IAEA-SM-367/13/06 SAFEGUARDS INFORMATION HANDLING AND TREATMENT

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1 IAEA-SM-367/13/06 SAFEGUARDS INFORMATION HANDLING AND TREATMENT Roland CARCHON, Jun LIU, Da RUAN, Michel BRUGGEMAN SCK CEN Dept. Safeguards and Physics Measurements Boeretang 200 B-2400 Mol Belgium Abstract This paper aims at the handling and treatment of nuclear safeguard relevant information by using the linguistic assessment approach. This is based on a hierarchical analysis of States nuclear activities in a multi-layer structure of the evaluation model. Special emphasis is given to the synthesis and evaluation analysis of the Physical Model indicator information. Accordingly, we focus on the aggregation process with consideration of the different kinds of qualitative criteria. Especially we consider the symbolic approach that acts by the direct computation on linguistic values instead of the approximation approach by using the associated membership function. In this framework, several kinds of ordinal linguistic aggregation operators are presented and analyzed. The application of these linguistic aggregation operators to the combination of the Physical Model indicator information is provided. The study is undertaken in the framework of the Belgian Support Programme to the IAEA (task BEL C 01323). 1. INTRODUCTION As a part of its efforts to strengthen international safeguards, including enhancing its ability to detect any undeclared nuclear activities, the International Atomic Energy Agency (IAEA) is using an increased amount of information on State s nuclear and nuclear-related activities: information provided by the State, information collected by IAEA, and information from open sources (e.g., media, etc.). This information can be of very different nature, it can be incomplete, imprecise, not fully reliable, conflicting, etc. In order to allow an adequate interpretation of the information and to reach a conclusion on undeclared activities and facilities in a State, there is a need to establish an evaluation method that enables the IAEA to draw the conclusion that "No nuclear material in the State is used for the manufacture of nuclear explosive devices"; this conclusion is derived from the information which is collected from the safeguards verification activities and from additional sources. The IAEA Physical Model [1] of the nuclear fuel cycle may be taken as a systematic and comprehensive indicator system, which includes all the main activities that may be involved in the nuclear fuel cycle from source materials acquisition to the production of weapons-usable materials. Especially, the Physical Model also identifies and describes indicators of the existence or development of a particular process. Within the IAEA study, 914 indicators were identified throughout the whole fuel cycle, from mining to reprocessing, that can have a different strength, but that are in one way or another signs for on-going activities. Indeed, the specificity of each indicator has been designated to a given nuclear activity and is used to determine the strength of an indicator. An indicator that is present only if the nuclear process exists or is under development, or whose presence is almost always accompanied by a nuclear activity is a strong indicator of that activity. Conversely, an indicator that is present for many other reasons, or is associated with many other activities, is a weak indicator. In between are medium indicators. The indicators associated with each process are placed in a quasi-logical structure: - a strong indicator: process P implies an indicator x and is implied by the indicator x. - a medium indicator: process P implies an indicator y and the indicator y may imply process P. - a weak indicator: process P may imply an indicator z and the indicator z may imply process P. 1

2 It was considered necessary to have a mathematical framework that provides a basis for synthesis across multidimensional information of varying quality (this means to consider indicators in combination), especially to deal with information that may be unquantifiable due to its nature, and that may be imprecise, too complex, ill-defined, etc. We make use of a linguistic assessment based on fuzzy logic [2]. The linguistic approach is an approximate technique appropriate for dealing with qualitative aspects of problems. Its application is beneficial because it introduces a more flexible framework for representing the information in a more direct and suitable way when it is impossible or unnecessary to express it accurately. For example, the assurance value which reflects the capacity of conducting a specific process at a given nuclear