Research Article An Approach to Evaluating Computer Network Security with Intuitionistic Trapezoidal Fuzzy Information

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1 Joural of Cotrol Sciece ad Egieerig, Article ID , 4 pages Research Article A Approach to Evaluatig Computer Network Security with Ituitioistic Trapezoidal Fuzzy Iformatio Mig Xue Hea Uiversity of Techology, Zhegzhou, Hea , Chia Correspodece should be addressed to Mig Xue; xuemig11980@163.com Received 29 Jue 2014; Accepted 9 July 2014; Published 17 July 2014 Academic Editor: Xiaofei Zhao Copyright 2014 Mig Xue. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. We ivestigate the multiple attribute decisio-makig problems for evaluatig the computer etwork security with ituitioistic trapezoidal fuzzy iformatio. We utilize the ituitioistic trapezoidal fuzzy weighted average (ITFWA) operator to aggregate the ituitioistic trapezoidal fuzzy iformatio correspodig to each alterative ad get the overall value of the alteratives ad the rak the alteratives ad select the most desirable oe(s) accordig to the distace betwee the overall value of the alteratives ad ideal solutio. Fially, a illustrative example for evaluatig the computer etwork security is give. 1. Itroductio With sciece ad techology developmet, computer techology improves costatly ad more ad more software ad hardware of educatio idustry have appeared 1. Uses i educatig the professio especially the software ad the hardware appear oe after aother, have brought a lot of coveiece for the school teachig maagemet, ad simultaeously have also provided may coveiet coditios for teacher s ad studet s daily life. The applicatio of these hightechs i the school coveiet for the educatioal circles also gave the educatioal circles a questio about the safety of the iformatio maagemet; the etwork security questio has become a ew questio to educatioal circles 2, 3. As a result of a oe-card appearace, the school has applied this techology i the first time. It provides the coveiece for both teachers ad studets. Meawhile, the school also must cosider the safety of the card. The ehacemet of etwork ad the server security is the most importat thig for schools. These high-techs, for example, multimedia slides, etwork iformatio, laser projectio, ad so o, brig about ew breakthrough to school educatio. The emergece of oe-card also as the educatio sector developmet has played a role ad sigificatly improved the maagemet of schoolsivariousfields4. The appearace of the card has solved a lot of igglig problems ad makes the campus cosumptios more coveiet. A card ca be slippery i school, ad it also facilitates schools i wealth maagemet. The developmet of the educatio sector is affected by the techical implicatios ad also costraied by ecoomic coditios, particularly those three-table istitutios or ogovermetal istitutios. They strive to build a moder campus ad, therefore, will ot abado advaced techology to serve schools. However, due to shortage of fuds, schools are ofte just goig to the applicatio but did ot cosider the quality ad future problems. I the teder, as log as the low price of whom, let someoe to do the costructio, this is wrog. For moder campus, improvig the techology is right, but it is also eeded to cosider the questio of safety ad quality, especially oe-card; security is aparticularlyimportatproblemwhichcaotbeigored. The author participated i a oe-card case of a uiversity ad is resposible for the costructio of a hardware ad server teder selectio ad purchasig also the maiteace work later. But due to the problem of school fuds, this makes some very good compaies usuccessful ad the midrage be elected. The author also wet to a survey of may istitutios admadearesearchabouttheoperatioofthecampuscard ad the cooperatios of those uiversities. All the istitutios the author picked are capable; they oly cosider the quality ottheprice.tomakethecardmoresecureforourschool, the author got the school s secret istructios ad carried

