Research Article An Approach to Evaluating Computer Network Security with Intuitionistic Trapezoidal Fuzzy Information Ming Xue Henan University of Technology, Zhengzhou, Henan 450001, China Correspondence should be addressed to Ming Xue; [email protected] Received 29 June 2014; Accepted 9 July 2014; Published 17 July 2014 Academic Editor: Xiaofei Zhao Copyright © 2014 Ming Xue. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the multiple attribute decision-making problems for evaluating the computer network security with intuitionis- tic trapezoidal fuzzy information. We utilize the intuitionistic trapezoidal fuzzy weighted average (ITFWA) operator to aggre- gate the intuitionistic trapezoidal fuzzy information corresponding to each alternative and get the overall value of the alternatives and then rank the alternatives and select the most desirable one(s) according to the distance between the overall value of the alternatives and ideal solution. Finally, an illustrative example for evaluating the computer network security is given. 1. Introduction With science and technology development, computer tech- nology improves constantly and more and more soſtware and hardware of education industry have appeared [1]. Uses in educating the profession especially the soſtware and the hardware appear one aſter another, have brought a lot of convenience for the school teaching management, and simul- taneously have also provided many convenient conditions for teacher’s and student’s daily life. e application of these high- techs in the school convenient for the educational circles also gave the educational circles a question about the safety of the information management; the network security question has become a new question to educational circles [2, 3]. As a result of a one-card appearance, the school has applied this technology in the first time. It provides the convenience for both teachers and students. Meanwhile, the school also must consider the safety of the card. e enhancement of network and the server security is the most important thing for schools. ese high-techs, for example, multimedia slides, network information, laser projection, and so on, bring about new breakthrough to school education. e emergence of one-card also as the education sector development has played a role and significantly improved the management of schools in various fields [4]. e appearance of the card has solved a lot of niggling problems and makes the campus consumptions more convenient. A card can be slippery in school, and it also facilitates schools in wealth management. e development of the education sector is affected by the technical implications and also constrained by economic conditions, particularly those three-table institutions or non- governmental institutions. ey strive to build a modern campus and, therefore, will not abandon advanced technol- ogy to serve schools. However, due to shortage of funds, schools are oſten just going to the application but did not consider the quality and future problems. In the tender, as long as the low price of whom, let someone to do the con- struction, this is wrong. For modern campus, improving the technology is right, but it is also needed to consider the question of safety and quality, especially one-card; security is a particularly important problem which cannot be ignored. e author participated in a one-card case of a university and is responsible for the construction of a hardware and server tender selection and purchasing also the maintenance work later. But due to the problem of school funds, this makes some very good companies unsuccessful and the midrange be elected. e author also went to a survey of many institutions and made a research about the operation of the campus card and the cooperations of those universities. All the institutions the author picked are capable; they only consider the quality not the price. To make the card more secure for our school, the author got the school’s secret instructions and carried Hindawi Publishing Corporation Journal of Control Science and Engineering Volume 2014, Article ID 604920, 4 pages http://dx.doi.org/10.1155/2014/604920
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Research ArticleAn Approach to Evaluating Computer Network Securitywith Intuitionistic Trapezoidal Fuzzy Information
Ming Xue
Henan University of Technology Zhengzhou Henan 450001 China
Correspondence should be addressed to Ming Xue xueming11980163com
Received 29 June 2014 Accepted 9 July 2014 Published 17 July 2014
Academic Editor Xiaofei Zhao
Copyright copy 2014 Ming Xue This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
We investigate the multiple attribute decision-making problems for evaluating the computer network security with intuitionis-tic trapezoidal fuzzy information We utilize the intuitionistic trapezoidal fuzzy weighted average (ITFWA) operator to aggre-gate the intuitionistic trapezoidal fuzzy information corresponding to each alternative and get the overall value of the alternativesand then rank the alternatives and select the most desirable one(s) according to the distance between the overall value of thealternatives and ideal solution Finally an illustrative example for evaluating the computer network security is given
1 Introduction
With science and technology development computer tech-nology improves constantly and more and more softwareand hardware of education industry have appeared [1] Usesin educating the profession especially the software and thehardware appear one after another have brought a lot ofconvenience for the school teachingmanagement and simul-taneously have also providedmany convenient conditions forteacherrsquos and studentrsquos daily lifeThe application of these high-techs in the school convenient for the educational circles alsogave the educational circles a question about the safety ofthe information management the network security questionhas become a new question to educational circles [2 3] Asa result of a one-card appearance the school has appliedthis technology in the first time It provides the conveniencefor both teachers and students Meanwhile the school alsomust consider the safety of the card The enhancement ofnetwork and the server security is the most important thingfor schoolsThese high-techs for example multimedia slidesnetwork information laser projection and so on bringabout new breakthrough to school educationThe emergenceof one-card also as the education sector development hasplayed a role and significantly improved the management ofschools in various fields [4] The appearance of the card hassolved a lot of niggling problems and makes the campus