facility will be determined by the assessment of presence of related indicators", which is observed or determined by the experts. Usually the assessment values are not limited to Yes or No, since the expert cannot always detect the indicators arising from the process, instead he may only get certain assurance or possibility of the existence of the indicator, which can be characterized by the fuzzy linguistic variable, and expressed, for example, as "very low, low, or high etc.". A linguistic evaluation model for strengthened safeguards information based on the symbolic approach is established in the present work. By using this evaluation model of States' nuclear activities, we can assess, with some uncertainty or in a qualitative level, the States' capabilities on processing nuclear materials. If we focus on the indicators of undeclared nuclear activities or misuse of declared facilities, then we can get an assurance of undeclared nuclear activities in a State. 2. EVALUATION PRINCIPLES The evaluation principle can be summarized by the multi-criteria evaluation method to get the overall linguistic assessment value for a given process with consideration of all indicators related to this process, as shown in Table 1. Table 1. Multi-expert, multi-indicator (classified) evaluation matrix for a process P F s (w s ) F m (w m ) F w (w w ) EW 1 EW 2 EW 3... EW p E 1 E 2 E 3... E p I s1 A s1,1 A s1,2 A s1,3... A s1,p I s2 A s2,1 A s2,2 A s2,3... A s2,p I st A st,1 A st,2 A st, 3... A st, p D 1 (F s ) D 2 (F s ) D 3 (F s ) D p (F s ) I m1 A m1,1 A m1,2 A m1,3... A m1,p I m2 A m2,1 A m2,2 A m2,3... A m2,p I mr A mr,1 A mr,2 A mr, 3... A mr, p D 1 (F m ) D 2 (F m ) D 3 (F m ) D p (F m ) I w1 A w1,1 A w1,2 A w1,3... A w1,p I w2 A w2,1 A w2,2 A w2,3... A w2,p I wk A wk,1 A wk,2 A wk, 3... A wk, p D 1 (F w ) D 2 (F w ) D 3 (F w ) D p (F w ) D 1 (A) D 2 (A) D 3 (A)... D p (A) D(A) Here E={E 1,, E p } represents the expert activities (detection or assessment is derived from different information sources); EW={EW 1,..., EW p } represents the importance of each expert activity; I={I s1, I st, I m1, I mr, I w1, I wk } represents the indicators related to the process P; A i,j denotes the assessment value of the indicator I i by an expert activity E j ; F s represents the set of all strong indicators related to P, F m represents the set of all medium indicators related to P, and F m represents the set of all weak indicators related to P; W={w s, w m, w w } represents the strength of indicators. D i (A) means the overall assessment of F s, F m, and F w by E i under consideration of the strength of indicators. 2 2

3 D(A) means the overall assessment of D i (A) under consideration of the importance of each expert activity. As a case study, we assume that the assessment value, the importance of each expert activity, and the strength are all taken from the linguistic term set S: S= {s 1 =none, s 2 =very low, s 3 =low, s 4 =medium, s 5 =high, s 6 =very high, s 7 =perfect}. Note that the values of A i,j and the importance of the expert activity are initially given, as these values should be determined according to the results of safeguards activities. 3. THE PROBLEM OF AGGREGATION OF INDICATOR INFORMATION A basic problem is how to deal with the aggregation of the indicator information; due to the different nature of strength of indicators, it is necessary to aggregate the indicators with different strength by using different aggregation operators, and some are given below: (1) Minimum aggregation function: Min. (2) Maximum aggregation function: Max. It should be noted that neither Min nor Max aggregation operator allows any compensation, i.e., a higher degree of satisfaction of one of the criteria cannot compensate for a lower degree of satisfaction of another criterion. Hence the following mean-type aggregation operators can be adopted. (3) Normative approach [3]. In this approach, the decision-maker adds all values relating to every alternative, by taking the average of all the values. For the ordinal case, we have the following normative operator: Norm(A 1,, A n )= Max j [Min(w j, b j )] where A i (i=1,..., n) is the value to be assessed, b j is the jth largest of the A i, w j are given such that for j=1 to n w j =s T(j) with ( m 1) j ( n m) T(j)= Int ( ) n 1 where Int(u) is the integer portion of u, and m is the cardinality of linguistic term set S. Note that Norm is an average-like operator using in the ordinal case. (4) The Hurwicz approach [4,5], i.e., H(A 1,..., A n )=a Max i [A i ]+(1 a) Min j [A j ] (a [0, 1]) This approach attempts to strike a balance between the Max and Min strategy. If the result is a decimal, then an approximate process, e.g., a round operator can be used to get the integer result. (5) Non-weighted median aggregation [3]: The process of taking the median requires an ordering of the arguments and the elements in the middle are significant. Let C={A 1,..., A n } be a collection of elements drawn from S. If we order the elements in C and denote this as {b 1,..., b n } such that b j is the jth largest of the A i in C, then b Med(C)= b n 1 n 2 2 if n is odd, if n is even. Note that the median operation is simply based on the ordering of the elements, it is also like the average in that it is a mean type aggregation. 3