2 2 Joural of Cotrol Sciece ad Egieerig out mock attacks i order to detect the oe-card server backgroud security issues. Although we spet less moey, to require security comes first. Oly school leadership ad the direct leadership kow about this actio. Sice those IP ad scree shots i the papers are ot real, they are very similar. Thistaskistobepossibletocotrolalloftheservers,so we ca require developers to do the upgrade or debuggig, guaratee the safety of the school etwork server, ad make future work be well prepared 5.This school cotais campus etwork, oe-card service, postal savigs, ad other fiacial systems. All of these four systems are i oe etwork, so the security is the most importat thig. The iformatio o the etwork is real moey; if ay problem occurs, the cosequece will be uable to be estimated. With the fast developmet of Iteret techologies recetly, computer etworks have played a icreasigly importat role i the fields of politics, ecoomy, military, ad social life. Although etwork techologies brig about edless coveiece for people s lifeadwork,theopeessaditercoectioofetworks make etwork attacks become more uiversal, ad etwork security problems have attracted wide attetio. Risk always exists i the real etwork eviromet. I order to esure ormal operatio of etworks, hidde troubles i etworks must be idetified ad aalyzed, ad proper measures must be adopted to decrease the risk accordig to aalysis results. Therefore, how to accurately evaluate the security of a etwork becomes a importat problem, ad it has bee oe of the research focuses i the field of etwork security 6. Hao ad Li 7 proposed a ew sortig method which used the possible degree matrix to solve the sortig problem of ituitioistic trapezoidal fuzzy umbers. Wag 8 reviewed the curret research o the multicriteria liguistic decisio-makig methods ad fuzzy multicriteria decisiomakig methods based o fuzzy umber, ituitioistic fuzzy set, ad vague set ad the proposed the defiitio of ituitioistic trapezoidal fuzzy umbers ad iterval ituitioistic trapezoidal fuzzy umber. Wag ad Zhag 9proposed a multicriteria decisio-makig approach for multicriteria decisio-makig problems i which weight iformatio was ot completely kow ad the criteria values were ituitioistic trapezoidal fuzzy umbers. Wa ad Dog 10 studied the multiattribute group decisio-makig method based o ituitioistic trapezoidal fuzzy umbers. Firstly, the expectatios ad the expected score of ituitioistic trapezoidal fuzzy umber were defied based o the fuctio of the gravity ceter of the image. Secodly the IT-OWA ad IT- HA operators were proposed. Based o these operators, the multiattribute group decisio-makig method based o ituitioistic trapezoidal fuzzy umber was preseted. Wag et al. 11 proposed the ituitioistic trapezoidal fuzzy geometric aggregatio operators,icludig the ituitioistic trapezoidal fuzzy weighted geometric (IT-WG) operator, ituitioistic trapezoidal fuzzy ordered weighted geometric (IT-OWG) operator, ad ituitioistictrapezoidal fuzzy hybrid geometric (IT-HG) operator. The the multicriteria decisiomakigmethodbasedotheaggregatiooperatorswas