consumptions more convenient A card can be slippery inschool and it also facilitates schools in wealth managementThe development of the education sector is affected by thetechnical implications and also constrained by economicconditions particularly those three-table institutions or non-governmental institutions They strive to build a moderncampus and therefore will not abandon advanced technol-ogy to serve schools However due to shortage of fundsschools are often just going to the application but did notconsider the quality and future problems In the tender aslong as the low price of whom let someone to do the con-struction this is wrong For modern campus improving thetechnology is right but it is also needed to consider thequestion of safety and quality especially one-card security isa particularly important problem which cannot be ignoredThe author participated in a one-card case of a university andis responsible for the construction of a hardware and servertender selection and purchasing also the maintenance worklater But due to the problem of school funds this makessome very good companies unsuccessful and themidrange beelectedThe author also went to a survey of many institutionsand made a research about the operation of the campus cardand the cooperations of those universities All the institutionsthe author picked are capable they only consider the qualitynot the price To make the card more secure for our schoolthe author got the schoolrsquos secret instructions and carried
Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2014 Article ID 604920 4 pageshttpdxdoiorg1011552014604920
2 Journal of Control Science and Engineering
out mock attacks in order to detect the one-card serverbackground security issues Althoughwe spent lessmoney torequire security comes first Only school leadership and thedirect leadership know about this action Since those IP andscreen shots in the papers are not real they are very similarThis task is to be possible to control all of the servers sowe can require developers to do the upgrade or debuggingguarantee the safety of the school network server and makefuturework bewell prepared [5]This school contains campusnetwork one-card service postal savings and other financialsystems All of these four systems are in one network so thesecurity is the most important thing The information on thenetwork is real money if any problem occurs the conse-quence will be unable to be estimated With the fast devel-opment of Internet technologies recently computer networkshave played an increasingly important role in the fields ofpolitics economy military and social life Although networktechnologies bring about endless convenience for peoplersquoslife and work the openness and interconnection of networksmake network attacks become more universal and networksecurity problems have attracted wide attention Risk alwaysexists in the real network environment In order to ensurenormal operation of networks hidden troubles in networksmust be identified and analyzed and proper measures mustbe adopted to decrease the risk according to analysis resultsTherefore how to accurately evaluate the security of a net-work becomes an important problem and it has been one ofthe research focuses in the field of network security [6]
Hao and Li [7] proposed a new sorting method whichused the possible degree matrix to solve the sorting prob-lem of intuitionistic trapezoidal fuzzy numbers Wang [8]reviewed the current research on the multicriteria linguisticdecision-making methods and fuzzy multicriteria decision-making methods based on fuzzy number intuitionistic fuzzyset and vague set and then proposed the definition of intu-itionistic trapezoidal fuzzy numbers and interval intuitionis-tic trapezoidal fuzzy number Wang and Zhang [9] proposeda multicriteria decision-making approach for multicriteriadecision-making problems in which weight information wasnot completely known and the criteria values were intuition-istic trapezoidal fuzzy numbers Wan and Dong [10] studiedthe multiattribute group decision-making method based onintuitionistic trapezoidal fuzzy numbers Firstly the expec-tations and the expected score of intuitionistic trapezoidalfuzzy number were defined based on the function of thegravity center of the image Secondly the IT-OWA and IT-HA operators were proposed Based on these operators themultiattribute group decision-makingmethod based on intu-itionistic trapezoidal fuzzy numberwas presentedWang et al[11] proposed the intuitionistic trapezoidal fuzzy geometricaggregation operatorsincluding the intuitionistic trapezoidalfuzzy weighted geometric (IT-WG) operator intuitionistictrapezoidal fuzzy ordered weighted geometric (IT-OWG)operator and intuitionistictrapezoidal fuzzy hybrid geo-metric (IT-HG) operator Then the multicriteria decision-making method based on the aggregation operators wasproposedWu and Liu [12] proposed the interval-valued intu-itionistic trapezoidal fuzzy weighted geometric (IVITFWG)operator the interval-valued intuitionistic trapezoidal fuzzy
ordered weighted geometric (IVITFOWG) operator andthe interval-valued intuitionistic trapezoidal fuzzy hybridgeometric (IVITFHG) operator Wu and Cao [13] and Wei etal [14] proposed the interval intuitionistic trapezoidal fuzzyweighted geometric (IITFWG) operator the interval intu-itionistic trapezoidal fuzzy ordered weighted geometric (IIT-FOWG) operator and interval intuitionistic trapezoidal fuzzyhybrid geometric (IITFHG) operator and based on theseoperators a new decision-making method was presented tosolve the MAGDM problems in which attribute values takethe form of interval intuitionistic trapezoidal fuzzy numbers
In this paper we investigate the multiple attribute deci-sion-making problems for evaluating the computer networksecurity with intuitionistic trapezoidal fuzzy informationWeutilize the intuitionistic trapezoidal fuzzy weighted average(ITFWA) operator to aggregate the intuitionistic trapezoidalfuzzy information corresponding to each alternative andget the overall value of the alternatives and then rank thealternatives and select the most desirable one(s) according tothe distance between the overall value of the alternatives andideal solution Finally an illustrative example for evaluatingthe computer network security is given
2 Preliminaries
In the following we will introduce some basic conceptsrelated to intuitionistic trapezoidal fuzzy numbers
Definition 1 Let 119886 be an intuitionistic trapezoidal fuzzynumber its membership function is [9 15]
120583
119886
(119909) =
119909 minus 119886
119887 minus 119886
120583
119886
119886 le 119909 lt 119887
120583
119886
119887 le 119909 le 119888
119889 minus 119909
119889 minus 119888
120583
119886
119888 lt 119909 le 119889
0 others
(1)
Its nonmembership function is
]119886
(119909) =
119887 minus 119909 + ]119886
(119909 minus 119886
1
)
119887 minus 119886
1
119886
1
le 119909 lt 119887
]119886
119887 le 119909 le 119888
119909 minus 119888 + ]119886
(119889
1
minus 119909)
119889
1
minus 119888
119888 lt 119909 le 119889
1
0 others
(2)
where 0 le 120583
119886
le 1 0 le ]119886
le 1 and 120583119886
+ ]119886
le 1 119886 119887 119888119889 isin 119877
In the following Wei developed a new operator calledintuitionistic trapezoidal fuzzy weighted average (ITFWA)operator [16]
Definition 2 (see [16]) Let 119886
119895
= ([119886
119895
119887
119895
119888
119895
119889
119895
] 120583
119886119895
]119886119895) (119895 = 1 2 119899) be a collection of intuitionistic
Journal of Control Science and Engineering 3
trapezoidalfuzzy numbers and let ITFWA 119876119899 rarr 119876if
ITFWA120596
(119886
1
119886
2
sdot sdot sdot 119886
119899
)
=
119899
⨁
119895=1
(120596
119895
otimes 119886
119895
)
= (
[
[
119899
sum
119895=1
120596
119895
119886
119895
119899
sum
119895=1
120596
119895
119887
119895
119899
sum
119895=1
120596
119895
