Mathematical models for decision-making about ISO 9001 and/or ISO under risk and fuzziness

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1 Mathematical models for decisio-makig about ISO 9001 ad/or ISO uder risk ad fuzziess Marti Flégl, Helea Brožová Abstract Quality decisio-makig is curretly oe of the most importat maagerial activities of each eterprise. Every day decisios differ oly by their importace ad complexity. Compaies are facig strog competitive eviromet o their markets ad they meet with problems based o ucertaity or fuzziess of the iformatio durig decisio-makig processes. If compaies wat to make their decisio precise they must fid the way how to work with this ucertaity. Rapidly growig ad chagig developmet geerates sigificat pressure o the compaies. This pressure is based o ever edig competitiveess ad challeges. Compaies ca gai stroger competitive positio by implemetatio of the ISO orms 9001 ad the ISO ISO certificatio i quality ad evirometal maagemet has grow oticeably i several last years. ISO certificatio is becomig more ad more obvious tha ust a exceptioal. Number of certified orgaizatios growth rapidly i last two decades. The evolutio i the Czech Republic copied the rapid evolutio ad i the last years Czech Republic reached leadig positio i ISO implemetatios of quality ad eviromet. The key elemet of ability how to make quality decisio is to fid the way how to work with ucertaity, how to express or use obtaied kowledge ad iformatio. Crossig the border betwee certaity ad ucertaity, this moves our decisios o higher level ad gives us the key competitive advatage. I our cotributio we will demostrate the applicatio of decisio-makig model based o fuzzy iformatio. Fuzzy decisio model (game agaist ature) will be used for the choice of the best decisio for the followig real problem: Maagemet has to decide if implemet ISO 9001 (Quality maagemet system) ad/or implemet ISO (Evirometal Maagemet Systems). Fidig out if customers are orieted towards the ISO 9001 or the ISO is based o the progress of umber of certified compaies. Model cotais fuzzy states of ature ad payoff of possible alteratives. Mauscript received May 11, 2011: Revised versio received xx.xx, This work was supported i part by the grat proect of the Miistry of Educatio, Youth ad Sports, the Czech Republic, No. MSM Iformačí a zalostí podpora strategického řízeí ( Iformatio ad kowledge support of strategic maagemet ). Marti Flégl is with the Dept. of Systems Egieerig, Faculty of Ecoomics ad Maagemet, Czech Uiversity of Life Scieces Prague, Kamýcka 129, Praha 6 Suchdol, the Czech Republic, (correspodig author to provide phoe: ; fax: ; Flegl@pef.czu.cz). Helea Brožová is with the Dept. of Systems Egieerig, Faculty of Ecoomics ad Maagemet, Czech Uiversity of Life Scieces Prague, Kamýcka 129, Praha 6 Suchdol, the Czech Republic, ( Brozova@pef.czu.cz). Keywords Decisio-makig, fuzzy decisio model, ISO orm certificatio, ISO 9001 ad C I. INTRODUCTION ONTEMPORARY ecoomic decisio-makig is a very complex ad complicated process which has a importat impact o firm competitiveess. Iterests of the most maagers are mostly focused o reachig positive ecoomic results ad as well as o extedig of the approaches how to reach these ecoomic results. Large attetio is ow givig to quality productio ad to eviromet. Durig the eds of 80s World Commissio o Eviromet ad Developmet (Uited Natios) published report, i which they have oted, that subsequet developmet of society, if the global eviromet will ot be threateed, has to cotiue based o a ew type of ecoomic developmet. This developmet was called as Sustaiable developmet [19]. Sustaiable developmet has three dimesios ecoomic, social ad evirometal. If i the past decades was sufficiet aim our cocetratio oly o quatitative ad ecoomical aspects of maagemets, owadays it is ecessary to maage qualitative ad time aspects as well. It is ot sufficiet supply relevat amout of products i specified price, but it is also ecessary guaratee required quality ad delivery time. Productio quality is ot oly a marketability coditio of the product, but quality or we ca better say o-quality i a form of defective productio does ot have isigificat impacts o effectiveess of maufacture. Losses from defective productio could be sigificat item i fiacial statemets. This sigificat item ca come up to several percets [21]. Durig 80s appeared first sigals which lead towards resposibility of producers i products quality. New uiversal stadards i quality were itroduced i form of orms ISO Quality maagemet system (QMS) is more ad more orieted o requiremets of establishig ISO 9001 ito the practice. O the other side, evirometal care also belogs amog the importat iteratioal problems of preset days. Existig experieces show us, that social ad especially techological developmet had basically egative impact o the eviromet. I this cotext it is ecessary reach sustaiability of techological developmet. Evirometal maagemet system (EMS) became relevat sice secod half of 90s i Issue 5, Volume 5,