proposed.wuadliu12proposedtheiterval-valuedituitioistic trapezoidal fuzzy weighted geometric (IVITFWG) operator, the iterval-valued ituitioistic trapezoidal fuzzy ordered weighted geometric (IVITFOWG) operator, ad the iterval-valued ituitioistic trapezoidal fuzzy hybrid geometric (IVITFHG) operator. Wu ad Cao 13 ad Wei et al. 14 proposed the iterval ituitioistic trapezoidal fuzzy weighted geometric (IITFWG) operator, the iterval ituitioistic trapezoidal fuzzy ordered weighted geometric (IIT- FOWG) operator, ad iterval ituitioistic trapezoidal fuzzy hybrid geometric (IITFHG) operator, ad based o these operators, a ew decisio-makig method was preseted to solve the MAGDM problems i which attribute values take the form of iterval ituitioistic trapezoidal fuzzy umbers. I this paper, we ivestigate the multiple attribute decisio-makig problems for evaluatig the computer etwork security with ituitioistic trapezoidal fuzzy iformatio. We utilize the ituitioistic trapezoidal fuzzy weighted average (ITFWA) operator to aggregate the ituitioistic trapezoidal fuzzy iformatio correspodig to each alterative ad get the overall value of the alteratives ad the rak the alteratives ad select the most desirable oe(s) accordig to thedistacebetweetheoverallvalueofthealterativesad ideal solutio. Fially, a illustrative example for evaluatig the computer etwork security is give. 2. Prelimiaries I the followig, we will itroduce some basic cocepts related to ituitioistic trapezoidal fuzzy umbers. Defiitio 1. Let a be a ituitioistic trapezoidal fuzzy umber; its membership fuctio is 9, 15 x a b a μ a, a x<b; { μ a, b x c; μ a (x) d x { d c μ a, c<x d; { 0, others. Its omembership fuctio is b x+ a (x a 1 ), a b a 1 x<b; 1 { a, b x c; a (x) x c+ a (d 1 x), c<x d { d 1 c 1 ; { 0, others, where 0 μ a 1; 0 a 1;adμ a + a 1; a, b, c, d R. I the followig, Wei developed a ew operator called ituitioistic trapezoidal fuzzy weighted average (ITFWA) operator 16. Defiitio 2 (see 16). Let a j (a j,b j,c j,d j ; μ aj, aj ) (j 1,2,...,) be a collectio of ituitioistic (1) (2)

3 Joural of Cotrol Sciece ad Egieerig 3 trapezoidalfuzzy umbers, ad let ITFWA: Q Q, if ITFWA ω ( a 1, a 2,, a ) (ω j a j ) ( ω j a j, 1 ω j b j, (1 μ aj ) ω j, ω j c j, ω j d j ; ( aj ) ω j), where ω(ω 1,ω 2,...,ω ) T is the weight vector of a j (j 1,2,...,)adω j 0, ω j 1; the ITFWA is called the ituitioistic trapezoidal fuzzy weighted average (ITFWA) operator. Defiitio 3 (see 16). For a ormalized ituitioistic trapezoidal fuzzy decisio-makig matrix R ( r ij ) m (a ij,b ij,c ij,d ij ; μ ij, ij ) m,where0 a ij b ij c ij d ij 1, 0 μ ij, ij 1,0 μ ij + ij 1, the ituitioistic trapezoidal fuzzy positive ideal solutio is defied as follows: (3) r + (a +,b +,c +,d + ;μ +, + ) (1, 1, 1, 1 ;1,0). (4) Defiitio 4 (see 16). Let a 1 (a 1,b 1,c 1,d 1 ; μ a1, a1 ) ad a 2 (a 2,b 2,c 2,d 2 ; μ a2, a2 ) be two ituitioistic trapezoidal fuzzy umbers; the the ormalized Hammig distace betwee a 1 ad a 2 is defied as follows: d( a 1, a 2 ) 1 8 ( (1 + μ a 1 a1 )a 1 (1+μ a2 a2 )a 2 a1 )b 1 (1+μ a2 a2 )b 2 a1 )c 1 (1+μ a2 a2 )c 2 a1 )d 1 (1+μ a2 a2 )d 2 ). (5) 3. Numerical Example With the popularizatio of computer techology, etwork provides great impetus for the advacemet of society. However, the developmet of the etwork techology faces great challeges uder the uceasig rigorous etwork situatio, ad traditioal sigle-poit heterogeeous security defese techologies, such as IDS, Firewall, ad VPN, ca ehace security performace of etwork system to a certai degree, amog which lack of effective collaboratio leads to beig uable to