University Mohammed V-Agdal, Mohammadia School of Engineers, Rabat, Morocco

Moder Applied Sciece; Vol. 9, No. 2; 205 ISSN 93-844 E-ISSN 93-852 Published by Caadia Ceter of Sciece ad Educatio Optimisig the Improvemet of a Global Idustrial Performace Based o AHP ad Sugeo Itegral Aggregatio: Case Study i Morocca Automotive Suppliers Mohamed Tarek CHAHID,4, Jamila EL ALAMI 2, Aziz SOULHI 3 & Nourdie EL ALAMI Uiversity Mohammed V-Agdal, Mohammadia School of Egieers, Rabat, Morocco 2 Uiversity Mohammed V-Agdal, Superior School of Techology Sale, Sale, Morocco 3 Natioal Superior School of Mies of Rabat, Rabat, Morocco 4 Morocca Istitute for Traiig i Automotive Idustry (IFMIAC), Casablaca, Morocco Correspodece: Mohamed Tarek CHAHID, Istitut de Formatio aux Métiers de l Idustrie Automobile de Casablaca, Voie EC 03, Nouvelle Zoe Idustrielle, Ahl Loughlam, Sidi Beroussi, BP 52, Casablaca, Morocco. Tel: 22-529-028-865. E-mail: t.chahid@giac.org Received: September 22, 204 Accepted: October 4, 204 Olie Published: December 0, 204 doi:0.5539/mas.v92p96 URL: http://dx.doi.org/0.5539/mas.v92p96 Abstract The performace measuremet systems (PMS) i the idustry are defied i terms of various measures to be combied for global performace. The proposed approach treats with a qualitative approach for multicriteria decisio with the improvemet strategy of a overall idustrial performace. The approach is based o a AHP ad Sugeo itegral aggregatio operator, permits to express the global performace, accordig to the fuzzy set theory of appropriate Key Performace Idicators (KPI), the oliearity of this model, makes data ambiguous i the process of multicriteria decisio-makig. Hece, this mauscript is a cotributio to the selectio of the strategy of the improvemet of the overall performace. The approach applies to the Morocca Automotive Suppliers to evaluate three strategies alteratives by usig a fuzzy Sugeo Itegral techique to deal with the complex iterrelatioships aspects betwee KPI. Keywords: performace measuremet systems, sugeo itegral aggregatio, cost, global performace, Improvemet strategy. Itroductio I the complex real world, fuzzy logic is usually used to treat with the problems of ambiguity, particularly those associated with subjective sesitivity. Covetioal aalytical approaches are isufficiet for dealig with such complex situatios, because, the criterios are geerally itercoected (Berrah ad Clivelle, 2007). Therefore, this work adopted the fuzzy logic methodology to deal with the imprecisio of huma perceptio. The fuzzy itegral is more appropriate whe the criteria are coected. Based o the ituitio of the maagers, the strategies of developmet i corporatios are fudametally complex aalytical processes. Several strategies have to be assessed cosiderig a vast body of data that are ofte hard to quatify (Berrah et al., 2008). Hece, this paper implemets Sugeo fuzzy itegral to estimate every alterative strategy i a complex eviromet with multicriteria dimesios. The fuzzy itegral was used to assess the performace of several strategies to reach the highest overall performace. It permits to have a better comprehesio of this more complex (i.e. Noliear) performace model. To date, there have bee o researches which usig λ-fuzzy measures ad Sugeo itegrals to select a best improvemet strategy i MCDM (Berrah, 203). This work is focused o decisio-support tools that could help maagers to better pla performaces improvemets. to the compay strategy to reach a goal while miimizig costs. This work is related to the cocept of efficiet improvemet; the cotributio of criterio Price availability to the overall performace improvemet has bee added to KPI already idetified i the Morocca automotive sector. 96