119888
119895
119899
sum
119895=1
120596
119895
119889
119895
]
]
1 minus
119899
prod
119895=1
(1 minus 120583
119886119895)
120596119895
119899
prod
119895=1
(]119886119895)
120596119895
)
(3)
where 120596 = (120596
1
120596
2
120596
119899
)
119879 is the weight vector of 119886119895
(119895 =1 2 119899) and 120596
119895
ge 0sum119899119895=1
120596
119895
= 1 then ITFWA is called theintuitionistic trapezoidal fuzzy weighted average (ITFWA)operator
Definition 3 (see [16]) For a normalized intuitionistic trap-ezoidal fuzzy decision-making matrix
119877 = (119903
119894119895
)
119898times119899
=
([119886
119894119895
119887
119894119895
119888
119894119895
119889
119894119895
] 120583
119894119895
]119894119895
)
119898times119899
where 0 le 119886119894119895
le 119887
119894119895
le 119888
119894119895
le 119889
119894119895
le 10 le 120583
119894119895
]119894119895
le 1 0 le 120583
119894119895
+ ]119894119895
le 1 the intuitionistic trapezoidalfuzzy positive ideal solution is defined as follows
119903
+
= ([119886
+
119887
+
119888
+
119889
+
] 120583
+
]+) = ([1 1 1 1] 1 0) (4)
Definition 4 (see [16]) Let 1198861
= ([119886
1
119887
1
119888
1
119889
1
] 120583
1198861 ]1198861) and
119886
2
= ([119886
2
119887
2
119888
2
119889
2
] 120583
1198862 ]1198862) be two intuitionistic trapezoidal
fuzzy numbers then the normalized Hamming distancebetween 119886
1
and 1198862
is defined as follows
119889 (119886
1
119886
2
) =
1
8
(
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119886
1
minus (1 + 120583
1198862minus ]1198862) 119886
2
1003816
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119887
1
minus (1 + 120583
1198862minus ]1198862) 119887
2
1003816
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119888
1
minus (1 + 120583
1198862minus ]1198862) 119888
2
1003816
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119889
1
minus (1 + 120583
1198862minus ]1198862) 119889
2
1003816
1003816
1003816
1003816
1003816
)
(5)
3 Numerical Example
With the popularization of computer technology networkprovides great impetus for the advancement of societyHowever the development of the network technology facesgreat challenges under the unceasing rigorous network sit-uation and traditional single-point heterogeneous securitydefense technologies such as IDS Firewall and VPN canenhance security performance of network system to a certaindegree among which lack of effective collaboration leads tobeing unable to monitor the whole network security situa-tion Under this circumstance the research about networksecurity situation awareness (NSSA) has upper academicvalue and comprehensive practical value But the researchesrelated to NSSA are still far away from maturation at thepresent Most of the situation awareness models are based onsingle-source environment quantification awareness meth-ods mainly depend on quantifying the raw alerts of thesecurity sensor and they cannot actualize the awareness ofattack steps and sequences The research about situationevaluation mainly focuses on the construction of indexsystem and is lack of deep study in evaluation model andmethod This section presents a numerical example to eval-uate the computer network security with uncertain linguisticinformation to illustrate the method proposed in this paperThere are five possible computer network systems 119860
119894
(119894 =1 2 3 4 5) for four attributes 119866
119895
(119895 = 1 2 3 4) The fourattributes include the tactics (119866
1
) technology and economy(1198662
) logistics (1198663
) and strategy (1198664
) respectively The fivepossible computer network systems 119860
119894
(119894 = 1 2 5) areto be evaluated using the intuitionistic trapezoidal fuzzyinformation by the decision maker under the above fourattributes whose weighting vector 120596 = (03 02 01 04)119879 aslisted in the following matrix
119877
=
[
[
[
[
[
[
([05 06 07 08] 05 04)
([06 07 08 09] 07 03)
([01 02 04 05] 06 04)
([03 04 05 06] 08 01)
([02 03 04 05] 06 02)
([01 02 03 04] 06 03)
([05 06 07 08] 07 02)
([02 03 05 06] 05 04)
([01 03 04 05] 06 03)
([03 04 05 06] 04 03)
([05 06 08 09] 03 06)
([04 05 07 08] 07 02)
([05 06 07 08] 05 03)
([01 03 05 07] 03 04)
([02 03 04 05] 07 01)
([04 05 06 07] 02 07)
([05 06 07 09] 04 05)
([03 05 07 09] 02 03)
([06 07 08 09] 02 06)
([05 06 07 08] 01 03)
]
]
]
]
]
]
(6)
Then we utilize the approach developed to get the mostdesirable computer network system(s)
Step 1 Utilize the weight vector 120596 = (03 02 01 04)119879 andby (3) we obtain the overall values 119903
119894
of the computer networksystems 119860
119894
(119894 = 1 2 3 4 5)119903
1
= ([037 046 065 071] 02435 06127)
119903
2
= ([046 052 066 084] 04780 04011)
119903
3
= ([030 043 061 072] 04203 04521)
119903
4
= ([022 043 051 067] 03055 04322)
119903
5
= ([023 035 042 051] 04954 03247)
(7)
Step 2 Calculate the distances between overall values 119903119894
=
([119886
119894
119887
119894
119888
119894
119889
119894
] 120583
119894
]119894
) and intuitionistic trapezoidal fuzzy
4 Journal of Control Science and Engineering
positive ideal solution 119903+ = ([119886+ 119887+ 119888+ 119889+] 120583+ ]+) = ([1 11 1] 1 0)
119889 (119903
1
119903
+
) = 08435 119889 (119903
2
119903
+
) = 06568
119889 (119903
3
119903
+
) = 07089 119889 (119903
4
119903
+
) = 07879
119889 (119903
5
119903
+
) = 07326
(8)
Step 3 Rank all the alternatives 119860119894
(119894 = 1 2 3 4 5) inaccordance with the distances 119889(119903
119894
119903
+
) between overall values119903
119894
= ([119886
119894
119887
119894
119888
119894
119889
119894
] 120583
119894
]119894
) and intuitionistic trapezoidal fuzzypositive ideal solution 119860
2
≻ 119860
3
≻ 119860
5
≻ 119860
4
≻ 119860
1
and thusthe most desirable computer network system is 119860
2
4 Conclusion
Computer network security assessment is an active securitytechnology which can make network information systemmore secure and robust Taking so many security factorssuch as threats assets and vulnerabilities into accountthe computer network security assessment technology canhelp administrators take an active attitude to identify thosepotential threats that their systems will be exposed to Nowit has become the fundamental work and the key link forthe national information assurance frameworkWhenwe relymore and more on the world of Internet day by day researchon network information risk assessment will be one of theresearch focuses in the network security fieldThe research ofthis dissertation focuses on the quantitative methodologiesof the network security assessment In this paper we inves-tigate the multiple attribute decision-making problems forevaluating the computer network security with intuitionistictrapezoidal fuzzy information We utilize the intuitionistictrapezoidal fuzzy weighted average (ITFWA) operator toaggregate the intuitionistic trapezoidal fuzzy informationcorresponding to each alternative and get the overall valueof the alternatives and then rank the alternatives and selectthe most desirable one(s) according to the distance betweenthe overall value of the alternatives and ideal solution Finallyan illustrative example for evaluating the computer networksecurity is given
