An Approach to Evaluating the Computer Network Security with Hesitant Fuzzy Information

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1 A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog, Frst ad Correspodg Author Ceter for Educato Techology, Zheag Iteratoal Studes Uversty, Hagzhou, 300, Cha, E-mal: dogf977@gmal.com Abstract The problem of evaluatg the computer etwork securty wth hestat fuzzy formato s the multple attrbute decso makg (MADM) problems. I ths paper, we vestgate the multple attrbute decso makg (MADM) problems for evaluatg the computer etwork securty wth hestat fuzzy formato. The, we utlze the hestat fuzzy geometrc Boferro mea (HFGBM) operator to aggregate the hestat fuzzy formato, the rak the alteratves ad select the most desrable oe(s) accordg to the score fucto. Fally, a llustratve example demostrates the practcalty ad effectveess of the proposed method. Keywords: Multple Attrbute Decso Makg (MADM), Hestat Fuzzy Iformato, Hestat Fuzzy Geometrc Boferro Mea (HFGBM) Operator, Computer Network Securty. Itroducto The tradtoal etwork securty techques have show ther drawbacks the creasgly complex ad severe etwork securty evromet. The truso detecto tools ca oly delver alerts o lmted kowledge of attacks, whle the alert stream s always poor qualty ad ca easly be overwhelmg, whch makes t very hard to kow how much threat the detected attacks pose to the etwork ad whch securty states the hosts are. Meawhle, the tradtoal securty assessmet approaches ca ot assess the real tme securty stuato. These problems make the securty operators very dffcult to kow the curret securty threat ad stuato by the tradtoal securty tools. Network securty threat ad stuato assessmet ams to extract kowledge of curret securty threat ad stuato from raw securty data reported by tradtoal securty tools, through the techques of data fuso, ad predct the future securty stuato based o hstorcal securty formato ad the preset attacks. Ths paper studed the approaches of threat assessmet, stuato assessmet ad stuato predcto. The threat of a etwork attack s determed by sx aspects of factor: attack severty, attack evromet, probablty to succeed, statstcal factors, correlato factors ad attack effect. Based o ths cocluso, a framework to threat assessmet s proposed, whch comprses of sx steps. The approaches of every step are troduced the paper ad mplemeted SATA (Securty Alert ad Threat Aalyss) system. The approach of qualtatve attack hazard gradato ad the CVSS mechasm are used severty assessmet. The values of assets ad securty polces are set to evaluate the evrometal factors[-5]. The Bayesa Network s used to calculate the relablty of the alerts. I statstcal assessmet, a ovel approach s proposed to fd the perodcty of alerts based o tme seres aalyss techques. A laguage of alert correlato s mplemeted the system. Ad a expermet of qualtatve attack effect assessmet s troduced. HMM (Hdde Markov Model) s used to assess the etwork securty stuato. The problems of observato evet classfcato ad parameter cofgurato lyg the approach are solved. To the frst problem, the result of threat assessmet s used to classfy the alerts based o ther threat scores, whch ca lmt the scale of the observato matrx of HMM ad mprove the accuracy of observato classfcato. To the latter, the geetc programmg algorthm s used. A mechasm of quattatvely evaluatg the ftess of stuato assessmet result s proposed. A set of rsk descrpto rules are defed ad the matchg degree betwee the result of stuato assessmet ad rules s calculated, whch determes the ftess of the result. The hoey et alerts are used to costruct rsk descrpto rule set. The comparatve tests valdated the effectveess of the approach. Fve characterstcs of the etwork stuato predcto problem are defed: ) there s relatoshp of causalty betwee the future attacks ad the past attacks; ) the possblty of dfferet attack types to have followg attacks are dfferet; 3)the evdece of Iteratoal Joural of Dgtal Cotet Techology ad ts Applcatos(JDCTA) Volume6,Number0,November 0 do:0.456/dcta.vol6.ssue