More precisely, we focused o the performace aggregatio problem. Also, we give a review of the fuzzy MCDM, with the oadditive fuzzy itegral. The, a case study is illustrated to show the effectiveess of the proposed model i the cotext of the Morocca automotive suppliers. Ad last, we preset a discussio of the results ad their implicatio. Fially, the cocludig observatios are illustrated.. Aggregatio of Performace Measuremet Expressios The performace of the maufacturig system is determied by the cofiguratio of equipmets, mapower, data flows, process ad techology, this cofiguratio give maufacturers competitive advatage (Bititci et al., 200). So the compay s performace is determied by its ability to achieve the objectives set by the busiess strategy (Michalska, 2005). The mai goal of PMS is to trasform the data measuremet ito iformatio to assess the effectiveess ad efficiecy of actio. It is i fact the establishmet of objectives, collect, aalysis ad iterpretatio of performace measures. O the other had, The system should fuctio as a thermostat, i a way that the process aim to evaluate the iequality betwee the actual result ad the target, to idetify those critical iequalities, to appreciate the roots of dysfuctios i order to itroduce corrective ad prevetive actios (Melyk et al., 204). I this sese, so-called performace measuremet systems (PMS s) are the istrumets to support decisio-makig (Kueg ad Krah, 999). I other word, a PMS ca be see as a multicriteria tool, based o performace expressios (Suwigjo et al., 2000). The mai difficulty i the desig of a performace measuremet system cocers the determiatio of expressios of performace that are useful for decisio-makig. I fact, the distictio should be made betwee the global objectives of the busiess; which are broke dow alog orgaizatioal levels (Ducq et al., 200). To make a decisio, all expressios of performace must be treated to compare differet situatios that occur i the idustrial cotext. Therefore, two types of performace expressios are ivolved i a PMS: elemetary expressios that idetify degrees reached differet objectives, ad the aggregate expressios that are the sythesis of elemetary performace expressios i the overall objectives. Also, aggregatio expressios defie the priorities i the strategy ad give the choice of the scearios based o their expressios of basic performace (Clivelle et al., 2006). The performace aggregatio is usually defied as the result step of the objective break-dow. The aggregatio treats with the arragemet of all the performace expressios cocered. Two kids of approach are kow, the moocriterio PMS ad the multi-criteria PMS. I the moocriterio PMS, the clause to the aggregatio is that all the performace expressios are formulated i a uiversal referece, such as delay, cost, quality (Azzoe et al., 99). So, the global performace is the result of the sum of elemetary expressio (cost, delay ). This aggregatio model based o moo-criterio PMS approach is o more adapted as a istrumet of decisio makig, i the curret idustrial cotext. Cosequetly, it s ecessary to express performace i multicriteria form (Neely, 999). The weighted arithmetic mea (WAM) operator aggregated the ivolved elemetary performaces to match the global performace. These weights measure the hierarchical liks of the elemetary expressios (Ducq et al., 200)..2 Fuzzy Measuremet The fuzzy sets basis is the fact that the buildig blocks of huma aalysis are ot umbers but liguistic markers; i that way, fuzzy logic follows this cocept ad utilized estimated iformatio to get exact resolutios (Takagi ad Sugeo, 985). These data are formulated i umerical ad/or liguistic values. So, performace formulatios are exact or iexact, sure or doubtful (Berrah et al., 2000). All measuremets are related to a vagueess. The ambiguity of the measuremet reveals the isufficiecy of precise kowledge, ad the fuzzy measuremets become a syergic method of processig measuremets (Rezik ad Dabke, 2004). Fuzzy Multicriteria decisio makig has bee commoly utilized to resolve decisio makig aspects cocerig multicriteria assessmet ad the choice of optios. The fuzzy cocepts have the followig features: ) their structures capture the depedecy betwee iputs ad outputs of a system; 2) the fuzzy liguistic sets give ambiguities; 3) they model oliear system; 4) the sigular ad liguistic outputs are created; 5) they are isesible to radom oise (Wag, ad Che, 204). 97

