AN IMPROVED METHOD OF HIERARCHIC ANALYSIS FOR CHOOSING OPTIMAL INFORMATION PROTECTION SYSTEM IN COMPUTER NETWORKS

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1 S. M. Kusemko, Cand. Sc. (Eng.), Ass. Prof.; V. M. Melnchuk AN IMPROVED METHOD OF HIERARCHIC ANALYSIS FOR CHOOSING OPTIMAL INFORMATION PROTECTION SYSTEM IN COMPUTER NETWORKS An mproved herarchc analyss method, based on the nterval estmate of the preferences of crtera and alternatves, s proposed and nvestgated. Key words: decson-makng, nterval calculatons, multcrteron problems. Introducton In up-to-date computer and telecommuncaton networks varous nformaton protecton systems and means are wdely used. They must provde the requred level of protecton and at the same tme should not be too complcated and expensve n the development and operaton []. As a large number of conflctng crtera s a general characterstc of nformaton protecton systems (e.g., prce qualty), the choce of a defnte archtecture for the nformaton protecton system s a complcated, multparametrc and optmzaton problem that, to a great extent, depends on the system of preferences of a person or persons who make the choce [2]. Currently, a large number of methods exst for solvng decson-makng problems wth many crtera: methods of crtera reducton to a sngle crteron (the methods of man component, complex crteron, of a justfed compromse, the method of Hermeyer, constructon and analyss of Edgeworth Pareto set) and methods for studyng psychologcal peculartes of a person that s makng decson (DMP) (multcrteron utlty theory, herarchc analyss method, methods for rankng multcreteron alternatves) [3]. For solvng the problem of choosng the optmal nformaton protecton system, methods based on the psychologcal study of a DMP are consdered to be the most feasble ones [3]. In ths group the method of herarchc analyss s the most wdely used one and the easest for understandng. However, ths method does not enable full descrpton of DMP system of preferences. Also, t cannot be used n case of several DMP wth conflctng systems of preferences. Therefore, t s feasble to mprove the herarchc analyss method. Problem statement Let us set the task of the development and nvestgaton of the method for choosng the optmal nformaton protecton system n the case of several DMP or when uncertantes are present n the system of DMP preferences. For ths we shall consder an mproved method of herarchc analyss. An mproved method of herarchcal analyss The tradtonal analyss of herarches was proposed by Saat [4]. In ths method a tree of crtera s used where general crtera are dvded nto crtera of specfc character. For each group of crtera the mportance coeffcents are determned. The alternatves are also compared wth one another accordng to ndvdual crtera. Importance coeffcents of the crtera and alternatves are determned by a parwse comparson. The results of comparson are evaluated accordng to a defnte scorng scale. On the bass of such calculatons the crtera mportance coeffcents, estmates of the alternatves are found and general estmate s found as a weghted sum of the crtera estmates. The usage of scorng evaluaton does not allow descrbng the uncertanty of DMP preference system or makng team decsons [4]. In order to solve the stated problem we propose an mproved method of herarchc analyss, based on the usage of nterval estmates for the preferences of crtera and alternatves. The mproved method of herarchc analyss ncludes the followng stages: Наукові праці ВНТУ, 200, 2