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] X Mo ldquoResearch on the computer network security evaluationbased on the ULCGM operator with uncertain linguistic infor-mationrdquo Journal of Convergence Information Technology vol 8no 3 pp 160ndash166 2013
[2] G Zhang H Li R Chen et al ldquoResearch and design onvulnerability testing in computer network security systemrdquoAdvances in Information Sciences and Service Sciences vol 5 no7 pp 1ndash10 2013
[3] G Song ldquoComputer network security and precaution evalua-tion based on incremental relevance vector machine algorithm
and ACOrdquo International Journal on Advances in InformationSciences and Service Sciences vol 5 no 1 pp 120ndash127 2013
[4] Y Li J Yin and G Wu ldquoModel for evaluating the computernetwork security with interval-valued intuitionistic fuzzy infor-mationrdquo International Journal of Digital Content Technology andIts Applications vol 6 no 6 pp 140ndash146 2012
[5] J Dong ldquoAn approach to evaluating the computer networksecurity with hesitant fuzzy informationrdquo International Journalof Digital Content Technology and Its Applications vol 6 no 20pp 633ndash639 2012
[6] Y Li X Shan and G Wu ldquoComprehensive evaluation modelfor computer network security with linguistic informationrdquoAdvances in Information Sciences and Service Sciences vol 3 no9 pp 126ndash131 2011
[7] F LHao andDQ Li ldquoAnewrankingmethod of fuzzy numbersrdquoJournal of Ordnance Engineering College vol 19 pp 73ndash75 2007
[8] J Q Wang ldquoOverview on fuzzy multi-criteria decision-makingapproachrdquo Control and Decision vol 23 pp 601ndash607 2008
[9] J Q Wang and Z Zhang ldquoMulti-criteria decision-makingmethod with incomplete certain information based on intu-itionistic fuzzy numbersrdquo Control and Decision vol 24 no 2pp 226ndash230 2009
[10] S P Wan and J Y Dong ldquoMethod of the intuitionistictrapezoidal fuzzy number for multi-attribute group decisionrdquoControl and Decision vol 25 no 5 pp 773ndash776 2010
[11] Y Wang S F Zhang and S Q Xie ldquoIntuitionistic trapezoidalfuzzy geometric aggregation operators and their application togroup decision makingrdquo Value Engineering vol 27 pp 159ndash1612012
[12] J Wu and Y Liu ldquoAn approach for multiple attribute groupdecision making problems with interval-valued intuitionistictrapezoidal fuzzy numbersrdquo Computers amp Industrial Engineer-ing vol 66 pp 311ndash324 2013
[13] JWu andQCao ldquoSame families of geometric aggregation oper-ators with intuitionistic trapezoidal fuzzy numbersrdquo AppliedMathematical Modelling vol 37 no 1-2 pp 318ndash327 2013
[14] G Wei X Zhao and H Wang ldquoAn approach to multipleattribute group decision making with interval intuitionistictrapezoidal fuzzy informationrdquo Technological and EconomicDevelopment of Economy vol 18 no 2 pp 317ndash330 2012
[15] J Wang and Z Zhang ldquoProgramming method of multi-criteriadecision-making based on intuitionistic fuzzy number withincomplete certain informationrdquo Control and Decision vol 23no 10 p 1145 2008
[16] G Wei ldquoSome arithmetic aggregation operators with intuition-istic trapezoidal fuzzy numbers and their application to groupdecision makingrdquo Journal of Computers vol 5 no 3 pp 345ndash351 2010
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2 Journal of Control Science and Engineering
out mock attacks in order to detect the one-card serverbackground security issues Althoughwe spent lessmoney torequire security comes first Only school leadership and thedirect leadership know about this action Since those IP andscreen shots in the papers are not real they are very similarThis task is to be possible to control all of the servers sowe can require developers to do the upgrade or debuggingguarantee the safety of the school network server and makefuturework bewell prepared [5]This school contains campusnetwork one-card service postal savings and other financialsystems All of these four systems are in one network so thesecurity is the most important thing The information on thenetwork is real money if any problem occurs the conse-quence will be unable to be estimated With the fast devel-opment of Internet technologies recently computer networkshave played an increasingly important role in the fields ofpolitics economy military and social life Although networktechnologies bring about endless convenience for peoplersquoslife and work the openness and interconnection of networksmake network attacks become more universal and networksecurity problems have attracted wide attention Risk alwaysexists in the real network environment In order to ensurenormal operation of networks hidden troubles in networksmust be identified and analyzed and proper measures mustbe adopted to decrease the risk according to analysis resultsTherefore how to accurately evaluate the security of a net-work becomes an important problem and it has been one ofthe research focuses in the field of network security [6]
Hao and Li [7] proposed a new sorting method whichused the possible degree matrix to solve the sorting prob-lem of intuitionistic trapezoidal fuzzy numbers Wang [8]reviewed the current research on the multicriteria linguisticdecision-making methods and fuzzy multicriteria decision-making methods based on fuzzy number intuitionistic fuzzyset and vague set and then proposed the definition of intu-itionistic trapezoidal fuzzy numbers and interval intuitionis-tic trapezoidal fuzzy number Wang and Zhang [9] proposeda multicriteria decision-making approach for multicriteriadecision-making problems in which weight information wasnot completely known and the criteria values were intuition-istic trapezoidal fuzzy numbers Wan and Dong [10] studiedthe multiattribute group decision-making method based onintuitionistic trapezoidal fuzzy numbers Firstly the expec-tations and the expected score of intuitionistic trapezoidalfuzzy number were defined based on the function of thegravity center of the image Secondly the IT-OWA and IT-HA operators were proposed Based on these operators themultiattribute group decision-makingmethod based on intu-itionistic trapezoidal fuzzy numberwas presentedWang et al[11] proposed the intuitionistic trapezoidal fuzzy geometricaggregation operatorsincluding the intuitionistic trapezoidalfuzzy weighted geometric (IT-WG) operator intuitionistictrapezoidal fuzzy ordered weighted geometric (IT-OWG)operator and intuitionistictrapezoidal fuzzy hybrid geo-metric (IT-HG) operator Then the multicriteria decision-making method based on the aggregation operators wasproposedWu and Liu [12] proposed the interval-valued intu-itionistic trapezoidal fuzzy weighted geometric (IVITFWG)operator the interval-valued intuitionistic trapezoidal fuzzy
ordered weighted geometric (IVITFOWG) operator andthe interval-valued intuitionistic trapezoidal fuzzy hybridgeometric (IVITFHG) operator Wu and Cao [13] and Wei etal [14] proposed the interval intuitionistic trapezoidal fuzzyweighted geometric (IITFWG) operator the interval intu-itionistic trapezoidal fuzzy ordered weighted geometric (IIT-FOWG) operator and interval intuitionistic trapezoidal fuzzyhybrid geometric (IITFHG) operator and based on theseoperators a new decision-making method was presented tosolve the MAGDM problems in which attribute values takethe form of interval intuitionistic trapezoidal fuzzy numbers