The AHP is the mai utilized tool by researchers ad maagers i multi criteria decisio makig. The fields of AHP s use are plaig, choosig best scearios, resource maagemet (Vaidya ad Kumar, 2006). AHP ca mix differet kids of data i multilevel decisio cofiguratio to get a full visualizatio of the maufacturig orgaizatio (Heradez-Matias et al., 2008). I scholarly literature, over 2000 AHPs applicatios were couted; they are used whe resolutios eed quatitative ad qualitative aspects (Subramaia & Ramaatha, 202)..3 Fuzzy Itegral The relatioship betwee criteria affect positively or egatively assessmets of the decisio to accept or reject a project. This reality caot be modeled with a traditioal best compromise strategy. Aggregatio based o fuzzy itegrals articulate a multiplicity of decisio maker behaviors (Buyukozka & Rua, 200). I classic multiple criteria assessmet methods, each criterio must ot be depedet of the others. So, the relatios ad mutual effects i a idustrial eviromet caot be treated with the classic additive measures (Berrah et al., 2004). The applicatio of fuzzy itegral as a aggregatio operator i Multi-Criteria Decisio Makig was offered by Grabisch (Grabisch, 995). The otio of the fuzzy itegral, itroduced by Sugeo (Sugeo & Takahiro, 993), ca be used to multi-criteria evaluatio. The distictive quality of a fuzzy itegral is the ability to represet iteractios betwee criterio, ragig egative iteractio to positive iteractio, which surmouts the iadequacy of modelig reliat factors as self-regulatig sets (Grabisch, 995). I additio, i this cotext, the fuzzy itegral family geeralizes the WAM (Weighted Arithmetic Mea) operator by quatifyig iteractios betwee factors (Grabisch, 995). I traditioal itegrals, we have siged the measure, but i fuzzy itegrals we have fuzzy measure, the divergece betwee them is o-additively, i fuzzy itegrals we have additive ad o additive but i classic itegral we have additive oly. Thus, the structured cofiguratio assessmet of huma subjective DM fuzzy itegrals (Jeg, 20). It ca be said that the Choquet itegral is suitable for cardial aggregatio, where the umber has real meaig, while the Sugeo itegral is more appropriated for ordial aggregatio, where oly rak make sese (Sugeo ad Takahiro, 993)..4 The Sugeo Itegral The mai reaso for the choice of λ-fuzzy measure ((λ is also called the degree of iteractio) is that fuzzy measures for subsets of iformatio sources is easy to calculate ad the umber of fuzzy measures to be kow is reduced from 2 2 ito due to the λ-rule (Sugeo ad Takahiro, 993). i Let a fiite set X = { x, x2,, x} be a set of iformatio sources ad a fuzzy desity g = g( { x }) describe the degree of importace of each source xi. Let the set of X to be 2X. The a λ-fuzzy measure is a real-valued oadditive set fuctio g: 2 X (0,). Satisfyig the followig properties: g( ) = 0; g( X ) = () g ( A) g( B) ifa B X (2) A, B XadA B = g( A B) = g( A) + g( B) +λ g( A) g( B) For λ (, ) (3) The parameter λ i Equatio (3) ca be determied by solvig a polyomial equatio (4). The equatio is derived by usig the secod boudedess property i equatio () ad the rule λ-rule i equatio (3). i (4) λ+= ( +λg ) Let a evaluatio fuctio f: [ 0,] i = X be sorted i ascedig order such that f( x() ) f( x(2) )... f( x( ) ). For partial iformatio source x i, sugeo fuzzy measure for a subset, ca be recursively characterized by the equatio (5). Here, f ( x () i ) deotes the i-th smallest fuctio: () i () i g( A() i ) = g + g( A( i+ ) ) +λ g + g( A( i+ ) ) with g( A ( i + ) ) = 0 (5) 98