2 coectio with acceptace of ew ISO orms Orgaizatios whose productios have impact o the eviromet have opportuities to obtai competitive advatages thaks to the ISO EMS icludes orgaizatioal structure, plaig activities, resposibilities, practices, procedures ad sources which they ca use for develop, implemet, reach, revisio ad sustetatio of evirometal policy [21]. Establish ad routie sustetatio of maagemet systems of quality ad eviromet i orgaizatios creates eviromet, which will geerate stadard maagerial ad operatioal practices. Certificate i form of certificatio is becomig decisive sigal (guaratee) especially for customers, employees ad relevat compaies aroud, that the compay is able to maage their processes. Sambasiva ad Fei [16] oted that with the progressively widespread adoptio of the ISO stadards, it is ot surprisig that, i the ear future, the implemetatio of a evirometal maagemet system (EMS), through registratio with ISO 14001, will be the orm rather tha the exceptio. We ca fully agree with this coclusio i ISO 9001 implemetatio. I this article we will aalyze decisio problem of the compay, if establish (implemet) or ot ISO orms (ISO problem). This problem will be solved by classical decisiomakig model uder the risk with usig EMV (Expected Moetary Value) criterio ad the with decisio-makig model uder fuzziess. II. BENEFITS, BARRIERS AND IMPACTS OF ISO IMPLEMENTATION Implemet ISO orm of quality should lead towards to higher compaies profit ad towards to icreasig competitiveess by optimizig processes with a particular focus o the costumers. Cagazzo et al. [4] described the mai impacts of ISO 9001 o compaies performace. The impacts o busiess performaces have bee classified as exteral ad iteral. The exteral impacts are divided by impact o: 1) Iteratioal trades, 2) Suppliers, 3) Customers, 4) Stakeholders, ad 5) Market. The iteral impacts are divided by impact o: 1) Quality system, 2) Product/service, 3) Competitiveess, 4) Fiacial performace, ad 6) Huma resource/orgaizatioal climate. From Cagazzo et al. survey [4] we see that the perceptio of the impact is mostly see i improvig operatig efficiecy (almost 70 % of all votes i iteral impacts compare to better cotrol of busiess operatios with 21 %). The perceptio of exteral impacts is mostly give to costumers satisfactio (more tha 30 %), the improvemet of compay image (26 %). We ca see that implemetatio of ISO 9001 has a huge impact o each compay who wats to adopt quality maagemet cocept. We ca fully agree with that. The similar survey, i coditio of the Czech Republic, was published by Šadr et al. [20]. They metioed that the mai assets from implemetatio are stroger positio o the market, icreasig of the market share, icreasig competitiveess, acquiremet of costumers satisfactio, costumers loyalty etc. O the other side we should metio that there exist several barriers or pitfalls as well. Cagazzo et al. [4] describes five mai barriers from the compay s side. They are 1) Short-sighted goal for gettig certified, 2) Over-expectatio o ISO stadard, 3) Madatory requiremet i some idustries, 4) Followig others (the tred) i certificatio, ad 5) Lack of ecessary guidace for certificatio. We ca compare these barriers with barriers which are importat for Šadr et al. [20]: 1) Bad commuicatio betwee compay s departmets, 2) Low iterest of employees, 3) Uwilligess to resposibility, ad fially 4) Low potetial of compaies iovatio. Obviously we ca also fid several beefits for implemetatio of ISO as well. Most of them correspod with beefits regard to ISO For Sambasiva ad Fei [16] the more importat beefits are: 1) Gai etry ito the global market 2) Maitai ad gai competitive positio i the global market, 3) Improve the compay s image, 4) Improve the compay s operatios, ad 5) Provide a clea eviromet through clea operatios. May orgaizatios seem as a mai problem of implemetatio of EMS difficulties i determiig the tagible ad itagible beefits or impacts cosiderig the cost icurred [16]. III. TENDENCY TO ISO IMPLEMENTATION We already discussed beefits ad barriers i ISO implemetatio. Each maagemet has to weight if the implemetatio will be a advatage for their compay or if it will ot. Now let us fid out what the treds i ISO 9001 ad ISO are. Quality maagemet had a sigificat growth i the last 15 years. There are a few reasos for this growth. Firstly there has bee a huge competitio o the markets. Markets were flooded by may products ad prices are i may cases pressed dow to the miimum. Secodly cosumers expect more tha ust a low price. There was a space for better quality productio. Table 1 summarizes the umber of ISO 9001 implemetatio o the World. Sice 1993 Europe is cosequetly the leader i Issue 5, Volume 5,