4 (6) Arithmetic Mean (AM) [5]: Let C= {A 1,..., A n } be a set of numerical values. The arithmetic mean is obtained dividing the sum of all values by their cardinality, i.e., n 1 AM(C) Ai. n i 1 If the result is a decimal, then the round operator can be used to get the integer result. Now we turn to the problem of synthesis and evaluation of indicator information. The evaluation procedure can be summarized in different steps: Step 1: Classification of indicators related to a given process P according to their different strengths, strong (F s ), medium (F m ) and weak (F w ). Step 2: Aggregation of the indicators within each category. Class 1 (aggregation of F s ). We will get the assessment of "conducting a specific process at a given facility". Considering that a strong indicator is a sufficient condition (even a necessary condition) for the corresponding process, from the safe point of view, we will propose to use the Max aggregation operator. It aggregates the values on the premise of maximum assurance or possibility of presence of those indicators. Hence, we have: D i (F s )=Max(A s1,i, A s2, i, A sp,i ) Class 2 (aggregation of F m ). Considering that a medium indicator is a necessary condition (not a sufficient condition) for the corresponding process, it follows that both of the indicators with the maximum assurance and those with the minimum assurance are equally important, so we need consider the Max and Min assurance simultaneously. Accordingly, there are two approaches available for this purpose: the Hurwicz approach (H), which attempts to strike a balance between the Max and Min strategy; the Arithmetic Mean (AM), which tries to strike the balance point or center from the set of all values. Note that the Hurwicz approach puts special emphasis on the extreme assurance. In fact it is considered reasonable to assume that the extreme values play an more important role in the aggregation process than the middle ones for the medium indicator. Hence, we propose to use the Hurwicz approach when its parameter a=0.5 which reflects an average of the Max and Min one, i.e., D i (F m )=H(A m1,i,, A mr,i ) (a=0.5) But the Arithmetic Mean (AM) can still be considered available on the premise of mean assurance or possibility of presence of those indicators, i.e., D i (F m )=AM(A m1,i,, A mr,i ) Class 3 (aggregation of F w ). From the definition of weak indicator, single weak indicator has little sense for the overall assessment and each assurance value of indicator is in the same status as those of other weak indicators. It follows that Max, Min and Med, which take the special values (the extreme value and the middle one respectively), are not considered reasonable for aggregation of weak indicators. Also only the Max and Min value are considered in the Hurwicz approach, so the Hurwicz approach is not considered feasible too. Hence, we propose to use the Normative operator (Norm) and the Arithmetical Mean which all take the average of all the values. It aggregates the values on the premise of normative (average) assurance, i.e., or D i (F w )= Norm(A w1,i, A w2,i, A wr,i ) D i (F w )= AM(A w1,i, A w2,i, A wr,i ) In addition, note that the linguistic labels are considered as being in ascending order: 4 4

5 S={s 1 =none, s 2 =very low, s 3 =low, s 4 =medium, s 5 =high, s 6 =very high, s 7 =perfect} We can also meaningfully assign ordered ascending integer values {1, 2, 3, 4, 5, 6, 7}. For convenience, we use these integers instead of s i (i=1,..., 7) to represent the linguistic terms. We use Table 2 to illustrate the aggregation result of indicators within each class by using different aggregation operators and indicate the feasibility of different aggregation operators. Without loss of generality, we use the same example for analysing strong, medium and weak indicators respectively. Table 2. Illustration of aggregation of indicators within each class Experts Indicators E 1 E 2 E 3 E 4 E 5 E 6 feasibility or acceptability I I I strong medium weak I I (1) 7 1 Min (1) 2 1 N N N Max (3) 7 6 Y N N Med (3) 2 6 N N N Norm (3) 3 6 N N Y Hurwicz (a=0.5) (2) N