Figu e 7. Simila i y g aph, see Table 1and (11).
Table 3and Figu e 7show ha he i s s a emen ( he uzzy simila i y equals 1) comple ely sui s
he que y. Fo he second and hi d s a emen , he uzzy simila i y is small. The ou h s a emen does
no sui he que y because he uzzy simila i y is ze o.
In his example, only one c i e ion/ a iable was aken. I is e y easy o ex end his issue o se e al
a iables. Mo eo e , his app oach may no only be used o selec ion, bu also o compa ison, e.g.,
inding ou dependence be ween a iables, as shown in he ollowing case s udy.
Sus ainabili y 2019,11, 5422 8 o 15
3. Case S udy
The p oposed me hod is applied o cus ome s o a mic o-en e p ise which has h ee employees.
This company is engaged in he p oduc ion o cookies and cakes om o ganic ing edien s and also
o ganizes baking cou ses o he public. The p esen ed case s udy is based on da a se s o 272
esponden s in e iewed o esea ch o a diploma hesis [
45
]. Quo a selec ion echnique was used o
de e mine he ele an sample o esponden s. Each esponden e alua ed MC media. The e alua ion
is based on a scale 0–10. The scale desc ibes he media impo ance pe cei ed by each esponden . Ze o
means ha a esponden conside s he communica ion channel comple ely unimpo an . Ze o in his
case accen ua es he ac ha he gi en communica ion channel makes no use a all. On he con a y,
a alue o en means ha he gi en communica ion channel is i ally impo an o he esponden .
Because he da a se does no mee basic assump ions o pa ame ic es s and because i is ha d o
say which a iable is a dependen a iable and which a iables a e independen , classical s a is ical
me hods a e ejec ed. The e o e, esponden s a e so ed in o i e segmen s by age wi h a a ious
numbe o membe s, see Tables 4and 5.
Table 4. Responden s.
Segmen Age Numbe o Responden s
S1 <18 14
S2 18–28 252
S3 29–39 59
S4 40–50 33
S5 >51 14
Table 5. Communica ions media.
Va iable Media
V1 E-mail
V2 Social ne wo ks—Facebook and Ins ag am
V3 Web pages
V4 Newspape s
V5 Pos e s and lea le s
V6 Phone calls
V7 Tex messages
V8 Radio
Basic empi ical cha ac e is ics ( he mean, he a iance) o each a iable a e calcula ed o each
segmen . These cha ac e is ics a e used o ans o m he s anda d scale o uzzy se s, see Figu e 1. The
uzzy se s (12), see Figu e 8, a e dic iona ies o all a iables om Table 5.
abcd
Ve y low (VLO) 0 0 1 3
Low (LOW) 2 3 4 5
Medium (MED) 4 5 6 7
High (HIG) 6 7 8 9
Ve y high (VHI) 8 910 10
(12)
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Figu e 8. Fuzzy se s o each medium.
A se o i e uzzy s a emen s was c ea ed wi h applica ion o he dic iona y (12), see Table 6.
Table 6. Fuzzy s a emen s.
Segmen Media
V1 V2 V3 V4 V5 V6 V7 V8
S1 LOW MED LOW VLO LOW LOW MED LOW
S2 MED MED MED VLO LOW LOW LOW LOW
S3 MED MED MED VLO LOW VLO LOW VLO
S4 MED MED LOW VLO LOW LOW LOW VLO
S5 VHI MED HIG LOW LOW LOW HIG LOW
The in e als (12) a e esul s o a discussion wi h expe s. To check, hey a e subjec ed o a
sensi i i y analysis. The sensi i i y analysis has shown ha uzzi ica ion (12) is no sensi i e and
he e o e i has li le e ec on he simila i y g aphs below.
Th ee simila i y g aphs a e s udied. The i s o al g aph (GT) ocuses on all media channels, he
second g aph (G1) con ains classical media channels, and g aph G2 includes online media channels,
see Table 7.
Table 7. Fuzzy simila i y g aphs and a iables.
Fuzzy Simila i y G aph Based on Va iables, See Table 5:
GT—To al g aph all a iables
G1—Classical V4, V5, V6, V8
G2—Online V1, V2, V3, V7
Nodes ep esen indi idual age segmen s o esponden s. Edges show he exis ing simila i ies
in he pe cep ion o indi idual media by hese segmen s o esponden s. Table 8–Table 10 gi e uzzy
pai wise simila i ies o h ee g aphs using o mulas (10).
I can be seen om he GT g aph (see Figu e 9) ha no edge leads o node 5. I all a iables
(media) a e aken in o accoun , segmen S5 (age: >51) di e s signi ican ly om he emaining
segmen s o esponden s. Respec i ely, S5 pe cei es he impo ance o indi idual media di e en ly
om he es o he segmen s. The e a e edges be ween he o he nodes. The segmen s S1, S2, S3, and
S4 pe cei e he media simila ly. The g ade o hese simila i ies is shown in Table 8.
Figu e 8. Fuzzy se s o each medium.
A se o i e uzzy s a emen s was c ea ed wi h applica ion o he dic iona y (12), see Table 6.
Table 6. Fuzzy s a emen s.
Segmen Media
V1 V2 V3 V4 V5 V6 V7 V8
S1 LOW MED LOW VLO LOW LOW MED LOW
S2 MED MED MED VLO LOW LOW LOW LOW
S3 MED MED MED VLO LOW VLO LOW VLO
S4 MED MED LOW VLO LOW LOW LOW VLO
S5 VHI MED HIG LOW LOW LOW HIG LOW
The in e als (12) a e esul s o a discussion wi h expe s. To check, hey a e subjec ed o a
sensi i i y analysis. The sensi i i y analysis has shown ha uzzi ica ion (12) is no sensi i e and
he e o e i has li le e ec on he simila i y g aphs below.
Th ee simila i y g aphs a e s udied. The i s o al g aph (GT) ocuses on all media channels, he
second g aph (G1) con ains classical media channels, and g aph G2 includes online media channels,
see Table 7.
Table 7. Fuzzy simila i y g aphs and a iables.
Fuzzy Simila i y G aph Based on Va iables, See Table 5:
GT—To al g aph all a iables
G1—Classical V4, V5, V6, V8
G2—Online V1, V2, V3, V7
Nodes ep esen indi idual age segmen s o esponden s. Edges show he exis ing simila i ies in
he pe cep ion o indi idual media by hese segmen s o esponden s. Tables 8–10 gi e uzzy pai wise
simila i ies o h ee g aphs using o mulas (10).
Table 8. Fuzzy pai wise segmen simila i ies o GT.
S1 S2 S3 S4
S2 0.375
S3 0.265 0.321
S4 0.296 0.247 0.298
S5 0 0 0 0