Sugeo itegral ca be viewed as a aggregatio operatio process betwee evaluatio fuctios ad fuzzy measures represetig the importace degrees of partial iformatio. Discrete Sugeo itegral (SI) with respect to Sugeo fuzzy measure g (A (I)) over X is formulated by: Max i= { () i () i } f( x) dgλ = Mi f( x, g( A ) (6) Where f x() f x(2) f x( ) ( ) ( )... ( ). As a WAM approach uses additive probability measures as weightig factors, the WAM approach does ot deal with the iteractio amog the criteria. O the cotrary, the SI approach based o λ-fuzzy measures hadles various grades of iteractio amog the criteria (Sugeo ad Takahiro, 993). It is foud that the aggregatio method selected i a modelig stage had a effect o both of rakig ad overall score. Furthermore, this Sugeo itegral approach ca provide more easily iterpretable iformatio tha the classical WAM does. Thus, it suggests that the proposed approach is oe of beeficial tools to aggregate two types of evidece. Also, a faster processig is realized by the Sugeo Itegral (Wag, ad Che, 204). 2. Method 2. Cotext of the Applicatio Maufacturig performace measuremet i the automotive idustry is importat i emergig coutries, especially i Morocco, which is cosidered as the best delivery platform for the Europea market with over 20 equipmet maufacturers, producig ear the amout of 2 500 millio, ad employig 60 000 employees resultig i the part of exported productio value at over 90 % (AMICA, 202). To date, there are o a performace measuremet study or model developed i morocco (AMICA, 202), so we propose a systematic scorig method for all Key Performace Idicators (KPI) i order to establish a performace measuremet model that reflects the mai characteristics of the Morocca automotive suppliers. The difficulty to be solved is to idetify the smallest costly strategy of the elemetary performaces to achieve a expected overall performace. The propositios of this mauscript iitiated from the maufacturers demad for a assistace to better uderstad the factors of success of Morocca automotive suppliers ad to moitor strategic actio plas. 2.2 Research Desig To reflect the multidimesioal aspect of performace, the use of questioaire was utilized to idetify improvemet areas. The questioaire was admiistrated durig 202 to 28 Morocca automotive suppliers from differet atioalities (USA, Japa, Germay, Spai, Frace ) that are employig 25.000 employees. A total of 24 resposes was received 7 of which were usable, yieldig the respose rate of 6%. The o respose bias is a result of the cofidetiality of these KPIs. The proposed method cosists of the AHP ad Sugeo itegral. The evaluatio procedure of the strategy improvemet project. The first step is to idetify the multiple criteria that are cosidered i the decisio-makig process for the DMs to make a objective decisio. The survey was used to defie the KPI affectio the global performace for the Morocca Automotive suppiers, the, we itegrate the Price Availability criterio i the global performace formula to take accout to cost costrait. The weights ca be estimated by the AHP. Fially, we coducted two algorithms i order to compare the efficiecy of each oe. The first oe was the liear model that quatifies the overall performace by calculatig a weighted mea of all performace expressios coupled with the differet diverse criteria that are traslated ito a commo referece. Cosequetly, the three strategies of improvemet (Quality security, Huma resources, Machie Maagemet) were raked. The applicatio of the secod algorithm (the Sugeo itegral) was performed to aggregate the elemetary performace expressio, to achieve the rakig of those strategies. The Sugeo itegral was performed i three steps: the costructio of Objectives, λ-fuzzy measure calculatio ad the results of Sugeo itegral. 99