Y N Arithmetic mean (2.6) N Y Y Rounded Arithmetic mean (3) 4 5 N Y Y Suppose I i (i=1,..., 5) in Table 2 are all medium indicators. Then the following remarks can be made: (1) For Med operator, it can be seen from E 2 that Med(I 1,..., I 5 )==1, which seems not reasonable. (2) It was seen that the same results were obtained by the Hurwicz approach in cases E 1, E 2, E 3 because they have the same extreme value (Max and Min values). That means we only strike the balance of Max and Min values and ignore the middle values. For case E 6, this value of I 5 is equal to 1, which would play more important role than other values (all equal to 6) because I 5 is a necessary condition for a given process. But we can see that Norm(E 6 )=6, it actually does not put more emphasis on I 5, and we have H(E 6 )=3.5 and Mean(E 6 )=5, which are considered more reasonable. Moreover, considering the case E 4, when I 5 =7, we have Norm(E 4 )=7, H(E 4 )=5, AM(E 4 )=3.8; when I 5 has a big change to 1, H(E 4 ) is changed to 2, and Mean(E 4 ) is changed to 2.6, which means the H and AM reflect the every changes when the input is different without loss of any information. But Norm(E 4 ) is still equal to 3, which shows that the Norm opeartor is not sensitive on the extreme value variation due to its formulation (with several approximate processes, like Max, Min and Round operations). This is also a reason why we skip using the Norm for the aggregation of medium indicator. (3) Compared with Mean and Hurwicz, the Mean takes the same attitude on the value of each medium indicator and the final result is an average one. the Hurwicz approach put more attention to the extreme Max and Min value. Step 3: Aggregation of F s, F m, and F w considering the corresponding strength of indicators. We need to use the weighted aggregation operator, i.e., D i (A)=Agg W ((w s,d i (F s )), (w m,d i (F m )), (w w,d i (F w ))) Here Agg W can be taken as a weighted aggregation operator to get the final assessment D i (A). According to the following analysis, we propose to use the weighted mean operator which aggregates the value on the premise of mean assurance under consideration of the strength. The following are some weighted aggregation operators maybe available: 5

6 (1) Min-type weighted aggregation (W-min) [7]: W-min((w 1, a 1 ), (w 2, a 2 ),..., (w n, a n ))=Min(g(w 1, a 1 ), g(w 2, a 2 ),..., g(w n, a n )) here g(w i, a i )=Max(Neg(w i ), a i ). Neg(w i ) is the negation of w i. (2) Max-type weighted aggregation (W-max) [6]: W-max((w 1, a 1 ), (w 2, a 2 ),..., (w n, a n )=Max(g(w 1, a 1 ), g(w 2, a 2 ),..., g(w n, a n )) here g(w, a)=min(w i, a i ). (3) Med-type weighted aggregation (W-med) [4,6]: W-med((w 1, a 1 ), (w 2, a 2 ),..., (w n, a n ))= Med(a + 1, a - 1, a + 2, a - 2,..., a + p, a - p ). Here the two elements a + i = Max(Neg(w i ), a i ), a - i =Min(w i, a i ). (4) Weighted mean aggregation operator (W-mean) [5,7]: Let X={a 1,..., a n } be a set of numerical values and W X ={w 1,..., w n } be their associated weights, such that, w 1 corresponds to a 1 and so on. The weighted mean will be: W-mean ((w 1, a 1 ), (w 2, a 2 ),..., (w n, a n )) n i 1aiwi n i 1wi. We use Table 3 to illustrate the weighted aggregation result of indicators for Step 3 by using different weighted aggregation operators and explain the feasibility of different aggregation operators. Table 3. Illustration of weighted aggregation of indicators expert E 1 E 2 E 3 E 4 E 5 E 6 E 7 indicators D(F s ) D(F m ) D(F w ) 1 (7) 1 (7) 1 (7) 1 (7) 1 (7) 1 (7) 1 (7) W-min 1 (1) 2 (2) 3 (3) 4 (4) 4 (4) 4 (4) 4 (4) W-max 1 (1) 2 (2) 3 (3) 4 (4) 5 (6) 6 (6) 7 (7) W-med 1 (1) 2 (2) 3 (3) 4 (4) 4 (4) 4 (4) 4 (4) W-mean 1 (1.5) 1.58 (2.08) 2.17 (2.67) 2.75 (3.25) 3.33 (3.83) 3.91 (4.42) 4.5 (5) rounded W-mean 1 (2) 2 (2) 2 (3) 3 (3) 3 (4) 4 (5) 5 (5) Remarks: From the column E 1 to the column E 6 in this table, we can seen that when D m =1, D s are all fixed and D w increases from 1 to 7, there is no difference in the aggregation results by using the different operator W-min, W-max and W-med. It shows that these three weighted aggregation operators are not reasonable. But it shows that the weighted mean results are reasonable. Step 4: Aggregation of several detecting activities. Steps 1-3 are the procedure to get the overall assessment by each indicator-detecting activity. In Step 4, we consider the evaluation about the assessment of process P with consideration of different importance of each expert activity. Note that the Min-type, Max-type or Med-type weighted aggregation operator will overstate the fused value due to the lose of too much information (shown in Step 3). It should be a consensus degree of all expert activities. Hence, we also propose to use the weighted mean operator to get the final assessment D(A). It aggregate the value on the premise of mean assurance under consideration of the importance of each expert activity, i.e., D i (A)=W-mean((EW 1, D 1 (F s )), (EW 2, D 2 (F m )),..., (EW p, D p (F w ))) 6 6

