Mul idisciplina y Jou nal o Educa ion, h p://dx.doi.o g/10.4995/muse.2016.6679
Social and Technological Sciences EISSN: 2341-2593
Llopis-Albe and Palacios-Ma qués (2016)
h p://polipape s.up .es/index.php/MUSE/ Mul . J. Edu. Soc & Tec. Sci. Vol. 3 Nº 2 (2016): 1-14 | 1
Applied Ma hema ical P oblems in Enginee ing
Llopis-Albe , Ca losa; Palacios-Ma ques, Danielb
a Depa amen o de Ingenie ía Mecánica y de Ma e iales, Uni e si a Poli ècnica de
València, Camí de Ve a s/n, Spain, 46022, email: [email p o ec ed].es
b Depa amen o de O ganización de Emp esas, Uni e si a Poli ècnica de València, Camí
de Ve a s/n, Spain, 46022, email: [email p o ec ed].es
Recei ed: 2016-04-02; Accep ed: 2016-07-21
Abs ac
The e is a close ela ionship be ween enginee ing and ma hema ics, which has led o he
de elopmen o new echniques in ecen yea s. Likewise he de elopmen s in echnology
and compu e s ha e led o new ways o eaching ma hema ics o enginee ing s uden s
and he use o mode n echniques and me hods. This esea ch aims o p o ide insigh on
how o deal wi h ma hema ical p oblems o enginee ing s uden s. This is pe o med by
means o a uzzy se /Quali a i e Compa a i e Analysis applied o con lic esolu ion o
Public Pa icipa ion P ojec s in suppo o he EU Wa e F amewo k Di ec i e.
Keywo ds: Fuzzy se s; Quali a i e Compa a i e Analysis; Public pa icipa ion p ojec ;
con lic esolu ion; decision-making
Mul idisciplina y Jou nal o Educa ion, h p://dx.doi.o g/10.4995/muse.2016.6679
Social and Technological Sciences EISSN: 2341-2593
Llopis-Albe and Palacios-Ma qués (2016)
h p://polipape s.up .es/index.php/MUSE/ Mul . J. Edu. Soc & Tec. Sci. Vol. 3 Nº 2 (2016): 1-14 | 2
1. In oduc ion
In eg a ed wa e esou ces managemen en ails echnical, scien i ic, poli ical, legisla i e,
and o ganiza ional aspec s o wa e sys em. Wa e esou ces managemen su e s om
con inual and g owing p essu es, which de i e om easons such as human ac i i y,
popula ion g ow h, li ing s anda ds inc ease, land-use and clima e changes, g owing
compe i ion o wa e , and pollu ion om indus ial, municipal, and ag icul u al sou ces.
The EU Wa e F amewo k Di ec i e (WFD) es ablishes a amewo k o he p o ec ion o
all wa e bodies by p omo ing sus ainable wa e use based on long- e m p o ec ion o
wa e esou ces, and enac s o achie e good quali a i e and quan i a i e s a us o all wa e
bodies by 2021. The EU WFD also s a es ha all membe s shall encou age he ac i e
in ol emen o s akeholde s in he implemen a ion o he di ec i e and de elopmen o
wa e shed managemen plans (EC, 2000).
A way o deal wi h s akeholde s' con lic esolu ion p oblems is by using a
con igu a ional compa a i e me hod. This is pe o med by means o a uzzy
se /quali a i e compa a i e analysis, sQCA (Ragin 2008), which o e comes some o he
limi a ions o s ic ly quali a i e o quan i a i e s udies. This echnique has been widely
used in he li e a u e o deal wi h quali a i e compa a i e analysis (e.g., Be begal-
Mi aben and Llopis-Albe , 2015).
Mul idisciplina y Jou nal o Educa ion, h p://dx.doi.o g/10.4995/muse.2016.6679
Social and Technological Sciences EISSN: 2341-2593
Llopis-Albe and Palacios-Ma qués (2016)
h p://polipape s.up .es/index.php/MUSE/ Mul . J. Edu. Soc & Tec. Sci. Vol. 3 Nº 2 (2016): 1-14 | 3
2. Public pa icipa ion p ojec s in he Wa e F amewo k Di ec i e
S akeholde s’ sa is ac ion depends on di e se ac o s, such as hei he e ogeneous
in e es s, educa ional backg ounds, employmen , knowledges, esou ces, expe iences,
places o p o enance, le els o pa icipa ion, e c.