2.3 Liear Model of the Morocca Automotive Suppliers 2.3. Quatificatio of Elemetary Performace Expressio We have idetified 6 KPI: Customer Complait (Cc), Scrap Rate (Qs), Machie Availability (Ma), Abseteeism (Ab), Number of Occupatioal Ijuries (Oi) ad Traiig Days per Perso (Tdb) as Key Performace Factors of Morocca automotive sector (Chahid et al., 204). The, we add Price Availability (Pa) as cost parameter i the process of decisio makig. Hece, they are used i the calculatio of the overall performace. I fact, each KPI are coupled with the appropriate weight (r, r 2, r 3, r 4, r 5, r 6, r 7 respectively). This associatio leads us to adopt the AHP method that allows KPIs to be compared i pairs to defie their relative importace through expert judgmet. The each KPI is assiged a absolute importace (weight) based o previous respective importace o a scale ratio, with the costrait that these weights sum up to. The AHP method is curretly the most commo method used i the idustrial applicatio to aggregate performace expressios. The outrakig method compares the differet criteria i five levels of importace to global satisfactio: equal, low, critical, prove ad absolute respectively quatified at, 3, 5, 7 ad 9. Itermediate values betwee two levels are accepted (Clivelle, 2004). The experts assig a itesity umber that represets the true preferece of each reaso with respect to other reasos. The itesity of factor i over factor j is equal to a ij, ad the itesity importace of factor j over i is equal to / a ij. If we have factors to compare, we develop a * matrix A to represet the importace of these factors: a a =Α (7) a a Where is the order of the matrix To determie the weight for each KPI, iterviews of experts (Geeral Maagers, Leaders of the Morocca Associatio of Automotive idustry) i the Morocca automotive idustry were performed usig pairwise comparisos that were give 5 pairwise comparisos as show i table. Table. Pairwise compariso matrix Cc Qs Ma Ab Oi Tdb Pa Cc /4 /7 5 6 /5 /5 Qs 4 /4 6 7 /2 /4 Ma 7 4 8 9 3 2 Ab /5 /6 /8 5 /7 /6 Oi /6 /7 /9 /5 /8 /7 Tdb 5 2 /3 7 8 3 Pa 5 4 /2 6 7 /3 SUM 22,37,56 2,46 33,20 43,00 5,30 6,76 Table 2 represets the matrix A as the ormalized compariso matrix that is calculated as show below: a a =Α a a ad a = a ij a ij i, j= for i,j=,2,,, (8) Table 2. Matrix A a ij Cc Qs Ma Ab Oi Tdb Pa Cc ()/22,37 (/4)/,56 (/7)/2,46 (5)/33,2 (6)/43,00 (/5)/5,30 (/5)/6,76 Qs (4)/22,37 ()/,56 (/4)/2,46 (6)/33,2 (7)/43,00 (/2)/5,30 (/4)/6,76 Ma (7)/22,37 (4)/,56 ()/2,46 (8)/33,2 (9)/43,00 (3)/5,30 (2)/6,76 Ab (/5)/22,37 (/6)/,56 (/8)/2,46 ()/33,2 (5)/43,00 (/7)/5,30 (/6)/6,76 Oi (/6)/22,37 (/7)/,56 (/9)/2,46 (/5)/33,2 ()/43,00 (/8)/5,30 (/7)/6,76 Tdb (5)/22,37 (2)/,56 (/3)/2,46 (7)/33,2 (8/43,00) ()/5,30 (3)/6,76 00

a ij Cc Qs Ma Ab Oi Tdb Pa Pa (5)/22,37 (4)/,56 (/2)/2,46 (6)/33,2 (7)/43,00 (/3)/5,30 ()/6,76 The table 3 calculates the eigevalue ad the eigevector w w w 2 = w ad ωι = i, j= a ij for i,j=,2,,, (9) The respective weight of each KPI (r, r 2, r 3, r 4, r 5, r 6 ) is give i table 3. Table 3. Determiatio of KPIs weight Qs Ma Ab Oi Tdb Pa Weight Cc 0,04 0,02 0,06 0,5 0,4 0,04 0,03 0,07 Qs 0,8 0,09 0,0 0,8 0,6 0,09 0,04 0,2 Ma 0,3 0,35 0,4 0,24 0,2 0,57 0,30 0,34 Ab 0,0 0,0 0,05 0,03 0,2 0,03 0,02 0,04 Oi 0,0 0,0 0,05 0,0 0,02 0,02 0,02 0,02 Tdb 0,22 0,7 0,4 0,2 0,9 0,9 0,44 0,22 Pa 0,22 0,35 0,20 0,8 0,6 0,06 0,5 0,9 The paradigm of the Morocca automotive idustry is the improvemet of materials ad the availability of mapower; also, the Cost dimesio ad the safety at work ad the iteral climate are itegrated i the overall performace of these maufactories. Traditioally, most plat maagers focused o the triagle of (Cost, Quality ad Delay). Subsequetly, our model shows that there are other Key Factor of Success (Traiig, iteral climate ad Safety) which should be itegrated i their strategic, tactical ad operatioal maagemet. 