In this paper we investigate the multiple attribute deci-sion-making problems for evaluating the computer networksecurity with intuitionistic trapezoidal fuzzy informationWeutilize the intuitionistic trapezoidal fuzzy weighted average(ITFWA) operator to aggregate the intuitionistic trapezoidalfuzzy information corresponding to each alternative andget the overall value of the alternatives and then rank thealternatives and select the most desirable one(s) according tothe distance between the overall value of the alternatives andideal solution Finally an illustrative example for evaluatingthe computer network security is given
2 Preliminaries
In the following we will introduce some basic conceptsrelated to intuitionistic trapezoidal fuzzy numbers
Definition 1 Let 119886 be an intuitionistic trapezoidal fuzzynumber its membership function is [9 15]
120583
119886
(119909) =
119909 minus 119886
119887 minus 119886
120583
119886
119886 le 119909 lt 119887
120583
119886
119887 le 119909 le 119888
119889 minus 119909
119889 minus 119888
120583
119886
119888 lt 119909 le 119889
0 others
(1)
Its nonmembership function is
]119886
(119909) =
119887 minus 119909 + ]119886
(119909 minus 119886
1
)
119887 minus 119886
1
119886
1
le 119909 lt 119887
]119886
119887 le 119909 le 119888
119909 minus 119888 + ]119886
(119889
1
minus 119909)
119889
1
minus 119888
119888 lt 119909 le 119889
1
0 others
(2)
where 0 le 120583
119886
le 1 0 le ]119886
le 1 and 120583119886
+ ]119886
le 1 119886 119887 119888119889 isin 119877
In the following Wei developed a new operator calledintuitionistic trapezoidal fuzzy weighted average (ITFWA)operator [16]
Definition 2 (see [16]) Let 119886
119895
= ([119886
119895
119887
119895
119888
119895
119889
119895
] 120583
119886119895
]119886119895) (119895 = 1 2 119899) be a collection of intuitionistic
Journal of Control Science and Engineering 3
trapezoidalfuzzy numbers and let ITFWA 119876119899 rarr 119876if
ITFWA120596
(119886
1
119886
2
sdot sdot sdot 119886
119899
)
=
119899
⨁
119895=1
(120596
119895
otimes 119886
119895
)
= (
[
[
119899
sum
119895=1
120596
119895
119886
119895
119899
sum
119895=1
120596
119895
119887
119895
119899
sum
119895=1
120596
119895
119888
119895
119899
sum
119895=1
120596
119895
119889
119895
]
]
1 minus
119899
prod
119895=1
(1 minus 120583
119886119895)
120596119895
119899
prod
119895=1
(]119886119895)
120596119895
)
(3)
where 120596 = (120596
1
120596
2
120596
119899
)
119879 is the weight vector of 119886119895
(119895 =1 2 119899) and 120596
119895
ge 0sum119899119895=1
120596
119895
= 1 then ITFWA is called theintuitionistic trapezoidal fuzzy weighted average (ITFWA)operator
Definition 3 (see [16]) For a normalized intuitionistic trap-ezoidal fuzzy decision-making matrix
119877 = (119903
119894119895
)
119898times119899
=
([119886
119894119895
119887
119894119895
119888
119894119895
119889
119894119895
] 120583
119894119895
]119894119895
)
119898times119899
where 0 le 119886119894119895
le 119887
119894119895
le 119888
119894119895
le 119889
119894119895
le 10 le 120583
119894119895
]119894119895
le 1 0 le 120583
119894119895
+ ]119894119895
le 1 the intuitionistic trapezoidalfuzzy positive ideal solution is defined as follows
119903
+
= ([119886
+
119887
+
119888
+
119889
+
] 120583
+
]+) = ([1 1 1 1] 1 0) (4)
Definition 4 (see [16]) Let 1198861
= ([119886
1
119887
1
119888
1
119889
1
] 120583
1198861 ]1198861) and
119886
2
= ([119886
2
119887
2
119888
2
119889
2
] 120583
1198862 ]1198862) be two intuitionistic trapezoidal
fuzzy numbers then the normalized Hamming distancebetween 119886
1
and 1198862
is defined as follows
119889 (119886
1
119886
2
) =
1
8
(
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119886
1
minus (1 + 120583
1198862minus ]1198862) 119886
2
1003816
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119887
1
minus (1 + 120583
1198862minus ]1198862) 119887
2
1003816
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119888
1
minus (1 + 120583
1198862minus ]1198862) 119888
2
1003816
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119889
1
minus (1 + 120583
1198862minus ]1198862) 119889
2
1003816
1003816
1003816
1003816
1003816
)
(5)
3 Numerical Example
With the popularization of computer technology networkprovides great impetus for the advancement of societyHowever the development of the network technology facesgreat challenges under the unceasing rigorous network sit-uation and traditional single-point heterogeneous securitydefense technologies such as IDS Firewall and VPN canenhance security performance of network system to a certaindegree among which lack of effective collaboration leads tobeing unable to monitor the whole network security situa-tion Under this circumstance the research about networksecurity situation awareness (NSSA) has upper academicvalue and comprehensive practical value But the researchesrelated to NSSA are still far away from maturation at thepresent Most of the situation awareness models are based onsingle-source environment quantification awareness meth-ods mainly depend on quantifying the raw alerts of thesecurity sensor and they cannot actualize the awareness ofattack steps and sequences The research about situationevaluation mainly focuses on the construction of indexsystem and is lack of deep study in evaluation model andmethod This section presents a numerical example to eval-uate the computer network security with uncertain linguisticinformation to illustrate the method proposed in this paperThere are five possible computer network systems 119860
119894
(119894 =1 2 3 4 5) for four attributes 119866
119895
(119895 = 1 2 3 4) The fourattributes include the tactics (119866
1
) technology and economy(1198662
) logistics (1198663
) and strategy (1198664
) respectively The fivepossible computer network systems 119860
119894
(119894 = 1 2 5) areto be evaluated using the intuitionistic trapezoidal fuzzyinformation by the decision maker under the above fourattributes whose weighting vector 120596 = (03 02 01 04)119879 aslisted in the following matrix
119877
=
[
[
[
[
[
[
([05 06 07 08] 05 04)
([06 07 08 09] 07 03)
([01 02 04 05] 06 04)
([03 04 05 06] 08 01)
([02 03 04 05] 06 02)
([01 02 03 04] 06 03)
([05 06 07 08] 07 02)
([02 03 05 06] 05 04)
([01 03 04 05] 06 03)
([03 04 05 06] 04 03)
([05 06 08 09] 03 06)
([04 05 07 08] 07 02)
([05 06 07 08] 05 03)
([01 03 05 07] 03 04)
([02 03 04 05] 07 01)
([04 05 06 07] 02 07)
([05 06 07 09] 04 05)
([03 05 07 09] 02 03)
([06 07 08 09] 02 06)
([05 06 07 08] 01 03)
]
]
]
]
]
]
(6)
Then we utilize the approach developed to get the mostdesirable computer network system(s)
Step 1 Utilize the weight vector 120596 = (03 02 01 04)119879 andby (3) we obtain the overall values 119903
119894
of the computer networksystems 119860
119894
(119894 = 1 2 3 4 5)119903
1
= ([037 046 065 071] 02435 06127)
119903
2
= ([046 052 066 084] 04780 04011)
119903
3
= ([030 043 061 072] 04203 04521)
119903
4
= ([022 043 051 067] 03055 04322)
119903
5
= ([023 035 042 051] 04954 03247)
(7)
Step 2 Calculate the distances between overall values 119903119894
=
([119886
119894
119887
119894
119888
119894
119889
119894
] 120583
119894
]119894
) and intuitionistic trapezoidal fuzzy
4 Journal of Control Science and Engineering