moitor the whole etwork security situatio. Uder this circumstace, the research about etwork security situatio awareess (NSSA) has upper academic valueadcomprehesivepracticalvalue.buttheresearches related to NSSA are still far away from maturatio at the preset. Most of the situatio awareess models are based o sigle-source eviromet; quatificatio awareess methods maily deped o quatifyig the raw alerts of the security sesor ad they caot actualize the awareess of attack steps ad sequeces. The research about situatio evaluatio maily focuses o the costructio of idex systemadislackofdeepstudyievaluatiomodelad method. This sectio presets a umerical example to evaluate the computer etwork security with ucertai liguistic iformatio to illustrate the method proposed i this paper. There are five possible computer etwork systems A i (i 1, 2, 3, 4, 5) forfourattributesg j (j 1, 2, 3, 4). The four attributes iclude the tactics (G 1 ), techology ad ecoomy (G 2 ), logistics (G 3 ), ad strategy (G 4 ), respectively. The five possible computer etwork systems A i (i 1,2,...,5)are to be evaluated usig the ituitioistic trapezoidal fuzzy iformatio by the decisio maker uder the above four attributes whose weightig vector ω (0.3, 0.2, 0.1, 0.4) T,as listed i the followig matrix R (0.5, 0.6, 0.7, 0.8 ; 0.5, 0.4) (0.6, 0.7, 0.8, 0.9 ; 0.7, 0.3) (0.1, 0.2, 0.4, 0.5 ; 0.6, 0.4) (0.3, 0.4, 0.5, 0.6 ; 0.8, 0.1) (0.2, 0.3, 0.4, 0.5 ; 0.6, 0.2) (0.1, 0.2, 0.3, 0.4 ; 0.6, 0.3) (0.5, 0.6, 0.7, 0.8 ; 0.7, 0.2) (0.2, 0.3, 0.5, 0.6 ; 0.5, 0.4) (0.1, 0.3, 0.4, 0.5 ; 0.6, 0.3) (0.3, 0.4, 0.5, 0.6 ; 0.4, 0.3) (0.5, 0.6, 0.8, 0.9 ; 0.3, 0.6) (0.4, 0.5, 0.7, 0.8 ; 0.7, 0.2) (0.5, 0.6, 0.7, 0.8 ; 0.5, 0.3) (0.1, 0.3, 0.5, 0.7 ; 0.3, 0.4) (0.2, 0.3, 0.4, 0.5 ; 0.7, 0.1) (0.4, 0.5, 0.6, 0.7 ; 0.2, 0.7) (0.5, 0.6, 0.7, 0.9 ; 0.4, 0.5) (0.3, 0.5, 0.7, 0.9 ; 0.2, 0.3) (0.6, 0.7, 0.8, 0.9 ; 0.2, 0.6) (0.5, 0.6, 0.7, 0.8 ; 0.1, 0.3). (6) The, we utilize the approach developed to get the most desirable computer etwork system(s). Step 1. Utilize the weight vector ω (0.3, 0.2, 0.1, 0.4) T,ad by (3), we obtai the overall values r i of the computer etwork systems A i (i 1, 2, 3, 4, 5): r 1 (0.37, 0.46, 0.65, 0.71 ; , ), r 2 (0.46, 0.52, 0.66, 0.84 ; , ), r 3 (0.30, 0.43, 0.61, 0.72 ; , ), r 4 (0.22, 0.43, 0.51, 0.67 ; , ), r 5 (0.23, 0.35, 0.42, 0.51 ; , ). Step 2. Calculate the distaces betwee overall values r i (a i,b i,c i,d i ; μ i, i ) ad ituitioistic trapezoidal fuzzy (7)

4 4 Joural of Cotrol Sciece ad Egieerig positive ideal solutio r + (a +,b +,c +,d + ; μ +, + ) (1, 1, 1, 1; 1, 0): d( r 1, r + ) , d ( r 2, r + ) , d( r 3, r + ) , d ( r 4, r + ) , d( r 5, r + ) Step 3. Rak all the alteratives A i (i 1, 2, 3, 4, 5) i accordace with the distaces d( r i, r + ) betwee overall values r i (a i,b i,c i,d i ; μ i, i ) ad ituitioistic trapezoidal fuzzy positive ideal solutio: A 2 A 3 A 5 A 4 A 1,adthus the most desirable computer etwork system is A Coclusio Computer etwork security assessmet is a active security techology, which ca make etwork iformatio system more secure ad robust. Takig so may security factors such as threats, assets, ad vulerabilities ito accout, the computer etwork security assessmet techology ca help admiistrators take a active attitude to idetify those potetial threats that their systems will be exposed to. Now it has become the fudametal work ad the key lik for the atioal iformatio assurace framework. Whe we rely moreadmoreotheworldofiteretdaybyday,research o etwork iformatio risk assessmet will be oe of the research focuses