3 Quality maagemet system implemetatio. It is a oteworthy metio the growth of Far East i the last decade. Europe ad Far East have regioal share 47 % ad 37,4 % respectively (Table 2). Table 1. ISO 9001 Quality maagemet system Requiremets - overview Year TOTAL Africa / West Asia Cetral / South America North America Europe Far East Australia / New Zealad Table 2. ISO 9001 Quality maagemet system Requiremets regioal share i % Year TOTAL 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% Africa / West Asia 2,7% 2,6% 2,7% 3,8% 3,9% 4,5% 5,0% 4,4% 3,9% 4,2% 4,0% 4,8% 6,2% 8,0% 8,3% 7,4% 7,3% Cetral / South America 0,3% 0,7% 1,0% 1,1% 1,3% 1,9% 2,6% 2,4% 2,8% 2,4% 1,9% 2,6% 2,9% 3,3% 4,1% 4,1% 3,4% North America 5,6% 7,0% 8,1% 10,4% 11,3% 12,3% 13,1% 10,5% 10,0% 9,6% 8,1% 7,6% 7,7% 6,8% 5,0% 4,9% 3,9% Europe 81,1% 78,7% 72,7% 67,6% 64,3% 61,2% 55,4% 58,8% 52,8% 52,1% 48,7% 48,6% 48,7% 46,2% 45,3% 46,3% 47,0% Far East 3,4% 4,4% 7,3% 11,3% 13,4% 13,9% 16,5% 17,9% 24,8% 26,4% 32,7% 33,5% 31,9% 33,5% 36,3% 36,3% 37,4% Australia / New Zealad 6,8% 6,6% 8,3% 5,8% 5,8% 6,2% 7,4% 6,0% 5,6% 5,2% 4,6% 3,0% 2,5% 2,2% 0,9% 1,0% 1,0% Table 3. Top 10 coutries for ISO 9001 growth i Russia Federatio Chia Italy Japa Romaia Czech Republic Vietam Polad Israel Ira 1090 I this cotributio we focus o Europea coutries ad maily o the Czech Republic. Whe we cosider ecoomic developmet i Czech Republic durig the last two decades we would say that this developmet has bee sigificat. Czech Republic adopted priciples of wester Europea coutries i quality ad eviromet. I the field of Quality maagemet system it icreased a lot i a few last years. Table 3 shows us that Czech Republic reached top 10 i ISO 9001 growth i Czech compaies, mostly with foreig owers, uderstad very well that i globalizatio time it is ecessary to improve their competitiveess ad Quality maagemet system i ISO 9001 stadard is a effective way. Our cotributio is focused o implemetatio of Eviromet maagemet system based o the priciples of ISO as well. So let us talk ow about the evolutio of eviromet thikig i global eviromet ad Europea too. Table 4 ad Table 5 describe the evolutio of ISO The evolutio is similar like i ISO 9001 stadard. Durig last decade the mai roles have played Europe ad Far East. They regioal share is 40 % for Europe ad approximately 50 % for Far East. ISO is ot globally exteded as much as ISO 9001 is. This stadard is i the most occasios implemeted as a elargemet for Quality maagemet system. There is cosiderably less cases whe compay implemets previously ISO before ISO May authors [5] poited out that the umber of ISO 9001 certificates i a give coutry is oe of the factors explaiig the umber of ISO certificates issued i the same coutry. Explaatio of their shares would be explaied due to large extesio amog compaies ad awareess amog customers. Other regios would have other stadards which their domestic compaies preferred. But ISO stadards are gettig more popular ad more iteratioally accepted. Issue 5, Volume 5,

4 Table 4. ISO Eviromet maagemet system Requiremets - overview Year TOTAL Africa / West Asia Cetral / South America North America Europe Far East Australia / New Zealad Table 5. ISO Eviromet maagemet system Requiremets regioal share i % Year TOTAL 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% Africa / West Asia 2,4% 2,8% 2,5% 2,7% 3,1% 3,3% 3,6% 3,8% 3,6% 4,1% 3,9% Cetral / South America 2,2% 2,4% 1,9% 2,9% 2,6% 3,3% 3,1% 3,4% 2,8% 2,5% 1,8% North America 7,0% 7,3% 7,4% 8,2% 8,1% 7,4% 6,4% 6,0% 4,7% 3,8% 3,3% Europe 51,8% 48,0% 49,2% 47,1% 47,6% 44,0% 43,0% 43,6% 42,1% 41,4% 40,0% Far East 31,1% 34,5% 35,1% 35,9% 36,5% 39,7% 42,1% 41,6% 46,2% 47,6% 50,3% Australia / New Zealad 5,5% 4,9% 3,9% 3,2% 2,2% 2,3% 1,8% 1,7% 0,6% 0,7% 0,7% Now let us focus o the Czech Republic agai. The evolutio i case of ISO is similar like i case of ISO Czech compaies have adopted this stadard due to requiremets for stroger competitiveess o the Europea market or global market respectively. Table 6 shows us that Czech Republic is i TOP 10 coutries worldwide i ISO implemetatios. If we cosider that Czech Republic is