positive ideal solution 119903+ = ([119886+ 119887+ 119888+ 119889+] 120583+ ]+) = ([1 11 1] 1 0)
119889 (119903
1
119903
+
) = 08435 119889 (119903
2
119903
+
) = 06568
119889 (119903
3
119903
+
) = 07089 119889 (119903
4
119903
+
) = 07879
119889 (119903
5
119903
+
) = 07326
(8)
Step 3 Rank all the alternatives 119860119894
(119894 = 1 2 3 4 5) inaccordance with the distances 119889(119903
119894
119903
+
) between overall values119903
119894
= ([119886
119894
119887
119894
119888
119894
119889
119894
] 120583
119894
]119894
) and intuitionistic trapezoidal fuzzypositive ideal solution 119860
2
≻ 119860
3
≻ 119860
5
≻ 119860
4
≻ 119860
1
and thusthe most desirable computer network system is 119860
2
4 Conclusion
Computer network security assessment is an active securitytechnology which can make network information systemmore secure and robust Taking so many security factorssuch as threats assets and vulnerabilities into accountthe computer network security assessment technology canhelp administrators take an active attitude to identify thosepotential threats that their systems will be exposed to Nowit has become the fundamental work and the key link forthe national information assurance frameworkWhenwe relymore and more on the world of Internet day by day researchon network information risk assessment will be one of theresearch focuses in the network security fieldThe research ofthis dissertation focuses on the quantitative methodologiesof the network security assessment In this paper we inves-tigate the multiple attribute decision-making problems forevaluating the computer network security with intuitionistictrapezoidal fuzzy information We utilize the intuitionistictrapezoidal fuzzy weighted average (ITFWA) operator toaggregate the intuitionistic trapezoidal fuzzy informationcorresponding to each alternative and get the overall valueof the alternatives and then rank the alternatives and selectthe most desirable one(s) according to the distance betweenthe overall value of the alternatives and ideal solution Finallyan illustrative example for evaluating the computer networksecurity is given
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] X Mo ldquoResearch on the computer network security evaluationbased on the ULCGM operator with uncertain linguistic infor-mationrdquo Journal of Convergence Information Technology vol 8no 3 pp 160ndash166 2013
[2] G Zhang H Li R Chen et al ldquoResearch and design onvulnerability testing in computer network security systemrdquoAdvances in Information Sciences and Service Sciences vol 5 no7 pp 1ndash10 2013
[3] G Song ldquoComputer network security and precaution evalua-tion based on incremental relevance vector machine algorithm
and ACOrdquo International Journal on Advances in InformationSciences and Service Sciences vol 5 no 1 pp 120ndash127 2013
[4] Y Li J Yin and G Wu ldquoModel for evaluating the computernetwork security with interval-valued intuitionistic fuzzy infor-mationrdquo International Journal of Digital Content Technology andIts Applications vol 6 no 6 pp 140ndash146 2012
[5] J Dong ldquoAn approach to evaluating the computer networksecurity with hesitant fuzzy informationrdquo International Journalof Digital Content Technology and Its Applications vol 6 no 20pp 633ndash639 2012
[6] Y Li X Shan and G Wu ldquoComprehensive evaluation modelfor computer network security with linguistic informationrdquoAdvances in Information Sciences and Service Sciences vol 3 no9 pp 126ndash131 2011
[7] F LHao andDQ Li ldquoAnewrankingmethod of fuzzy numbersrdquoJournal of Ordnance Engineering College vol 19 pp 73ndash75 2007
[8] J Q Wang ldquoOverview on fuzzy multi-criteria decision-makingapproachrdquo Control and Decision vol 23 pp 601ndash607 2008
[9] J Q Wang and Z Zhang ldquoMulti-criteria decision-makingmethod with incomplete certain information based on intu-itionistic fuzzy numbersrdquo Control and Decision vol 24 no 2pp 226ndash230 2009
[10] S P Wan and J Y Dong ldquoMethod of the intuitionistictrapezoidal fuzzy number for multi-attribute group decisionrdquoControl and Decision vol 25 no 5 pp 773ndash776 2010
[11] Y Wang S F Zhang and S Q Xie ldquoIntuitionistic trapezoidalfuzzy geometric aggregation operators and their application togroup decision makingrdquo Value Engineering vol 27 pp 159ndash1612012
[12] J Wu and Y Liu ldquoAn approach for multiple attribute groupdecision making problems with interval-valued intuitionistictrapezoidal fuzzy numbersrdquo Computers amp Industrial Engineer-ing vol 66 pp 311ndash324 2013
[13] JWu andQCao ldquoSame families of geometric aggregation oper-ators with intuitionistic trapezoidal fuzzy numbersrdquo AppliedMathematical Modelling vol 37 no 1-2 pp 318ndash327 2013
[14] G Wei X Zhao and H Wang ldquoAn approach to multipleattribute group decision making with interval intuitionistictrapezoidal fuzzy informationrdquo Technological and EconomicDevelopment of Economy vol 18 no 2 pp 317ndash330 2012
[15] J Wang and Z Zhang ldquoProgramming method of multi-criteriadecision-making based on intuitionistic fuzzy number withincomplete certain informationrdquo Control and Decision vol 23no 10 p 1145 2008
[16] G Wei ldquoSome arithmetic aggregation operators with intuition-istic trapezoidal fuzzy numbers and their application to groupdecision makingrdquo Journal of Computers vol 5 no 3 pp 345ndash351 2010
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International Journal of
Journal of Control Science and Engineering 3
trapezoidalfuzzy numbers and let ITFWA 119876119899 rarr 119876if
ITFWA120596
(119886
1
119886
2
sdot sdot sdot 119886
119899
)
=
119899
⨁
119895=1
(120596
119895
otimes 119886
119895
)
= (
[
[
119899
sum
119895=1
120596
119895
119886
119895
119899
sum
119895=1
120596
119895
119887
119895
119899
sum
119895=1
120596
119895
119888
119895
119899
sum
119895=1
120596
119895
119889
119895
]
]
1 minus
119899
prod
119895=1
(1 minus 120583
119886119895)
120596119895
119899
prod
119895=1
(]119886119895)
120596119895
)
(3)
where 120596 = (120596
1
120596
2
120596
119899
)
119879 is the weight vector of 119886119895
(119895 =1 2 119899) and 120596
119895
ge 0sum119899119895=1
120596
119895
= 1 then ITFWA is called theintuitionistic trapezoidal fuzzy weighted average (ITFWA)operator
Definition 3 (see [16]) For a normalized intuitionistic trap-ezoidal fuzzy decision-making matrix
119877 = (119903
119894119895
)
119898times119899
=
([119886
119894119895
119887
119894119895
119888
119894119895
119889
119894119895
] 120583
119894119895
]119894119895
)
119898times119899
where 0 le 119886119894119895
le 119887
119894119895
le 119888
119894119895
le 119889
119894119895
le 10 le 120583
119894119895
]119894119895
le 1 0 le 120583
119894119895
+ ]119894119895
le 1 the intuitionistic trapezoidalfuzzy positive ideal solution is defined as follows
119903
+
= ([119886
+
119887
+
119888
+
119889
+
] 120583
+
]+) = ([1 1 1 1] 1 0) (4)
Definition 4 (see [16]) Let 1198861
= ([119886
1
119887
1
119888
1
119889
1
] 120583
1198861 ]1198861) and
119886
2
= ([119886
2
119887
2
119888
2
119889
2
] 120583
1198862 ]1198862) be two intuitionistic trapezoidal
fuzzy numbers then the normalized Hamming distancebetween 119886
1
and 1198862
is defined as follows
119889 (119886
1
119886
2
) =
1
8
(
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119886