2 . Structurng of the task n the form of a herarchc structure: objectves; crtera; alternatves. 2. By questonng of DMP or a group of DMP, usng an nterval scorng scale, a matrx of parwse comparson of preferences for the crtera s flled. Relatve coeffcents of the crtera mportance are determned by the formula: w = n n q, j j = where w nterval estmate for the relatve coeffcent of Q crteron mportance; q nterval j scorng estmate for the preference of crteron Q to crteron Q j. 3. By questonng DMP or a group of DMP, usng an nterval scorng scale, matrces of parwse comparson for the alternatves for each crteron are flled. Relatve coeffcents of the crtera mportance are determned by the formula: where V jk = n n a j = V jk nterval value of the relatve mportance coeffcent for alternatve a j by crteron Q k ; a k j nterval score estmate for the preference of alternatve a to alternatve a j by crteron Q k. 4. Quanttatve qualty ndcator for each alternatve s calculated by the formula: Q (a ) = j where Q ( a j ) s nterval global estmate of alternatve a j. If a team decson s beng taken, at stages 2, 3 each DMP bulds matrces of parwse comparson of crtera and alternatves. Then general matrces of parwse comparson of crtera and alternatves are calculated by the formulas: q j Наукові праці ВНТУ, 200, 2 2 N = k j, w V j, g g { q };max{ q } j 2j g = q ;q = mn, j 2j g k k [ ] = { } { } gk gk a j;a 2j mn q j ;max q 2j g g k a =,, j where q g j, q g 2 j are lower and upper lmts of the nterval scorng estmate of Q crteron preference to Q j crteron of the g-th DMP; a gk j, q gk 2 j nterval scorng estmate of a alternatve preference to a j alternatve by crteron Q k of the g-th DTP. Arthmetc operatons wth nterval estmates are performed by the followng formulas [5]: [ c ;c ] = [ a + b ;a b,] a + b = c = a b = c = [ c ;c2] = [ mn{ a b j} ;max{ a x b j} ], [ ] [ { } { } n a = c = c ;c = mn n a ;max n a ], a = c = 2 [ c ;c ] = mn{ };max{ }, 2 a a

3 where a, b, c are nterval numbers. Expermental nvestgaton of ths method s performed by the example of solvng multcrteron problem of optmal nformaton protecton system selecton under varous condtons. In the frst case the problem s characterzed by the uncertanty n the system of preferences of one DMP and n the second case by the presence of two DMP wth controversal preference systems. Expermental nvestgatons Let us consder general condton of the problem of choosng the optmal nformaton protecton system. Informaton protecton system must be chosen so that t would meet the followng requrements: maxmal protecton degree, reasonable prce, user-frendlness. Three alternatves are avalable: a protecton degree extremely hgh, very expensve IPS, very complex n use; a 2 protecton degree hgh, expensve IPS, not user-frendly; a 3 protecton degree moderately hgh, nexpensve IPS, user-frendly. In order to solve a multcrteron decson-makng problem, a opt { a, a 2, a 3 } must be determned. The problem of choosng the optmal IPS s characterzed by the followng crtera: Q protecton degree; prce; Q 3 complexty n servce. For parwse comparson of crtera and alternatves the followng scale of relatve mportance wll be used: The scale of relatve mportance Relatve mportance ntensty Defnton Equal mportance 3 Moderate advantage 5 Essental advantage 7 Strong advantage 9 Very strong advantage 2, 4, 6, 8 Intermedate values The frst case one DMP wth uncertantes n the system of preferences. Usng nterval estmates, a matrx of parwse comparsons for the crtera was bult. On the bass of ths matrx relatve coeffcents of the crtera mportance were calculated. Calculaton results are presented n table. Table Parwse comparson matrx for the crtera Q (protecton degree) (prce) Q 3 (complexty n servce) Egenvector Q (protecton degree) (prce) [2;4] Q 3 (complexty n servce) [5;6] [2; 4] [5; 6] [2, 6; 2, 88] [3; 4] [0,9;,26] [0,35; 0,4] The egenvector elements are calculated as the n-th root of the product of correspondng matrx Наукові праці ВНТУ, 200, 2 3

4 row elements. Ther values are relatve mportance coeffcents of the correspondng crtera. By questonng DMP, matrces of parwse comparson are bult for the alternatves for each crteron, and usng the proposed formulas correspondng nterval estmates of the relatve mportance coeffcents for the alternatves are calculated. The results are presented n tables 2 3. Parwse comparson matrx for the alternatves connected wth crtera Q and Q2 Egenvector Egenvbector Q a a 2 a 3 a a 2 a 3 a a 2 [3; 4] [4; 5] [2,29; 2,7] [2; 3] [0,79; ] a a 2 [3; 4] [0,3; 0,36] [7;8] [0,84; ] [4;5] Таблица 2 a 3 [4;5] [2;3] [0,4; 0,5] a 3 [7; 8] [4; 5] [3,04; 3,42] Таблица 3 Parwse comparson matrx for the alternatves connected wth crteron Q3 Q 3 a a 2 a 3 a Egenvector [0,32; 0,38] [6;8] a 2 a 3 [3; 4] [6; 8] [3; 4] [0,9;,] [2,62; 3,7] Let us calculate the global crteron for each alternatve: Q ( a) wv =[5,34; 8,36], = 3 = Q ( a2) wv2 =[2,78; 4,58], = 3 = Q ( a3) wv3 =[4,55;7,0]. = 3 = The alternatve wth maxmal values of the upper and lower lmt of Q s consdered to be the best one,.e. n our case a opt = a. The second case two DMP wth conflctng preference systems. Table 4 presents parwse comparson matrces for the frst and the second DMP. Наукові праці ВНТУ, 200, 2 4