i the etwork security field. The research of this dissertatio focuses o the quatitative methodologies of the etwork security assessmet. I this paper, we ivestigate the multiple attribute decisio-makig problems for evaluatig the computer etwork security with ituitioistic trapezoidal fuzzy iformatio. We utilize the ituitioistic trapezoidal fuzzy weighted average (ITFWA) operator to aggregate the ituitioistic trapezoidal fuzzy iformatio correspodig to each alterative ad get the overall value of the alteratives ad the rak the alteratives ad select the most desirable oe(s) accordig to the distace betwee theoverallvalueofthealterativesadidealsolutio.fially, a illustrative example for evaluatig the computer etwork security is give. Coflict of Iterests The author declares that there is o coflict of iterests regardig the publicatio of this paper. Refereces (8) ad ACO, Iteratioal Joural o Advaces i Iformatio Scieces ad Service Scieces,vol.5,o.1,pp , Y. Li, J. Yi, ad G. Wu, Model for evaluatig the computer etwork security with iterval-valued ituitioistic fuzzy iformatio, Iteratioal Joural of Digital Cotet Techology ad Its Applicatios,vol.6,o.6,pp , J. Dog, A approach to evaluatig the computer etwork security with hesitat fuzzy iformatio, Iteratioal Joural of Digital Cotet Techology ad Its Applicatios,vol.6,o.20, pp , Y.Li,X.Sha,adG.Wu, Comprehesiveevaluatiomodel for computer etwork security with liguistic iformatio, Advaces i Iformatio Scieces ad Service Scieces,vol.3,o. 9, pp , F.L.HaoadD.Q.Li, Aewrakigmethodoffuzzyumbers, Joural of Ordace Egieerig College,vol.19,pp.73 75, J. Q. Wag, Overview o fuzzy multi-criteria decisio-makig approach, Cotrol ad Decisio,vol.23,pp , J. Q. Wag ad Z. Zhag, Multi-criteria decisio-makig method with icomplete certai iformatio based o ituitioistic fuzzy umbers, Cotrol ad Decisio, vol. 24, o. 2, pp , S. P. Wa ad J. Y. Dog, Method of the ituitioistic trapezoidal fuzzy umber for multi-attribute group decisio, Cotrol ad Decisio,vol.25,o.5,pp , Y. Wag, S. F. Zhag, ad S. Q. Xie, Ituitioistic trapezoidal fuzzy geometric aggregatio operators ad their applicatio to group decisio makig, Value Egieerig,vol.27,pp , J. Wu ad Y. Liu, A approach for multiple attribute group decisio makig problems with iterval-valued ituitioistic trapezoidal fuzzy umbers, Computers & Idustrial Egieerig,vol.66,pp , J. Wu ad Q. Cao, Same families of geometric aggregatio operators with ituitioistic trapezoidal fuzzy umbers, Applied Mathematical Modellig,vol.37,o.1-2,pp , G. Wei, X. Zhao, ad H. Wag, A approach to multiple attribute group decisio makig with iterval ituitioistic trapezoidal fuzzy iformatio, Techological ad Ecoomic Developmet of Ecoomy,vol.18,o.2,pp , J. Wag ad Z. Zhag, Programmig method of multi-criteria decisio-makig based o ituitioistic fuzzy umber with icomplete certai iformatio, Cotrol ad Decisio, vol.23, o. 10, p. 1145, G. Wei, Some arithmetic aggregatio operators with ituitioistic trapezoidal fuzzy umbers ad their applicatio to group decisio makig, Joural of Computers, vol.5,o.3,pp , X. Mo, Research o the computer etwork security evaluatio based o the ULCGM operator with ucertai liguistic iformatio, Joural of Covergece Iformatio Techology,vol.8, o. 3, pp , G. Zhag, H. Li, R. Che et al., Research ad desig o vulerability testig i computer etwork security system, Advaces i Iformatio Scieces ad Service Scieces,vol.5,o. 7, pp. 1 10, G. Sog, Computer etwork security ad precautio evaluatio based o icremetal relevace vector machie algorithm

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