globally a small coutry it is a very iterestig situatio. Czech Republic has reached its positio thaks to successful implemetatio i 2009 (Table 7). The popularity icreased durig the last years whe Czech compaies saw the big advatages which they gaied from successful Quality maagemet system implemetatio. This situatio has cofirmed their belief that this implemetatio will have a positive impact oto their competitiveess. Aother importat issue is oied to icreasig global evirometal care. Most govermets, Europea are ot a exceptio, pay a bigger attetio to the eviromet proects ad to the evirometal behaviour. Evirometal maagemet system is curretly a importat requiremet for those orgaizatios wishig to sell their products i the cotext of the global market [6]. Implemetatio may affect o compay s capability sell products globally. Table 6. ISO top 10 coutries 1 Chia Japa Spai Italy Uited Kigdom Republic of Korea Romaia Germay USA Czech Republic 4684 However there is a large dissemiatio of both stadards, we have see a certai drop i the umber of certificates i several of the coutries which had historically bee leaders i these areas [5]. Potetially there could be a saturatio of implemetatio of ISO 9001 or ISO Issue 5, Volume 5,

5 Table 7. Top 10 coutries for ISO growth i Chia Japa Romaia Italy Uited Kigdom Czech Republic Frace Thailad Russia Federatio Republic of Korea 710 IV. REASONS OF DECISION-MAKING IN ISO IMPLEMENTATION I our opiio all of the mai barriers have similar reasos. I compaies where implemetatio of ISO orms was ot successful, there exists low stress o the commuicatio betwee departmets ad adequate expectatios. Whe compay has to cosider all of those barriers, impacts ad beefits, there is a sigificat reaso, why compay should thik about decisio-makig method as a tool for the right decisio. The implemetatio of the ISO orms ca be cosidered, i some sese, as a iovative behaviour. Pekovic ad Galia [12] ivestigated the impact of quality system of ISO 9001 o iovatio. They poited out that ISO 9000 certificatio seems to be positively associated with iovatio performace (correlatio betwee ISO 9000 ad iovatio is positive ad sigificat cocerig products, processes ad iovatio). I order to icrease profits from implemetatio the ISO orms, i.e. higher productio quality ad icrease of awareess of compay s evirometal care, it is appropriate to iclude key customers ad suppliers ito the compay s iovative suggestios. We see marketig research as a isufficiet compare to ISO implemetatio s impact. Pitra [13] metioed relatio betwee quality maagemet system ad iovatios. Implemetatio ISO orms ad effective fuctio of quality maagemet is ecessary coditio for successful developmet of iovative activities. Iovatios are positively oied with kowledge of the compay itself. Lee [11] poited out the usage of ISO 9001 to reach the kowledge applicatio of the busiess. So why is there a reaso for decisio-makig methods? Compaies have to be for hudred percet sure that there will be a positive impact. By positive impact we mea ot oly a bigger profit or stroger competitiveess positio. We already metioed above that i ISO implemetatio is difficult to recogize tagible ad itagible beefits. Decisio-makig model is a oe of the tools which we ca use for solvig this problem, for aswer the questio if there will be a sigificat profit (beefit) for orgaizatio. We ca calculate all possible future evets. Future evets as high or low customer prefereces i the ISO orms, costs ad profit impact of implemetatio etc. V. ISO PROBLEM FORMULATION AND SOLVING IMPLEMENT ISO 9001 AND/OR ISO 14001? The real compay i the Czech ICT market, which does ot wish to be desigated, provides complex spectrum of services i the field of system itegratio. Curretly the compay is lookig for ew opportuities how to icrease their competitiveess. First possible way is establish Quality maagemet system based o ISO 9001 ad/or establish Evirometal maagemet system based o ISO It is goig to be decisio-makig uder the risk, because there is much iformatio (reports) which iclude forecasts of the future tred (progressio) o the market [7]. Aother reaso why it is goig to be a decisio-makig uder risk ca be due to the poits which we described i chapter II ad correspodig to [4] ad [20]. Ucertaity i this problem comes primarily through the maer of defiitio of the states of ature i the model. We will costruct model with fuzzy states of ature ad crisp alteratives, but the evaluatio of each combiatio alterative-fuzzy states of ature will be crisp values. This model is compared with decisio-makig model uder risk. A. Decisio-Makig uder Risk Decisio model