2 A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog future attacks ca reflect mportat formato of future attacks by tself; 4) the attack pla ca be recogzed based o the accumulato of evdece; 5)there s relatoshp betwee the evdece of future attacks ad the tred of etwork stuato. Based o the characterstcs, a approach to stuato predcto s proposed. Frst, the evdece of future attacks s extracted from IDS alerts accordg to the attack sequece patters ad the predctablty of attack types. The predctablty of attack types represets the possblty of the attacks to be the evdece of future attacks. The attack sequece patters are geerated by a data mg algorthm. The the future securty stuato ca be predcted based o the evdece. D-S evdece theory s used for pla recogto, ad the HMM model betwee the evdece ad the tred of securty stuato s costructed to predct the probablty dstrbuto of future securty states. The expermet wth DARPA data sets shows the effectveess of the approach[5-]. The problem of evaluatg the computer etwork securty wth hestat fuzzy formato s the multple attrbute decso makg (MADM) problems.the am of ths paper s to vestgate the MADM problems for evaluatg the computer etwork securty wth hestat fuzzy formato. The, we utlze the hestat fuzzy geometrc Boferro mea (HFGBM) operator to aggregate the hestat fuzzy formato, the rak the alteratves ad select the most desrable oe(s) accordg to the score fucto. The remader of ths paper s set out as follows. I the ext secto, we troduce some basc cocepts related to hestat fuzzy sets. I Secto 3 we troduce the MADM problem to evaluate the computer etwork securty wth hestat fuzzy formato, whch the formato about attrbute weghts s correlatve, ad the attrbute values take the form of hestat fuzzy formato. The, we utlze the hestat fuzzy geometrc Boferro mea (HFGBM) operator to aggregate the hestat fuzzy formato, the rak the alteratves ad select the most desrable oe(s) accordg to the score fucto. I Secto 4, a llustratve example s poted out. I Secto 5 we coclude the paper ad gve some remarks.. Prelmares Boferro [] orgally troduced a mea type aggregato operator, called Boferro mea, whch ca provde for aggregato lyg betwee the max, m operators ad the logcal or ad ad operators, whch was defed as follows: Defto 4[]. Let, 0 The the aggregato fuctos: pq ad a,,, be a collecto of o-egatve real umbers. p q BM a, a,, a a a (3), are called the Boferro mea (BM) operator. Zhu et al. [3] further troduced a mea type aggregato operator, called geometrc Boferro mea, whch ca provde for aggregato lyg betwee the max, m operators ad the logcal or ad ad operators, whch was defed as follows: Defto 4[3]. Let, 0 The the aggregato fucto: pq ad a,,, pq be a collecto of o-egatve real umbers. 634

3 A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog GBM a a a pa qa p q,,, (3) s called the geometrc Boferro mea (GBM) operator. Recetly, Torra [4] orgally developed the hestat fuzzy set whch covers argumets wth a set of possble values: Defto []. Gve a fxed set X, the a hestat fuzzy set (HFS) o X s terms of a fucto that whe appled to X returs a suset of 0,. To be easly uderstood, Xu ad Xa[5] express the HFS by mathematcal symbol: where elemet x, E, E xh x x X, (4) he x s a set of some values X to the set E. For coveece, Xu ad Xa[5,6] call h h x 0,, deotg the possble membershp degree of the E a hestat fuzzy elemet(hfe) ad H the set of all HFEs. I mult-crtera decso makg, the performace of a alteratve uder a crtero may be represeted by several possble values. To aggregate all the possble values of a alteratve uder the crtera, Zhu et al.[3] gve a exteso of the GBM, whch s defed as follows: h,,, be a collecto of HFEs, ad let 0. If Defto 8. Let HFGBM h, h,, h, ph qh ph qh p q (8) the HFGBM s called the hestat fuzzy geometrc Boferro mea (HFGBM) operator. Based o the operatos laws of the hestat fuzzy values descrbed, we ca drve the Theorem [3]. Theorem. Let h,,, be a collecto of HFEs, the ther aggregated value by usg the HFGBM operator s also a HFE, ad,,, ph qh ph qh HFGBM h h h p q,,, pq (9) 635

4 A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog ca be cosdered as the bodg satsfacto factor where, ph qhph qh used as a calculato ut, capturg the coecto betwee h ad h,,,,, ;, the HFGBM s called the hestat fuzzy geometrc Boferro mea (HFGBM) operator. It ca be easly proved that the HFGBM operator has the followg propertes[3]. Theorem. (Idempotecy) If all h,,, are equal,.e. h h for all, the HFGBM h, h,, h h Theorem 3. (Boudedess) Let h,,, (0) be a collecto of HFEs, ad let The h m h, max h h h HFGBM h, h,, h h () Theorem 4. (Mootocty) Let h,,, ad h,,, be two set of HFEs, f h h, for all, the pq HFGBM h,, h,, h HFGBM h, h,, h () Theorem 5. (Commutatvty) Let h,,, ad h,,, the be two set of HFEs,,,, pq,,, pq HFGBM, h h h HFGBM, h h h where h,,, s ay permutato of h,,, (8). 3. A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato The problem of evaluatg the computer etwork securty wth hestat fuzzy formato s the multple attrbute decso makg (MADM) problems. The followg assumptos or otatos are used to represet the MADM problems for evaluatg the computer etwork securty wth hestat fuzzy formato. Let A A, A,, Am be a dscrete set of alteratves, ad G G, G,, G be the state of ature. If the decso makers provde several values for the alteratve A uder the state of ature G wth aoymty, these values ca be cosdered as a hestat fuzzy elemet h. I the case where two decso makers provde the same value, the the value h. Suppose that the decso matrx H h emerges oly oce s the hestat fuzzy decso m matrx, where h,,, m,,,, are the form of HFEs. I the followg, we apply the HFGBM operator to MADM for evaluatg the computer etwork securty wth hestat fuzzy formato. 636