1
minus (1 + 120583
1198862minus ]1198862) 119886
2
1003816
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119887
1
minus (1 + 120583
1198862minus ]1198862) 119887
2
1003816
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119888
1
minus (1 + 120583
1198862minus ]1198862) 119888
2
1003816
1003816
1003816
1003816
1003816
+
1003816
1003816
1003816
1003816
1003816
(1 + 120583
1198861minus ]1198861) 119889
1
minus (1 + 120583
1198862minus ]1198862) 119889
2
1003816
1003816
1003816
1003816
1003816
)
(5)
3 Numerical Example
With the popularization of computer technology networkprovides great impetus for the advancement of societyHowever the development of the network technology facesgreat challenges under the unceasing rigorous network sit-uation and traditional single-point heterogeneous securitydefense technologies such as IDS Firewall and VPN canenhance security performance of network system to a certaindegree among which lack of effective collaboration leads tobeing unable to monitor the whole network security situa-tion Under this circumstance the research about networksecurity situation awareness (NSSA) has upper academicvalue and comprehensive practical value But the researchesrelated to NSSA are still far away from maturation at thepresent Most of the situation awareness models are based onsingle-source environment quantification awareness meth-ods mainly depend on quantifying the raw alerts of thesecurity sensor and they cannot actualize the awareness ofattack steps and sequences The research about situationevaluation mainly focuses on the construction of indexsystem and is lack of deep study in evaluation model andmethod This section presents a numerical example to eval-uate the computer network security with uncertain linguisticinformation to illustrate the method proposed in this paperThere are five possible computer network systems 119860
119894
(119894 =1 2 3 4 5) for four attributes 119866
119895
(119895 = 1 2 3 4) The fourattributes include the tactics (119866
1
) technology and economy(1198662
) logistics (1198663
) and strategy (1198664
) respectively The fivepossible computer network systems 119860
119894
(119894 = 1 2 5) areto be evaluated using the intuitionistic trapezoidal fuzzyinformation by the decision maker under the above fourattributes whose weighting vector 120596 = (03 02 01 04)119879 aslisted in the following matrix
119877
=
[
[
[
[
[
[
([05 06 07 08] 05 04)
([06 07 08 09] 07 03)
([01 02 04 05] 06 04)
([03 04 05 06] 08 01)
([02 03 04 05] 06 02)
([01 02 03 04] 06 03)
([05 06 07 08] 07 02)
([02 03 05 06] 05 04)
([01 03 04 05] 06 03)
([03 04 05 06] 04 03)
([05 06 08 09] 03 06)
([04 05 07 08] 07 02)
([05 06 07 08] 05 03)
([01 03 05 07] 03 04)
([02 03 04 05] 07 01)
([04 05 06 07] 02 07)
([05 06 07 09] 04 05)
([03 05 07 09] 02 03)
([06 07 08 09] 02 06)
([05 06 07 08] 01 03)
]
]
]
]
]
]
(6)
Then we utilize the approach developed to get the mostdesirable computer network system(s)
Step 1 Utilize the weight vector 120596 = (03 02 01 04)119879 andby (3) we obtain the overall values 119903
119894
of the computer networksystems 119860
119894
(119894 = 1 2 3 4 5)119903
1
= ([037 046 065 071] 02435 06127)
119903
2
= ([046 052 066 084] 04780 04011)
119903
3
= ([030 043 061 072] 04203 04521)
119903
4
= ([022 043 051 067] 03055 04322)
119903
5
= ([023 035 042 051] 04954 03247)
(7)
Step 2 Calculate the distances between overall values 119903119894
=
([119886
119894
119887
119894
119888
119894
119889
119894
] 120583
119894
]119894
) and intuitionistic trapezoidal fuzzy
4 Journal of Control Science and Engineering
positive ideal solution 119903+ = ([119886+ 119887+ 119888+ 119889+] 120583+ ]+) = ([1 11 1] 1 0)
119889 (119903
1
119903
+
) = 08435 119889 (119903
2
119903
+
) = 06568
119889 (119903
3
119903
+
) = 07089 119889 (119903
4
119903
+
) = 07879
119889 (119903
5
119903
+
) = 07326
(8)
Step 3 Rank all the alternatives 119860119894
(119894 = 1 2 3 4 5) inaccordance with the distances 119889(119903
119894
119903
+
) between overall values119903
119894
= ([119886
119894
119887
119894
119888
119894
119889
119894
] 120583
119894
]119894
) and intuitionistic trapezoidal fuzzypositive ideal solution 119860
2
≻ 119860
3
≻ 119860
5
≻ 119860
4
≻ 119860
1
and thusthe most desirable computer network system is 119860
2
4 Conclusion
Computer network security assessment is an active securitytechnology which can make network information systemmore secure and robust Taking so many security factorssuch as threats assets and vulnerabilities into accountthe computer network security assessment technology canhelp administrators take an active attitude to identify thosepotential threats that their systems will be exposed to Nowit has become the fundamental work and the key link forthe national information assurance frameworkWhenwe relymore and more on the world of Internet day by day researchon network information risk assessment will be one of theresearch focuses in the network security fieldThe research ofthis dissertation focuses on the quantitative methodologiesof the network security assessment In this paper we inves-tigate the multiple attribute decision-making problems forevaluating the computer network security with intuitionistictrapezoidal fuzzy information We utilize the intuitionistictrapezoidal fuzzy weighted average (ITFWA) operator toaggregate the intuitionistic trapezoidal fuzzy informationcorresponding to each alternative and get the overall valueof the alternatives and then rank the alternatives and selectthe most desirable one(s) according to the distance betweenthe overall value of the alternatives and ideal solution Finallyan illustrative example for evaluating the computer networksecurity is given
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] X Mo ldquoResearch on the computer network security evaluationbased on the ULCGM operator with uncertain linguistic infor-mationrdquo Journal of Convergence Information Technology vol 8no 3 pp 160ndash166 2013
[2] G Zhang H Li R Chen et al ldquoResearch and design onvulnerability testing in computer network security systemrdquoAdvances in Information Sciences and Service Sciences vol 5 no7 pp 1ndash10 2013
[3] G Song ldquoComputer network security and precaution evalua-tion based on incremental relevance vector machine algorithm
and ACOrdquo International Journal on Advances in InformationSciences and Service Sciences vol 5 no 1 pp 120ndash127 2013
[4] Y Li J Yin and G Wu ldquoModel for evaluating the computernetwork security with interval-valued intuitionistic fuzzy infor-mationrdquo International Journal of Digital Content Technology andIts Applications vol 6 no 6 pp 140ndash146 2012
[5] J Dong ldquoAn approach to evaluating the computer networksecurity with hesitant fuzzy informationrdquo International Journalof Digital Content Technology and Its Applications vol 6 no 20pp 633ndash639 2012
[6] Y Li X Shan and G Wu ldquoComprehensive evaluation modelfor computer network security with linguistic informationrdquoAdvances in Information Sciences and Service Sciences vol 3 no9 pp 126ndash131 2011
[7] F LHao andDQ Li ldquoAnewrankingmethod of fuzzy numbersrdquoJournal of Ordnance Engineering College vol 19 pp 73ndash75 2007