2.3.2 Choice of Strategies based o the Liear Model of the Morocca Automotive Suppliers The global performace (GP) is expressed, based o the WAM as the aggregatio operator, i the formula below (Che, 2008): 7 GP = 00 ( P AKPI r i ) (0) Therefore, the formula for overall performace of Morocca automotive suppliers is calculated as follows: i= GP = 00 (0,07 PCc + 0,2 PQs + 0,34 PMa + 0,04 PAb + 0,02 POi + 0,22PTdb 0,9 PPa ) () Relevat performace idicators ad their relatioships to strategic ad operatioal goals eed to be determied ad aalyzed. (Popova ad Sharpaskykh, 200) The alterative improvemet strategies adopted i this research are summarized followig the KSF (Key Success Factors) of Morocca Automotive suppliers: (S QS ) Quality ad security, (S HR ) Huma Resources & climate social, (S MM ) Maiteace Maagemet. By applyig the WAM operator, a overall performace of strategies, ca be expressed as show i Table 4. The decisio-maker ca ow rak the strategies S QS S HR S MM. The coclusio is to retai the best strategy with regards to the overall performace: 0

Table 4. Overall performace of strategies P Cc P Qs P Ma P Ab P Oi P Tdb P Pa GP S QS 0.9 0.5 0,2 0,8 0,7 0.5 0,62 S HR 0,8 0,8 0,7 0,8 0.5 0.7 0,78 S MM 0,8 0,9 0, 0.5 0,7 0,9 0,84 The decisio-maker ca rak the best strategy (S QS, S HR, S MM ) by retaiig the best strategy with regards to the overall performace, i this case, the choice of Machie Maagemet is chose i the first rak, the the Huma resource strategy occupies the secod place followed by the Quality security strategy. However, the choice of ay strategy does ot provide idicatios about reducig the ivestmet because the busiess policy is too geerous regardig a key factor or simply maitai ivestmet because a satisfactory level has bee reached. Furthermore, the decisio maker caot combie performace parameters liearly i a maer to assist maagemet i formulatig the most suitable decisio. So, the aim of this research is to treat with the complex ad dyamic iterrelatioships aspects of KPIs. 2.4 The Aggregated Performace Expressio by Sugeo Itegral 2.4. Costructio of Objectives We itroduce the otios of a space of states X = { x, x2,, x} ad a decisio space (a space of alteratives). S = { s, s2,, s} We cosider a decisio model i which alteratives s, s 2,,, s S act as strategies used to improve the overall performace. The strategies should ifluece m states s, s 2,, s S, which are idetified with m KPI correspodig to KSF. Table 5. The efficiecy of the elemetary performace Effectiveess U (g) Noe 0 Almost oe 0. Very little 0.2 Little 0.3 Rather little 0.4 Medium 0.5 Rather large 0.6 Large 0.7 Very large 0.8 Almost complete 0.9 Complete The expert s opiio has judged the relatioship betwee the efficiecy of the elemetary performace ad strategies followig the table 5. We express the coectio i the table 6. Table 6. Relatioship amog Efficiecy of the Elemetary Performace ad Stategies S QS P Cc P Qs P Ma P Ab P Oi P Tdb P Pa complete Almost Medium Very little Very large large Medium f(x )=g = complete f(x 3 )=g 3 =0.5 f(x 4 )=g 4 =0.2 f(x 5 )=g 5 =0.8 f(x 6 )=g 6 =0.7 f(x 7 )=g 7 =0.5 f(x 2 )=g 2 =0.9 S HR Very large Very large large Very large Medium complete large f(x )=g 2 =0.8 f(x 2 )=g 22 =0.8 f(x 3 )=g 23 =0.7 f(x 4 )=g 24 =0.8 f(x 5 )=g 25 =0.5 f(x 6 )=g 26 = f(x 7 )=g 27 =0.7 S MM Very large Almost complete Almost oe Medium large Almost f(x )=g 2 =0.8 complete f(x 2 )=g 32 =0.9 f(x 3 )=g 33 = f(x 4 )=g 34 =0. f(x 5 )=g 35 =0.5 f(x 6 )=g 36 =0.7 complete f(x 7 )=g 37 =0,9 02

2.4.2 Costructio of Sugeo Itegral The weights w,w 2,w 3,, w, W act as the rages of the fuctio g λ : X W = [ 0,] w = g λ (x ), w 2 = g λ (x 2 ), w 3 = g λ (x 3 ),, w = g λ (x ). So, w =w Cc= g λ (x )= 0,07 ; w 2 =w Qs = g λ (x 2 )= 0,2; w 3 =w Ma = g λ (x 3 )= 0,34; w 4 =w Ab = g λ (x 4 )= 0,04; w 5 =w Oi = g λ (x 5 )= 0,02; w 6 =w Tdb = g λ (x 6 )= 0,22; w 7 =w Pa = g λ (x 7 )= 0,9 Accordig to (4) i λ+= ( +λg ) i = We had the polyomial equatio below: 0=0.39 λ 2 + 0.75 λ 3 + 0.008 λ 4 + 0.0004 λ 5 + 0.000005 λ 6 + 9.550.0-08 λ 7 (2) Ad the roots of the above equatio will be λ = {0; 0; (- 0.523); (- 64.689343 + 34.28964i); (- 64.689343-34.28964i); (9.9769409 + 36.84507i); (9.9769409-36.84507i)} But λ (, ) We will take λ = - 0.523 oly, because λ = 0 is additively. If λ = - 0.523the: g(x,x2) 0,856068 g(x,x3) 0,3975526 g(x,x4) 0,085356 g(x,x5) 0,0892678 g(x,x6) 0,289458 g(x,x7) 0,253044 g(x2,x3) 0,438666 g(x2,x4) 0,574896 g(x2,x5) 0,387448 g(x2,x6) 0,326928 g(x2,x7) 0,2980756 g(x3,x4) 0,3728872 g(x3,x5) 0,3564436 g(x3,x6) 0,5208796 g(x3,x7) 0,496242 g(x4,x5) 0,059586 g(x4,x6) 0,2553976 g(x4,x7) 0,2260252 g(x5,x6) 0,2376988 g(x5,x7) 0,208026 g(x6,x7) 0,388386 g(x,x2,x3) 0,49260299 g(x,x2,x4) 0,22723906 g(x,x2,x5) 0,203665353 g(x,x2,x6) 0,384250882 g(x,x2,x7) 0,35763052 g(x,x3,x4) 0,4292358 g(x,x3,x5) 0,433942 g(x,x3,x6) 0,578098 g(x,x3,x7) 0,548047798 g(x,x4,x5) 0,2740038 g(x,x4,x6) 0,36047494 g(x,x4,x7) 0,28775047 g(x,x5,x6) 0,298996647 g(x,x5,x7) 0,270397259 g(x,x6,x7) 0,443928846 g(x2,x3,x4) 0,469484799 g(x2,x3,x5) 0,4540732 g(x2,x3,x6) 0,6088996 g(x2,x3,x7) 0,58507797 g(x2,x4,x5) 0,75842259 g(x2,x4,x6) 0,359368847 g(x2,x4,x7) 0,33839858 g(x2,x5,x6) 0,342780823 g(x2,x5,x7) 0,34957729 g(x2,x6,x7) 0,48377902 g(x3,x4,x5) 0,3889868 g(x3,x4,x6) 0,549982799 g(x3,x4,x7) 0,525833399 g(x3,x5,x6) 0,5354399 g(x3,x5,x7) 0,5023799 g(x3,x6,x7) 0,6599794 g(x4,x5,x6) 0,2727264 g(x4,x5,x7) 0,243660976 g(x4,x6,x7) 0,4200874 g(x5,x6,x7) 0,40407867 g(x,x2,x3) 0,49260299 g(x,x2,x4) 0,22723906 g(x,x2,x5) 0,203665353 g(x,x2,x6) 0,384250882 g(x,x2,x7) 0,35763052 g(x,x3,x4) 0,4292358 g(x,x3,x5) 0,433942 g(x,x3,x6) 0,578098 g(x,x3,x7) 0,548047798 g(x,x4,x5) 0,2740038 g(x,x4,x6) 0,36047494 g(x,x4,x7) 0,28775047 g(x,x5,x6) 0,298996647 g(x,x5,x7) 0,270397259 g(x,x6,x7) 0,443928846 g(x2,x3,x4) 0,469484799 g(x2,x3,x5) 0,4540732 g(x2,x3,x6) 0,6088996 g(x2,x3,x7) 0,58507797 g(x2,x4,x5) 0,75842259 g(x2,x4,x6) 0,359368847 g(x2,x4,x7) 0,33839858 g(x2,x5,x6) 0,342780823 g(x2,x5,x7) 0,34957729 g(x2,x6,x7) 0,48377902 g(x3,x4,x5) 0,3889868 g(x3,x4,x6) 0,549982799 g(x3,x4,x7) 0,525833399 g(x3,x5,x6) 0,5354399 g(x3,x5,x7) 0,5023799 g(x3,x6,x7) 0,6599794 g(x4,x5,x6) 0,2727264 g(x4,x5,x7) 0,243660976 g(x4,x6,x7) 0,4200874 g(x5,x6,x7) 0,40407867 03

g(x,x2,x3,x4) 0,52229696 g(x,x2,x3,x5) 0,50744958 g(x,x2,x3,x6) 0,65592339 g(x,x2,x3,x7) 0,63365238 g(x,x2,x4,x5) 0,239404674 g(x,x2,x4,x6) 0,4622353 g(x,x2,x4,x7) 0,3896920 g(x,x2,x5,x6) 0,4002367 g(x,x2,x5,x7) 0,37342727 g(x,x2,x6,x7) 0,53606787 g(x,x3,x4,x5) 0,444745993 g(x,x3,x4,x6) 0,599847929 g(x,x3,x4,x7) 0,576582638 g(x,x3,x5,x6) 0,585829063 g(x,x3,x5,x7) 0,5623528 g(x,x3,x6,x7) 0,70498948 g(x,x4,x5,x6) 0,33274637 g(x,x4,x5,x7) 0,304740548 g(x,x4,x6,x7) 0,47464854 g(x2,x3,x4,x5) 0,484573988 g(x2,x3,x4,x6) 0,635465878 g(x2,x3,x4,x7) 0,62832095 g(x2,x3,x5,x6) 0,62827537 g(x2,x3,x5,x7) 0,59895946 g(x2,x3,x6,x7) 0,737753436 g(x3,x4,x5,x6) 0,564229979 g(x3,x4,x5,x7) 0,54033382 g(x3,x4,x6,x7) 0,68533008 g(x4,x5,x6,x7) 0,435625344 g(x,x2,x3,x4,x5) 0,536833735 g(x,x2,x3,x4,x6) 0,68220473 g(x,x2,x3,x4,x7) 0,66039632 g(x,x2,x3,x5,x6) 0,66906243 g(x,x2,x3,x5,x7) 0,64702435 g(x,x2,x3,x6,x7) 0,780744283 g(x,x2,x4,x5,x6) 0,43858772 g(x,x2,x4,x5,x7) 0,4056503 g(x,x2,x4,x6,x7) 0,564853332 g(x,x2,x5,x6,x7) 0,550460602 g(x,x3,x4,x5,x6) 0,6357359 g(x,x3,x4,x5,x7) 0,59055584 g(x,x3,x4,x6,x7) 0,7302404 g(x,x3,x5,x6,x7) 0,7765229 g(x,x4,x5,x6,x7) 0,4896770 g(x2,x3,x4,x5,x6) 0,64888905 g(x2,x3,x4,x5,x7) 0,6264287 g(x2,x3,x4,x6,x7) 0,76239634 g(x3,x4,x5,x6,x7) 0,69862446 g(x,x2,x3,x4,x5,x6) 0,695065645 g(x,x2,x3,x4,x5,x7) 0,673488566 g(x,x2,x3,x4,x6,x7) 0,80442 g(x,x2,x3,x5,x6,x7) 0,792577697 g(x,x2,x4,x5,x6,x7) 0,578944966 g(x,x3,x4,x5,x6,x7) 0,74260279 g(x2,x3,x4,x5,x6,x7) 0,77434577 g(x,x2,x3,x4,x5,x6,x7) 3. Results The costructio of Sugeo itegral i the strategies order follows equatio (6): Where f x() f x(2) f x( ) ( ) ( )... ( ). Max i= { () i () i } f( x) dgλ = Mi f( x, g( A ) (6) For S QS, we have: f(x 4 )=g 4 =0.2; f(x 7 )=g 7 =0.5; f(x 3 )=g 3 =0.5; f(x 6 )=g 6 =0.7; f(x 5 )=g 5 =0.8; f(x 2 )=g 2 =0.9; f(x )=g =. So, f ( x(4) ) f( x(7) ) = f( x(3) ) f( x(6) ) f( x(5) ) f( x(2) ) f( x() ) S QS = fdg λ = max(mi(f(x 4 ), g λ (x,x 2,x 3,x 4,x 5,x 6, x 7 ));mi(f(x 7 ), g λ (x,x 2,x 3,x 5,x 6, x 7 )); mi(f(x 3 ), g λ (x,x 2,x 3,x 5,x 6 ));mi(f(x 6 ), g λ (x,x 2,x 5,x 6 ));mi(f(x 5 ), g λ (x,x 2, x 5 )); mi(f(x 2 ), g λ (x,x 2 )); mi(f(x ), g λ (x )) S QS = fdg λ = max(mi(0.2;);mi(0.5; 0.792577697); mi(0.5; 0.66906243); mi(0.7;0.4002367); mi(0.8; 0.203665353); mi(0.9; 0,856068); mi(; 0.07)) S QS = max(0.2; 0.5; 0.5; 0.4; 0.203; 0.8; 0.07) S QS = 0.5 04