helps to choose the best decisio alterative ([1], [14], [17]). I fact, it is a model of games agaist ature. The decisio maker selects oe of alteratives that are available. Their effect depeds o possible future states of ature ad its probability. Payoffs are associated with each combiatio alterative state of ature. The geeral format of a decisio model is i a decisio table (Table 1). Table 8. Decisio table with crisp states of ature States of ature S 1 S 2... S v 11 v v 1 Alteratives A 2 v 21 v v A m v m1 m2 v... v m Probability P p 1 p 2... p where A i is the i-th alterative, i = 1,..., m, S is the -th state of ature, = 1,...,, v i is the payoff of alterative A i ad state of ature S combiatio, ad p is probability of state of ature S. The appropriated alterative is selected accordig to the decisio criterio; typically the best alterative maximizes the payoff value. Commoly used criterio is Expected moetary value criterio (EMV), the alterative A I is selected, if it has the maximal mea value of payoff (1). EMV A : I i = p vi i = 1,..., m (1) = 1 EMV I = max i= 1,...,m EMV i Issue 5, Volume 5,

6 The decisio theory ad decisio models eable the decisio-maker to make ratioal decisios. There are may priciples for decisio model solvig, but all of them eed crisp data assessig. This may ofte lead to usatisfactory results because of the accuracy of data estimatio ([2], [3], [7], [8], [9]). B. Decisio-Makig uder Fuzzy The decisio theory ad decisio models ca be used also i the case of so called soft defied problems whe the decisiomaker is ot able to make a crisp defiitio of problem [15]. For this reaso some methods exist for decisio model solvig wheever the crisp formalizatio ad quatificatio is difficult or impossible. Oe possible way of softeig decisio model is icludig fuzzy iformatio ito model costructio. Suppose ow that we are ot able to set exact defiitio of states of ature. I this situatio we have to defie elemets of uiverse of states of ature, tha fuzzy state of ature ad values of membership fuctio of elemets of uiverse ito all fuzzy states of ature ad probability of elemets of uiverse [15]. Fuzzy decisio table has to be elarged comparig it to crisp decisio table ([8], [14]). It has to iclude all these data ad iformatio. The decisio model with fuzzy state of ature is described i a followig decisio table (Table 9). Sirbiladze et al. [18] shows a applicatio of fuzzy methods i optimizatio model icludig expert kowledge ad compariso betwee crisp approach ad fuzzy approach accordig to the applicatio of the optimal choice of cadidates. Table 9. Decisio table with fuzzy states of ature Uiversum Alteratives Fuzzy states of ature F... F F 1 2 S 1 µ ( s 1 ) µ ( s 1 )... µ ( s 1 ) P 1 F1 F2 S 2 µ s ) µ s )... µ s ) P 2 ( F1 2 ( F2 2 F ( F S r µ ( ) µ ( )... µ ( ) P r F s r 1 F s r 2 F s r v 11 v v 1 A 2 v 21 v v A m v m1 m2 v... v m where A i is the i-th alterative, i = 1,..., m, F is the -th fuzzy state of ature, = 1,...,, S k is elemet of uiversum of fuzzy states of ature, k = 1,, r µ ( ) F s k is membership fuctio of elemets S k i F v i is the payoff of alterative A i ad state of ature F combiatio. P P k is probability of S k. All fuzzy states of ature are defied o a uiverse of umerical rates. The fuzzy states F will be required to be orthogoal fuzzy sets. This orthogoality coditio meas that for the fuzzy states membership fuctio values will be hold = 1 µ ( x ) = 1 k = 1,..., (2) F k The first step i process of the best alterative selectio by fuzzy Bayesia decisio method is to calculate expected payoff of crisp alterative A i : EMV where i = = 1 = 1 µ p( F ) (3) i p( F ) = µ ( x ) p( x ) (4) F k The best alterative will be chose as A I : I i= 1,..., m k EMV = max EMV (5) C. Additioal iformatio i I may decisio situatios we are askig, if we ca obtai more iformatio, which could help us make decisio-makig process more precise. Make fial decisio later whe we will have more iformatio or we will kow more, it is ot always possible regard to compay s chagig eviromet (prices, iflatio etc.). I fact of this problem we are tryig to obtai additioal iformatio which would cofirm our forecasts or fill them i ad lowered potetial risks. We ca obtai ew useful iformatio for the states of ature from research, experimets etc. Additioal iformatio ca be used for upgradig origial probabilities. Firstly we cosidered probabilities as the crisp values. I this situatio additioal iformatio will be used as a weight for them. Decisio-makig process will cotiue as ormally, but at the ed we will compare both results ad if the result with additioal iformatio will be higher tha without additioal iformatio, this iformatio has ow utility. Next we ca cosider additioal iformatio as a fuzzy value. It meas that additioal iformatio ca be oied with ucertaity. This ucertaity ca exist wherever aroud us. Additioal iformatio will be a uiverse of discourses suitable for ew iformatio. Next step is creatio of fuzzy states of ature o this iformatio as a good iformatio, average iformatio or bad iformatio. All fuzzy iformatio will have member-ship fuctio. Issue 5, Volume 5,