[8] J Q Wang ldquoOverview on fuzzy multi-criteria decision-makingapproachrdquo Control and Decision vol 23 pp 601ndash607 2008
[9] J Q Wang and Z Zhang ldquoMulti-criteria decision-makingmethod with incomplete certain information based on intu-itionistic fuzzy numbersrdquo Control and Decision vol 24 no 2pp 226ndash230 2009
[10] S P Wan and J Y Dong ldquoMethod of the intuitionistictrapezoidal fuzzy number for multi-attribute group decisionrdquoControl and Decision vol 25 no 5 pp 773ndash776 2010
[11] Y Wang S F Zhang and S Q Xie ldquoIntuitionistic trapezoidalfuzzy geometric aggregation operators and their application togroup decision makingrdquo Value Engineering vol 27 pp 159ndash1612012
[12] J Wu and Y Liu ldquoAn approach for multiple attribute groupdecision making problems with interval-valued intuitionistictrapezoidal fuzzy numbersrdquo Computers amp Industrial Engineer-ing vol 66 pp 311ndash324 2013
[13] JWu andQCao ldquoSame families of geometric aggregation oper-ators with intuitionistic trapezoidal fuzzy numbersrdquo AppliedMathematical Modelling vol 37 no 1-2 pp 318ndash327 2013
[14] G Wei X Zhao and H Wang ldquoAn approach to multipleattribute group decision making with interval intuitionistictrapezoidal fuzzy informationrdquo Technological and EconomicDevelopment of Economy vol 18 no 2 pp 317ndash330 2012
[15] J Wang and Z Zhang ldquoProgramming method of multi-criteriadecision-making based on intuitionistic fuzzy number withincomplete certain informationrdquo Control and Decision vol 23no 10 p 1145 2008
[16] G Wei ldquoSome arithmetic aggregation operators with intuition-istic trapezoidal fuzzy numbers and their application to groupdecision makingrdquo Journal of Computers vol 5 no 3 pp 345ndash351 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
4 Journal of Control Science and Engineering
positive ideal solution 119903+ = ([119886+ 119887+ 119888+ 119889+] 120583+ ]+) = ([1 11 1] 1 0)
119889 (119903
1
119903
+
) = 08435 119889 (119903
2
119903
+
) = 06568
119889 (119903
3
119903
+
) = 07089 119889 (119903
4
119903
+
) = 07879
119889 (119903
5
119903
+
) = 07326
(8)
Step 3 Rank all the alternatives 119860119894
(119894 = 1 2 3 4 5) inaccordance with the distances 119889(119903
119894
119903
+
) between overall values119903
119894
= ([119886
119894
119887
119894
119888
119894
119889
119894
] 120583
119894
]119894
) and intuitionistic trapezoidal fuzzypositive ideal solution 119860
2
≻ 119860
3
≻ 119860
5
≻ 119860
4
≻ 119860
1
and thusthe most desirable computer network system is 119860
2
4 Conclusion
Computer network security assessment is an active securitytechnology which can make network information systemmore secure and robust Taking so many security factorssuch as threats assets and vulnerabilities into accountthe computer network security assessment technology canhelp administrators take an active attitude to identify thosepotential threats that their systems will be exposed to Nowit has become the fundamental work and the key link forthe national information assurance frameworkWhenwe relymore and more on the world of Internet day by day researchon network information risk assessment will be one of theresearch focuses in the network security fieldThe research ofthis dissertation focuses on the quantitative methodologiesof the network security assessment In this paper we inves-tigate the multiple attribute decision-making problems forevaluating the computer network security with intuitionistictrapezoidal fuzzy information We utilize the intuitionistictrapezoidal fuzzy weighted average (ITFWA) operator toaggregate the intuitionistic trapezoidal fuzzy informationcorresponding to each alternative and get the overall valueof the alternatives and then rank the alternatives and selectthe most desirable one(s) according to the distance betweenthe overall value of the alternatives and ideal solution Finallyan illustrative example for evaluating the computer networksecurity is given
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper
References
[1] X Mo ldquoResearch on the computer network security evaluationbased on the ULCGM operator with uncertain linguistic infor-mationrdquo Journal of Convergence Information Technology vol 8no 3 pp 160ndash166 2013
[2] G Zhang H Li R Chen et al ldquoResearch and design onvulnerability testing in computer network security systemrdquoAdvances in Information Sciences and Service Sciences vol 5 no7 pp 1ndash10 2013
[3] G Song ldquoComputer network security and precaution evalua-tion based on incremental relevance vector machine algorithm
and ACOrdquo International Journal on Advances in InformationSciences and Service Sciences vol 5 no 1 pp 120ndash127 2013
[4] Y Li J Yin and G Wu ldquoModel for evaluating the computernetwork security with interval-valued intuitionistic fuzzy infor-mationrdquo International Journal of Digital Content Technology andIts Applications vol 6 no 6 pp 140ndash146 2012
[5] J Dong ldquoAn approach to evaluating the computer networksecurity with hesitant fuzzy informationrdquo International Journalof Digital Content Technology and Its Applications vol 6 no 20pp 633ndash639 2012
[6] Y Li X Shan and G Wu ldquoComprehensive evaluation modelfor computer network security with linguistic informationrdquoAdvances in Information Sciences and Service Sciences vol 3 no9 pp 126ndash131 2011
[7] F LHao andDQ Li ldquoAnewrankingmethod of fuzzy numbersrdquoJournal of Ordnance Engineering College vol 19 pp 73ndash75 2007
[8] J Q Wang ldquoOverview on fuzzy multi-criteria decision-makingapproachrdquo Control and Decision vol 23 pp 601ndash607 2008
[9] J Q Wang and Z Zhang ldquoMulti-criteria decision-makingmethod with incomplete certain information based on intu-itionistic fuzzy numbersrdquo Control and Decision vol 24 no 2pp 226ndash230 2009
[10] S P Wan and J Y Dong ldquoMethod of the intuitionistictrapezoidal fuzzy number for multi-attribute group decisionrdquoControl and Decision vol 25 no 5 pp 773ndash776 2010
[11] Y Wang S F Zhang and S Q Xie ldquoIntuitionistic trapezoidalfuzzy geometric aggregation operators and their application togroup decision makingrdquo Value Engineering vol 27 pp 159ndash1612012
[12] J Wu and Y Liu ldquoAn approach for multiple attribute groupdecision making problems with interval-valued intuitionistictrapezoidal fuzzy numbersrdquo Computers amp Industrial Engineer-ing vol 66 pp 311ndash324 2013
[13] JWu andQCao ldquoSame families of geometric aggregation oper-ators with intuitionistic trapezoidal fuzzy numbersrdquo AppliedMathematical Modelling vol 37 no 1-2 pp 318ndash327 2013
[14] G Wei X Zhao and H Wang ldquoAn approach to multipleattribute group decision making with interval intuitionistictrapezoidal fuzzy informationrdquo Technological and EconomicDevelopment of Economy vol 18 no 2 pp 317ndash330 2012
[15] J Wang and Z Zhang ldquoProgramming method of multi-criteriadecision-making based on intuitionistic fuzzy number withincomplete certain informationrdquo Control and Decision vol 23no 10 p 1145 2008
[16] G Wei ldquoSome arithmetic aggregation operators with intuition-istic trapezoidal fuzzy numbers and their application to groupdecision makingrdquo Journal of Computers vol 5 no 3 pp 345ndash351 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
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