For S HR, we have: f(x 5 )=g 25 =0.5; f(x 7 )=g 27 =0.7; f(x 3 )=g 23 =0.7; f(x )=g 2 =0.8; f(x 2 )=g 22 =0.8; f(x 4 )=g 24 =0.8; f(x 6 )=g 26 = So, f ( x(5) ) f( x(7) ) = f( x(3) ) f( x() ) = f( x(2) ) = f( x(4) ) f( x(6) ) S HR = fdg λ = max(mi(f(x 5 ), g λ (x,x 2,x 3,x 4,x 5,x 6, x 7 ));mi(f(x 7 ), g λ (x,x 2,x 3,x 4,x 6, x 7 )); mi(f(x 3 ), g λ (x,x 2,x 3,x 4,x 6 ));mi(f(x ), g λ (x,x 2,x 4,x 6 ));mi(f(x 2 ), g λ (x 2,x 4,x 6 )); mi(f(x 4 ), g λ (x 4,x 6 )); mi(f(x 6 ), g λ (x 6 )) S HR = fdg λ = max(mi(0.5;); mi(0.7; 0.8); mi(0.7; 0.68); mi(0.8; 0.42); mi(0.8; 0.36); mi(0.8; 0.25); mi(; 0.22)) S HR =max(0.5; 0.7; 0.68; 0.42; 0.36; 0.25; 0.22) S HR = 0.7 For S MM, we have: f(x 4 )=g 34 =0.; f(x 5 )=g 35 =0.5; f(x 6 )=g 36 =0.7; f(x )=g 2 =0.8; f(x 2 )=g 32 =0.9; f(x 7 )=g 37 =0,9; f(x 3 )=g 33 = So, f ( x(4) ) f( x(5) ) f( x(6) ) f( x() ) f( x(2) ) = f( x(7) ) f( x(3) ) S MM = fdg λ = max(mi(f(x 4 ),g λ (x,x 2,x 3,x 4,x 5,x 6, x 7 ));mi(f(x 5 ),g λ (x,x 2,x 3,x 5,x 6, x 7 )); mi(f(x 6 ),g λ (x,x 2,x 3,x 6,x 7 ));mi(f(x ),g λ (x,x 2,x 3,x 7 ));mi(f(x 2 ),g λ (x 2,x 3,x 7 )); mi(f(x 7 ), g λ (x 3,x 7 )); mi(f(x 3 ), g λ (x 3 )) S MM = fdg λ = max(mi(0.; ); mi(0.5; 0,79); mi(0.7; 0.78); mi(0.8; 0.63); mi(0.9; 0.58); mi(0.9; 0.49); mi(; 0.34)) S MM =max(0.; 0.5; 0.7; 0.63; 0.58; 0.49; 0.34) S MM = 0.7 The iterpretatio of Sugeo itegral i the strategy rakig gives S HR = S MM S QS I the liear model, we foud i the first rak Machie Maagemet strategy with the overall performace equal to 0.83, the the Huma resource strategy with 0.789, followed by the Quality security strategy with 0.6535. The rakig of Huma resource strategy was improved, occupyig the first place tied with Machie Maagemet strategy with the score of 0.7. I this case, the priority of actio would be first to implemet Huma resource strategy or Machie Maagemet strategy, ad secod Quality security strategy. That adjustmet ca substitute for other expesive strategies such whom cocerig 4. Discussio A techique for measurig the causal iteractios betwee the differet factors affectig the global performace has bee desiged ad applied. For the top maagemet the foremost profit is the performace formulatio of various measures ito a dimesioless item at all the corporatio stages. The secod beefit is associated with the decisio makig help for adoptig the suitable strategy. Admiistrators frequetly vacillate betwee differet strategies permit them to cofirm their perceptio. Our model has several suppleess for dealig with i the itrisic ad extrisic eviromet chages, but oly below the suppositios of small differeces of the objective stadards ad of the weight ad the relatios of the performace factors. At last, the proposed method is ot exclusive to our case study. It ca duplicate across differet maufacturers where eough expertise regardig particular circumstaces is idispesable to describe the weight ad the relatios of criterio. 5. Coclusio The Sugeo itegral as a operator of aggregatio is well fitted to deal with the iteractios betwee the performace factors. A idustrial applicatio has permitted us to show the pertiece of such method. The algorithm studied ca be used to determie the best distributio of resources o performace criteria. This method has prove its efficiecy by structurig assessmet of huma subjective decisio makig by usig λ-fuzzy measures ad sugeo itegrals. Certaily, this approach requires a great maager proficiecy of the method: to make the structure of the global 05

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