7 D. Crisp ISO Problem - The Best Alterative uder Risk Aalysis of solve decisio problem result i the followig defiitio of crisp ISO problem. There are three possible strategies: o ISO orm establish A 2 establish oly ISO 9001 A 3 establish ISO 9001 ad ISO Uiverse of all possible (crisp) states of ature is divided ito followig five subsets crisp defied states of ature: S 1 o preferece of ISO orms by cosumers S 2 low preferece, market begis oriet oto ISO 9001 S 3 average preferece, market requires ISO 9001 S 4 higher preferece, market requires ISO 9001 ad teds also oto ISO S 5 absolute preferece, market requires both ISO 9001 ad ISO Profit i the sector of system itegratio was evaluated aroud 500 millio Czech crow. Our compay has market share 25 %. We will cosider compay s profit i the amout 125 millio Czech crows. Estimatio of expeses ecessary for implemetatio maagerial approaches correspods to customer s satisfactio, i.e. curret probabilities of states of ature. Ito the expectig profits were calculated costs eeded for implemetatio ISO orms. These costs are: 1) Costs for implemetatio from exteral compay, 2) Costs for iteral ad exteral audit, 3) Ruig costs, ad 4) Cotrol audit from Certificatio Compay ([7], [8], [9]). The decisio-makig model is evaluated with profit estimatio as it is show below (Table 10). Table 10. Decisio model of crisp ISO problem Profit S 1 S 2 S 3 S 4 S A A Probability 0,1 0,3 0,4 0,1 0,1 Next elemets are probabilities of all states of atures. Curretly customers (market) do ot overly require ISO certificatio, i.e. their orietatios oto certificated systems are average or rather lower. I this fact, higher probabilities will be situated i states of ature S 2 ad S 3. It is outlied i Table 10. The best alterative accordig to the EMV criterio is the secod variat A 2 with the highest EMV value (Table 11). The alterative A 3 yields also a good value of EMV. Table 11. EMV criterio values usig formula (1) EMV 1 115,5 A 2 EMV 2 136,7 A 3 EMV E. Fuzzy ISO Problem - The Best Alterative Uder Fuzzy Aalysis of decisio problem ad its soft character result i the followig defiitio of fuzzy ISO decisio-problem. Our alteratives or possible strategies are agai: o ISO orm establish A 2 establish oly ISO 9001 A 3 establish ISO 9001 ad ISO Uiverse of discourses of all possible states of ature is divided ito followig five subsets crisp defied states of ature as above: S 1 o preferece of ISO orms by cosumers S 2 low preferece, market begis oriet oto ISO 9001 S 3 average preferece, market requires ISO 9001 S 4 higher preferece, market requires ISO 9001 ad teds also oto ISO S 5 absolute preferece, market requires both ISO 9001 ad ISO O this uiverse we will describe four fuzzy states of ature: 1 F market o-orieted oto ISO orms F 2 market orieted oly oto ISO 9001 F 3 market orieted oly oto ISO F market orieted simultaeously oto ISO 9001 ad 4 ISO Next step is a defiitio of probabilities of each states of ature from uiverse. Curretly our customers are ot a lot satisfied i certificatio of ISO orms. It meas that their orietatio for certificated systems is rather low-average (accordig our states of ature). Due to this situatio bigger probabilities will be at states S 2 ad S 3 P = (0,1 0,3 0,4 0,1 0,1) Compay s profit or model pay-offs are estimated usig same priciple as above. The decisio model will be costructed as it is show below (Table 12, Table 13). Table 12. ISO problem with fuzzy states of ature Profit F F 1 2 F 3 F A A The followig step is defiig of membership fuctio values for each fuzzy states of ature. Evaluatio of Issue 5, Volume 5,