S akeholde s a e selec ed by conside ing all g oups who in some way will be
a ec ed by he implemen a ion o measu es, which includes hose who ha e in e es s,
claims o igh s (e hical o legal) o he bene i s o he measu es unde aken, a e likely o
bea i s cos s o ad e se impac s wha e e i s o e all wo h.
The s akeholde s in ol ed in he wa e decision-making o a PPP ange om
go e nmen s, wa e agencies au ho i ies, en i onmen al o ganiza ions, i iga ion use
communi ies, p i a e i ms, uni e si ies and esea ch agencies, poli ical pa ies, labo
unions, expe s, ad iso s, mass-media, ci izens o in e na ional o ganiza ions.
Table 1 p esen s he ac o s o condi ions ha leads o he s akeholde s'
sa is ac ion in he decision-making p ocess o a PPP o a wa e shed managemen , which
co e en i onmen al objec i es pu sued, he ac ual capaci y o e icien ly ca ying ou
hose objec i es, he socio-economic de elopmen o he egion, he le el and
mechanisms o s akeholde s’ pa icipa ion in he PPP, and he al e na i e policies and
measu es ha should be implemen ed in he hyd ological plans.
Mul idisciplina y Jou nal o Educa ion, h p://dx.doi.o g/10.4995/muse.2016.6679
Social and Technological Sciences EISSN: 2341-2593
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h p://polipape s.up .es/index.php/MUSE/ Mul . J. Edu. Soc & Tec. Sci. Vol. 3 Nº 2 (2016): 1-14 | 4
3. Me hodology
This s udy uses ac o s belonging o di e en wa e sheds and coun ies o assess
s akeholde s' p e e ences o deg ees o accep ance ega ding he di e se ac o s o
condi ions ha lead o hei sa is ac ion. Then his wo k deals wi h di e en wa e sheds
eali ies and na ional legisla ions, and p esen s a gene al o e iew o he Eu opean
s akeholde s' sa is ac ion in he decision-making p ocess o PPP o wa e esou ces
managemen . The di e si y o wa e sheds in e ms o he managemen s a egies hey
apply and hei s akeholde engagemen makes his wo k e en mo e sui able o s udying
how combina ions o condi ions in he decision-making p ocess can esul in s akeholde
sa is ac ion.
E en ually, we will iden i y wha combina ions o he conside ed condi ions a e
necessa y o su icien o achie e he s akeholde s’ sa is ac ion in PPP.
The s udy is based on di e en Eu opean epo s (EU, 2003; OECD 2015; OECD
2014), esea ch pape s dealing wi h hese issues (e.g., Ve weij e al., 2013; S ini asan e
al., 2012), online epo s om webpages o Eu opean wa e agencies au ho i ies, mass-
media in o ma ion, mee ings, pe sonal in e iews, su eys, and expe judgmen . Da a
ha e been collec ed du ing long- ime pe iod o yea s, so ha a longi udinal iew on he
cou se o he s akeholde s’ p e e ences has been ob ained.
The e o e, we a e in ended o iden i y which combina ions o ac o s a e su icien
o explain he ou come by means o a Quali a i e Compa a i e Analysis (QCA) o
Mul idisciplina y Jou nal o Educa ion, h p://dx.doi.o g/10.4995/muse.2016.6679
Social and Technological Sciences EISSN: 2341-2593
Llopis-Albe and Palacios-Ma qués (2016)
h p://polipape s.up .es/index.php/MUSE/ Mul . J. Edu. Soc & Tec. Sci. Vol. 3 Nº 2 (2016): 1-14 | 5
o e come some o he limi a ions o s ic ly quali a i e o quan i a i e me hods, and o
mo e sys ema ically analyze conjunc u al causal pa e ns
A con igu a ion is a combina ion o ac o s -which is named as condi ions in QCA
e minology- ha is minimally necessa y and/o su icien o ob aining a speci ic
ou come. These con igu a ions consis o condi ions o ac o s ha can be posi i e,
nega i e, o absen . Condi ions a e su icien and necessa y only in combina ion wi h
o he condi ions o which a e only one al e na i e among o he s ha only apply o some
cases bu no o o he s.
Con a y o QCA, which can only analyze bina y a iables, sQCA o e comes
his limi a ion by inco po a ing he possibili y o examine a ying le els o membe ship
o cases o a pa icula se . Fi s calib a ion p ocedu e o ou comes and an eceden
condi ions in o uzzy se s is equi ed, which ca ego izes meaning ul g oupings o cases
(Ragin, 2008). Fuzzy alues ange om ull membe ship (1) o ull non-membe ship (0).