5 A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog Step. Utlze the decso formato gve matrx R, ad the HFGBM operator ( geeral, we ca take p q ) r HFGBM r, r,, r pr k qrk prk qrk pq,,, to derve the overall values r,,, mof the alteratve A. Step. Calculate the scores Sr,,, m values r,,, mto rak all the alteratves A,,, m oe(s). Step 3. Rak all the alteratves A,,, m Sr,,, m. Step 4. Ed. 4. Numercal example pq, k,,, m. () of the collectve overall hestat fuzzy preferece ad the to select the best ad select the best oe(s) accordace wth Ths secto presets a umercal example to evaluate the computer etwork securty wth hestat fuzzy formato to llustrate the method proposed ths paper. There are fve possble computer etwork systems A,, 3, 4,5 for four attrbutes,, 3, 4 attrbutes clude the tactcs G, techology ad ecoomy G, logstcs 3 G 4 evaluate the fve possble computer etwork systems,,, 5 G. The four G ad strategy, respectvely. I order to avod fluece each other, the decso makers are requred to H h h,,3, 4,,,3, 4 are the form of HFEs. aoymty ad the decso matrx 44 where A uder the above four attrbutes s preseted Table, Table. Hestat fuzzy decso matrx G G G 3 G 4 A (0.4,0.3) (0.,0.,0.3) (0.5,0.6) (0.,0.5) A (0.5,0.7) (0.5,0.7) (0.4,0.5) (0.7,0.8,0.9) A 3 (0.8,0.9) (0.8,0.9) (0.3, 0.4,0.5) (0.3, 0.4,0.5) A 4 (0.7,0.8) (0.4,0.5) (0.5, 0.7) (0.6, 0.7,0.8) A 5 (0.4,0.7) (0.6,0.9) (0.3, 0.5) (0.5, 0.7) 637

6 A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog The, we utlze the approach developed to get the most desrable computer etwork systems. Step. We utlze the decso formato gve matrx H, ad the HFGBM operator to obta the overall preferece values h of the alteratves A,, 3, 4. Take computer etwork systems A for a example, we have h HFGBM r, r,, r 4 HFGBM 0.4,0.3, 0.,0.,0.3, 0.5,0.6, 0.,0.5 4 pr k qrk prk qrk p q, pq 4,, 0.55,0.5457,0.5845,0.6036,0.645,0.676,0.6376,0.6498,0.6499,0.6543,0.6658,0.6787, 0.695,0.7043,0.74,0.736,0.7345,0.7497,0.7567,0.7587,0.7598,0.7647,0.7897, Step. Calculate the scores,,3, 4,5 h,,3, 4,5 : s h of the overall hestat fuzzy values , sh s h 0.76, s h , s h s h 4 5 Step 3. Rak all the computer etwork systems,, 3, 4,, 3, 4 A accordace wth the scores s h of the overall hestat fuzzy values: A3 A5 A A A4, ad thus the most desrable computer etwork system s A Cocluso The problem of evaluatg the computer etwork securty wth hestat fuzzy formato s the multple attrbute decso makg (MADM) problems. I ths paper, we vestgate the multple attrbute decso makg (MADM) problems for evaluatg the computer etwork securty wth hestat fuzzy formato. The, we utlze the hestat fuzzy geometrc Boferro mea (HFGBM) operator to aggregate the hestat fuzzy formato, the rak the alteratves ad select the most desrable oe(s) accordg to the score fucto. Fally, a llustratve example demostrates the practcalty ad effectveess of the proposed method. 6. Refereces [] Duol Lu, "E-commerce System Securty Assessmet Based o Grey Relatoal Aalyss Comprehesve Evaluato", JDCTA: Iteratoal Joural of Dgtal Cotet Techology ad ts Applcatos, Vol. 5, No. 0, pp ,

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