5 Таблица 4 The frst DMP Parwse comparson matrx for the crtera for the frst and the second DMP Q Q 3 The second DMP Q Q 3 Q [0,25; 0,5] [4; 4,5] [5; 6] Q 3 [0,33; 0,5] [0,33; 0,5] Q [0,25; 3] Q 3 [,37;,5] Q [2; 3] [0,39; 4] [4; 5] Q 3 [0,4; 0,66] [0,4; 0,66] The matched parwse comparson matrx for the crtera Q Q 3 An mproved method of herarchc analyss, based on the nterval estmaton of the preferences of crtera and alternatves, s proposed and nvestgated. The research has demonstrated the possblty to solve the problem of choosng optmal nformaton protecton systems when uncertantes are present n DMP preference systems and whle takng team decsons. It should be noted that n the case when a sngle optmal alternatve cannot be objectvely determned on the bass of the avalable nformaton, the method makes t possble to reduce the set of ntal Наукові праці ВНТУ, 200, 2 5 Egenvector [3,90; 4,50] [4;6] [2,5; 3,00] [0,33; 66] [0,33; 66] [,37;2,67] [0,70; 2] [0,3; 0,48] [2,5; 2,67] Таблица 5 Parwse comparson matrces for the alternatves for two DMP are matched and they consde wth the matrces from tables 2, 3 for the prevous task. Let us calculate the global crteron for each alternatve: Q ( a) wv =[6,042; 9,0024], = 3 = Q ( a2) wv2 =[2,845; 5,528], = 3 = Q ( a3) wv3 =[4,962; 9,866]. = 3 = The alternatve wth maxmal values of the upper and lower lmts Q s consdered to be the best one, but n ths case there s no such an alternatve because the lower lmt of a 3 estmate s smaller than the lower lmt of a, and at the same tme upper lmt of a 3 estmate s hgher than the upper lmt of a estmate. Ths means that alternatves a and a 3 are ncomparable. The alternatve a 2 s worse than a and a 3. Therefore, the two potentally optmal alternatves wll be the fnal choce. To determne the more optmal from the two alternatves, further nvestgaton of DMP preference systems s requred, possbly, wth the applcaton of other methods or through negotatons between DMP n order to reduce contradctons between the preference systems by certan compromses. Conclusons

6 alternatves and to obtan a subset of potentally optmal alternatves and ncomparable alternatves. In further research the apparatus of the theory of fuzzy sets wll be used to evaluate the preferences of crtera and alternatves. REFERENCES. Домарев В. В. Безопасность информационных технологий. Методология создания систем защиты / В. В. Домарев К.: ООО "ТИД "ДС", с. 2. Титоренко Г. А. Информационные технологии управления: учебное пособие для вузов / под ред. проф. Г. А. Титоренко. 2-е изд., доп. М.: ЮНИТИ-ДАНА, с. 3. Курчиков Л. Н. Неопределенность и определенность / Л. Н. Курчиков М., с. 4. Таха Хемди Введение в исследование операций / Таха Хемди [7-е изд.]. Пер. с ан. М.: Вильямс, с. 5. Аленфельд Г. Введение в интервальные вычисления / Г. Аленфельд, Ю. Херцбергер М: Мир, 987, 360 с. Sergey Kuzemko Cand. Sc. (Eng.), Ass. Prof. of the Computer Engneerng Department. kuzemko@yandex.ru. Volodymyr Melnychuk Student. Vnnytsa Natonal Techncal Unversty. Наукові праці ВНТУ, 200, 2 6