A c osso e poin (0.5) ep esen s nei he in no ou o he se . Second he u h able is
cons uc ed, which is a ma ix space wi h 2k ows, whe e k is he numbe o an eceden
condi ions and ep esen s all he logically possible combina ions o causal condi ions and
so s he cases acco ding o hese logically possible combina ions. Each column
ep esen s a condi ion, and each empi ical case co esponds o a con igu a ion depending
on which an eceden condi ions he case mee s.
Thi d a educ ion o he he numbe o ows in he u h able is ca ied ou . We
ha e used a e sion o he Quine–McCluskey algo i hm (Quine, 1952), al hough se e al

Mul idisciplina y Jou nal o Educa ion, h p://dx.doi.o g/10.4995/muse.2016.6679
Social and Technological Sciences EISSN: 2341-2593
Llopis-Albe and Palacios-Ma qués (2016)
h p://polipape s.up .es/index.php/MUSE/ Mul . J. Edu. Soc & Tec. Sci. Vol. 3 Nº 2 (2016): 1-14 | 6
algo i hms can also minimize a u h able. This allows o ob ain a se o combina ions o
causal condi ions by using Boolean algeb a, whe e each combina ion is minimally
su icien o p oduce he ou come. The ow educ ion depends on wo c i e ia: a) he
co e age, which indica es he empi ical ele ance o a solu ion, ha is., i measu es he
p opo ion o membe ships in he ou come ha is explained by he comple e solu ion; b)
he consis ency, which quan i ies he deg ee o which ins ances sha ing simila condi ions
display he same ou come. On he o he hand, he aw co e age indica es which sha e o
he ou come is explained by a ce ain al e na i e con igu a ion, while he unique co e age
indica es which sha e o he ou come is exclusi ely explained by a ce ain al e na i e
pa h. T u h ables a e analyzed by he s/QCA so wa e (Ragin 2008).
4. Resul s and discussion
The main aim is o de e mine which pa icula combina ions o hese condi ions
lead o s akeholde s’ sa is ac ion by examining which combina ions o he condi ions a e
necessa y o su icien o achie e i . The deg ee o accep ance o p e e ence ega ding he
di e en ac o s is analyzed by means o using a con inuous uzzy se . I is anged om 0
o 1, i.e., om low deg ee o accep ance o ag eemen o high deg ee o accep ance o
ag eemen . We ha e conside ed 7 ac o s, which comp ises se e al sub- ac o s as shown
in Table 1. Fo each s akeholde and ac o he agg ega e inal sco e is he a i hme ic
a e age o he uzzy sco es o each sub- ac o . The calib a ion p ocess has allowed
Mul idisciplina y Jou nal o Educa ion, h p://dx.doi.o g/10.4995/muse.2016.6679
Social and Technological Sciences EISSN: 2341-2593
Llopis-Albe and Palacios-Ma qués (2016)
h p://polipape s.up .es/index.php/MUSE/ Mul . J. Edu. Soc & Tec. Sci. Vol. 3 Nº 2 (2016): 1-14 | 7
ans o ming he di e si y o ac o s used in his wo k in o uzzy a iables, so ha hey
ma ch o con o m o ex e nal s anda ds.
Fuzzy sco es calib a ion is based on di e en epo s, esea ch pape s, online
epo s om webpages o Eu opean wa e agencies au ho i ies, mass-media in o ma ion,
mee ings, pe sonal in e iews, su eys, and expe judgmen .
The u h able is ob ained a e se e al ounds o analyses and because he e a e 7
ac o s he dimensions a e (27) ows and 7 columns, which en ails 128 possible
con igu a ions. The ma ix is checked o necessa y condi ions o he ou come and also
o he nega ion o he ac o s indica ed by he ilde (~) sign.
A condi ion has been conside ed as necessa y when i s consis ency sco e exceeds
he h eshold alue o 0.9. Resul s show ha he e a e only 2 necessa y condi ions, which
a e he en i onmen al objec i es and he socio-economic de elopmen o he egion.