8 membership fuctio is based o expert estimatio of weight of S k accordig to the descriptio of F For example fuzzy is defied o the combiatio of S 1 ad S 2 i proportio 0,4 ad 0,7. The proportio of splittig of all fuzzy states of ature correspods to the similarities amog them ad uiverse of discourses. The fuzzy sets i Table 13 satisfy the orthogoal coditio due to (2). Table 13. Membership values for fuzzy states F 1 F 2 3 F F 4 S ,1 S 2 0,6 0, ,3 S 3 0 0,7 0,2 0,1 0,4 S ,4 0,6 0,1 S ,1 Probabilities for fuzzy states of ature are calculated by usig formula (4) ad are show i Table 14: Table 14. Probabilities of fuzzy states of ature p ( F 1 ) 0,28 p ( F 2 ) 0,4 p ( F 3 ) 0,12 p F ) 0,2 ( 4 The biggest expected mea value (EMV) we will gai if we will choose alterative A 2 (Table 15). Compay s profit will icrease from 125 millio to 136,24 millio Czech crows (icluded all expeses). Almost the same result we ca gai from alterative A 3 (132,4 millio). Alterative is the worst ad lead to lower potetial profit tha is curret compay s profit. This tred correspods with expectatios which we discussed i chapter II. Now we would like to discuss the further results of aalyzed decisio alteratives of implemetig ISO orms. As we metioed above i the previous chapters there is a costat pressure to the productio quality ad to the evirometal care. If we cosider developmet of market situatio it is legitimate to cosider the chage of the probabilities of states of ature i both decisio models. Table 15. EMV criterio values usig formula (3) EMV 1 114,8 A 2 EMV 2 136,24 A 3 EMV 3 132,4 P F. Possible further developmet of market situatio I the Czech Republic there is a give weight to Quality maagemet system ad to Evirometal maagemet system. The iitial probabilities were set as follows P = (0,1 0,3 0,4 0,1 0,1) It described a situatio where cosumers pay low-average attetio to ISO 9001 ad miimal to ISO Due to the icreasig amout of successful implemetatio of ISO (Table 7), the probabilities will be chaged toward the preferece of both ISO orms. Higher expectatio will be put to state of ature S4 (higher preferece, market requires ISO 9001 ad teds also oto ISO 14001) ad to state of ature S5 (absolute preferece, market requires both ISO 9001 ad ISO 14001). The ew estimatio of probabilities vector for descriptio of the future situatio could be estimated as follows P = (0,05 0,05 0,25 0,4 0,25) This chage leads to the differet result of both crisp ad fuzzy decisio-makig model which show the icreasig profit i relatio with ISO certificatio. Table 16. EMV criterio values for crisp ad fuzzy model Crisp model Fuzzy model EMV ,075 A 2 EMV 2 136,1 136,285 A 3 EMV 3 140,4 141,6 These results do ot chose as a best alterative A 2 (establish oly ISO 9001) which expected profit did ot be chaged. The alterative A 3 (establish ISO 9001 ad ISO 14001) becomes the best alterative because its expected profit is icreasig from 132 mil CZK to 140,4 resp. 141,6 mil CZK. We must also cosider that implemetatio ISO stadards is ot a easy ad cheap issue. Implemet both stadards would be difficult. So compaies who have already adopted Quality maagemet system (ISO 9001) should pay their attetio towards implemetatio of Evirometal maagemet system (ISO 14001). Compaies who have ot adopted the ISO 9001 yet, should pay their attetio towards the Quality maagemet system. VI. Coclusio This cotributio shows a applicatio of fuzzy decisiomakig model ad its compariso with classical decisiomakig model. The decisio-makig models were calculated for the real problem where Czech ICT compay wated to solve the ISO implemetatio problem. First model which was situated o the preset days give us for crisp ad fuzzy versio very similar results. The best alterative is A 2 - establish oly ISO The secod alterative A 3 could be also selected as a good oe if we cosider that the differece betwee these Issue 5, Volume 5,

9 two alteratives is ot sigificat. Due to the Czech icreasig umbers i ISO 9001 ad ISO certificatios we proceeded to modify the probability vector. The possibilities moved from lower costumer orietatios o ISO certificatio to the higher orietatio o both maagerial systems. After this modificatio as the best alterative was calculated by both form of models A 3 - establish ISO 9001 ad ISO with expected moetary value more tha 140 mil. CZK. Ad fially we ca say that the implemetatio (certificatio) of ISO 9001 ad ISO is gettig more ad more importat ad compaies without these certificatios will probably ot be successful i the ear future. It is ot certai what the future ecoomic treds will be but it is certai that the competitors will be stroger ad competitive advatage will play the mai role. Due to this coclusio compaies should focus o the implemetatio of system QMS ad EMS. We suppose further testig ad implemetig of soft decisio-makig models for solvig of various decisio problems. Especially we wat to adopt fuzzy pay-offs ad aalyze the differece amog models with fuzzy, probabilistic ad iterval pay-offs. We will also cosider additioal fuzzy iformatio. REFERENCES [1] Boii, Ch. P., Hausma, W. H., Bierma, H.: Quatitative aalysis for maagemet, Irwi, Bosto, [2] Brožová, H.: Applicatio of ordial iformatio i decisio models, I: Quatitative Methods i Ecoomics (Multiple Criteria Decisio Makig XI), Proceedigs of Iteratioal Coferece, ISBN , pp , SPU Nitra, [3] Brožová, H.: Decisio theory problems with iterval payoffs, I: Mathematical Methods i Ecoomics 2001, ISBN , pp , Hradec Králové, [4] Cagazzo, L., Taticchi, P., Fuiao, F.: Beefits, Barriers ad Pitfalls Comig from the ISO 9000 implemetatio: the impact o busiess performaces, WSEAS Trasactio o Busiess ad Ecoomics, Issue 4, Vol. 7, p. 10. ISSN [5] Casadesús, M., Marimo, F., Heras, I.: ISO diffusio after the success of the ISO 9001 model, J. of Cleaer Productio, 16, pp , Elsevier, [6] Elizabete, M., Seiffert, B.: Evirometal impact evaluatio usig a cooperative model for implemetig EMS (ISO 14001) i small ad medium-sized eterprises, J. of Cleaer Productio, 16, pp , Elsevier, [7] Flégl, M.: Rozhodovací modely s fuzzy ohodoceím (Decisio models with fuzzy evaluatio), Diploma thesis. Czech Uiversity of Life Scieces, Prague, [8] Flégl, M., Brožová, H.: Decisio makig models with fuzzy values, I: Mathematical Methods i Ecoomics 2010, České Buděovice, 2010, ISBN , pp [9] Flégl, M., Brožová, H.: Fuzzy Decisio-Makig for Implemetig ISO 9001 ad/or ISO 14001, I: WSEAS Proceedigs: Mathematics ad Computers i Biology, Busiess ad Acoustics, pp , ISBN: [10] ISO. The ISO survey Geeva: ISO. upublished [11] Lee, S.-C.: The Study of ISO 9001 Processes as basis for busiess explicit kowledge, WSEAS Trasactio o Busiess ad Ecoomics, Issue 12, Vol. 6, p. 10. ISSN [12] Pekovic, S., Galia, F.: From quality to iovatio: evidece from two Frech employer surveys, Techovatio, 29, pp , Elsevier, [13] Pitra, Z.: Maagemet iovačích aktivit, Professioal Publishig, [14] Raiffa, H.: Decisio aalysis: itroductory readigs o choices uder iucertaity. McGraw Hill ISBN X [15] Ross, T. J.: Fuzzy logic with egieerig applicatios. 2d editio. Chichester : Wiley, p. ISBN [16] Sambasiva, M., Fei, N.-Y.:. Evaluatio of critical success factors of implemetatio of ISO 14001usig aalytic hierarchy process (AHP): A case study from Malaysia, J. of Cleaer Productio, 16, pp , Elsevier, [17] Shelto, R. B.: Gamig the market: applyig game theory to create wiig tradig strategies, Wiley Fiace, Joh Wiley ad Sos, [18] Sirbiladze, G., Ghvaberidze, B., Sikharulidze, A., Matsaberidze, B., Devadze, D.: Fuzzy coverig ad partitioig problems based o the expert valuatios: applicatio i optimal choice of cadidates, WSEAS Trasactio o Iformatio Sciece ad Applicatios, Issue 11, Vol. 6, 2009, pp , ISSN: [19] Státí politika životího prostředí České republiky ( ), (Natioal evirometal policy of the Czech Republic), Praha: Miisterstvo životího prostředí, p. ISBN [20] Šadr, I., Hercík, P., Vítková, R., Petříková, R., Vápeíček, A.: Efektivost certifikovaých systémů, (Efectivity of certificated systems), Praha, Národí iformačí středisko pro podporu akosti, p. ISBN [21] Veber, J., Plášková, A., Hůlová, M..: Maagemet kvality, evirometu a bezpečosti práce : Legislativa, metody, systémy, praxe. 2. (Maagemet of quality, eviromet ad work safety: Legislatio, methods, practice), Praha: Maagemet Press, p. ISBN Marti Flégl has obtaied his Master Degree i Systems Egieerig at Faculty of Ecoomics ad Maagemet, Czech Uiversity of Life Scieces Prague. He studied at ESDES busiess school i Lyo as well. Curretly he is a Ph.D. studet at Czech Uiversity of Life Scieces Prague at the Departmet of Systems Egieerig. His research area icludes Decisio-Makig Models, Fuzzy Logic ad Quatitative Methods i Ecoomy ad Maagemet. He is a member of Czech Society for Operatioal Research. Helea Brožová, Ass. Prof. She obtaied her Master Degree i Operatios Research ad Maagemet Theory at the Faculty of Mathematics ad Physics, Charles Uiversity i Prague, Ph.D. Degree i Ecoomics at the Faculty of Ecoomics ad Maagemet, Czech Uiversity of Life Scieces (DSE FEM CULS). She is the Assistat professor i Systems Egieerig. She works at the DSE FEM CULS (former Uiversity of Agriculture). She teaches may subects as Mathematical Methods i Ecoomics, Supply Chais Maagemet, Multiple Criteria Decisio-makig, System Theory ad Applied System Sciece, ad Decisio Support Systems. Her research area cosists of practical implemetatio of Operatios Research ad System Scieces, ad especially cocers of processes of Multiple Criteria Decisio Makig ad Decisio-Makig models. She is a member of Czech Society of Operatio Research ad Iteratioal Society of Multiple Criteria Decisio Makig. She is a member of the proect team for the scietific proect Iformatio ad Kowledge Support of Strategic Maagemet. Issue 5, Volume 5,