A e he minimiza ion p ocess using he co e age and consis ency alues, he
combina ions o causal condi ions a e ob ained, hus p o iding he combina ions o
ac o s ha a e minimally su icien o p oduce he ou come (see Table 2). In his able
black ci cles () indica e he p esence o a condi ion, whi e ci cles (⭕) deno e i s
absence, and blank cells ep esen ambiguous condi ions. Resul s also sugges ha : a) no
uni ying causal pa h explains he ou come; b) all con igu a ions p esen accep able
consis ency indices (<0.80); c) high aw co e age alues a e ob ained; d) apa om he
necessa y condi ions, he p esence o policies (bo h con ol measu es and echnical
measu es) appea in mos o he con igu a ions, which shows ha he ou come s ongly
Mul idisciplina y Jou nal o Educa ion, h p://dx.doi.o g/10.4995/muse.2016.6679
Social and Technological Sciences EISSN: 2341-2593
Llopis-Albe and Palacios-Ma qués (2016)
h p://polipape s.up .es/index.php/MUSE/ Mul . J. Edu. Soc & Tec. Sci. Vol. 3 Nº 2 (2016): 1-14 | 8
depends on he ypes o policies unde aken; e) he g ea e unde s anding o he p oblem
( o ins ance, using a ma hema ical echniques like ha he p esen ed o models aking
in o accoun he key unde lying biophysical p ocesses, e.g., Llopis-Albe e al., 2014;
2015) he be e managemen p ac ices and consensus will be achie ed among he
di e en ac o s; ) be e esul s a e ob ained i ac o s a e in ol ed a ea ly s ages, on
accoun o hey a e less likely o obs uc decisions and mo e likely o suppo hem; g)
good ou comes in a PPP a e also ela ed o clea goals, s ong con ol o ime,
o ganiza ion and in o ma ion.
Table 1. Va iables o ac o s conside ed in he uzzy se /Quali a i e Compa a i e Analysis applied
o PPP in suppo o he EU Wa e F amewo k Di ec i e.
En i onmen al in e es s
–
Objec i es pu sued
(1)
Good quan i a i e s a us o wa e bodies, bo h su ace and
g oundwa e
Good chemical s a us o wa e bodies
Good s a us o wa e dependen ecosys ems
Low en i onmen al impac s o u u e land-use land-co e
changes and clima e changes
Socio-economic
in e es s -
Objec i es
pu sued
(2)- (3)
Ope a i e
e iciency
(2)
Sho ealiza ion ime
Low implemen a ion cos s
Low main enance, managemen and in as uc u es
cons uc ion cos s
Socio-economic
de elopmen o he
egion (ag icul u e,
indus y and
ou ism)
(3)
Maximize wa e o ag icul u al and indus ial use
Maximize wa e o ou ism and u ban use
C ea e employmen , social equi y
Inc ease u u e wa e demands
Le el o
s akeholde s’
engagemen in he
wa e decision-
making p ocess
(4)
Pe cei ed obs acles
o he in eg a ion o
s akeholde
engagemen in
wa e policies and
p ac ices
(4.1)
Lack o poli ical will and he shi o powe
Lack o knowledge
Weak legal amewo ks
Scan pa icipa ion le el
Pe cei ed obs acles
hinde ing he
Lack o cla i y on he use o engagemen p ocesses
Lack o unding
Mul idisciplina y Jou nal o Educa ion, h p://dx.doi.o g/10.4995/muse.2016.6679
Social and Technological Sciences EISSN: 2341-2593
Llopis-Albe and Palacios-Ma qués (2016)
h p://polipape s.up .es/index.php/MUSE/ Mul . J. Edu. Soc & Tec. Sci. Vol. 3 Nº 2 (2016): 1-14 | 9
e ec i e
implemen a ion o
engagemen
p ocesses
(4.2)
Lack o quali y and accessibili y o in o ma ion
In ensi y and numbe o con lic s
Too much o oo ew ac o s
P e e ed mechanisms used o
s akeholde engagemen
(5)
Mee ings
Wo kshops / con e ences
Expe panels
Web-based communica ion echnologies
Wa e associa ions
Consul a ions in egula o y p ocesses
Su eys / polls
Ri e basin o ganiza ions
O he s
P e e ed measu es
and policies o
sus ainable wa e
esou ces
managemen
(6)- (7)
Con ol
mechanisms
(6)
Con ol o educ ion o wa e demand by economic
ins umen s
Con ol o educ ion o pollu an s by economic ins umen s
Se up o use ’s communi ies as a con ol mechanism
Con ol o wa e esou ces by applica ion o sa elli e emo e
sensing
Mo e in e en ion o he EU Common Ag icul u al Policy
Inc ease o wa e con ol and sanc ions by wa e agencies
Al e na i e
echnical ac ions
(7)
E icien conjunc i e use o su ace wa e and g oundwa e
Use o ex e nal wa e esou ces by means o ans e s
Use o desalina ion plan s
Cons uc ion o new in as uc u es
Es ablishmen o p o ec ed a eas
G ea e unding o wa e esou ces esea ch
O he s
Ou come
S akeholde s'
sa is ac ion
Ou come: s akeholde s’ sa is ac ion