7 As an example we consider a specific evaluation to illustrate our method. Let it be required to evaluate the possibility of conducting a specific process Gaseous diffusion enrichment within the evaluation of production of highly enriched uranium (in short HEU) as shown in Table 4. Although we have described different term sets for strength, importance and the assessment value, we need to unify them into one common set in order to operate them. Assume the common set if the set of the assessment value S, the set of strength terms will be changed to S from an aggregation operative point of view, the corresponding transformation is: strong is equivalent to 7, medium is equivalent to 4, and weak is equivalent to 1, i.e., here we take the weight vector of indicator from S as W I =(7 4 1), and suppose that the importance of expert activity is also taken from S. In Table 4, the importance vector EW of E i (i=1,..., 4) is (3, 5, 4, 2). Table 4. Evaluation of the process A - Gaseous diffusion Enrichment E 1 (3) E 2 (5) E 3 (4) E 4 (2) Compressor for pure UF F s Gaseous diffusion barrier (7) Heat exchanger for cooling pure UF D(F s ) (Max) Diffuser housing/vessel Gas blower for UF F m (4) F w (1) Rotary shaft seal Special control value (large aperture) Special shut-off value (large apertue) Chlorine trifluoride Nickel power, high purity D(F m ) (Mean) D(F m ) (Hurwicz) Gasket, large Feed system/product and tails withdrawal Expansion bellows Header piping system Vacuum system and pump Alumnium oxide power Nickel power PTFE(teflon) Large electrical switching yard Large heat increase in air or water Larger specific power consumption Larger cooling requirements (towers) D(F w ) (Mean) D(F w ) (Norm) D i (A)(max-mean-norm) D i (A)(max-mean-mean) D i (A)(max-H-norm) D i (A)(max-H-mean) D(A)(max-mean-norm) 4.64 D(A)(max-mean-mean) 4.74 D(A)(max-H-norm) 4.76 D(A)(max-H-mean) 4.77 Rounded D(A) 5 Here, D(F s ) (max), D(F m ) (mean) and D(F w ) (mean) means that the aggregation result in each class by using Max, Mean and Mean respectively in. Others has the similar meaning. D i (A)(max-mean-norm) means the weighted aggregation of the results gotten from Step 2 where Max, Mean and Norm are 7

8 applied on the aggregation of strong, medium and weak indicators respectively. Others has the similar meanings. D(A)(max-mean-norm) is the corresponding weighted aggregation result from Step 3. All the results in Table 4 are based on the formulation from Steps 1-4. The calculations were made by the MATLAB software, but can also be made by hand. A software becomes necessary with a huge amount of data. The assessment of conducting a specific process Gaseous diffusion enrichment is s 5, i.e., high. 4. CONCLUSION A mathematical formulation was developed towards decision making based on information that can be vague, incomplete, conflicting etc. Soft computing with words is applied. To manipulate the linguistic information, we worked with aggregation operators for combining the linguistic un-weighted and weighted values by direct computation on labels. Based on the above analysis, we presented the multi-criteria, multi-expert evaluation method to get the overall linguistic assurance value for a given process, taking into account the particular nature of the indicators and the specific differences among the experts activities through the aggregation process. A case study on the application of these aggregation operators to the fusion of safeguards relevant information is given. A sensitivity study is made to detect in what sense the overall assessment is influenced by the choice of the aggregation operators. By using this evaluation model of States s nuclear activities, we can assess, with some uncertainty or in a qualitative level, the States s capabilities on processing nuclear materials. If we focus on the indicators of undeclared nuclear activities or misuse of declared facilities, then we can get an assurance of undeclared nuclear activities or misuse of declared facilities in a State. Some related work what we have done can be seen in [8-12]. The way to represent the expert s assessment can be changed and does not necessary to be formulated in the linguistic value context but can also be made in the numerical way. From the application point of view, this issue will be further investigated in the future. REFERENCES [1] IAEA - Physical model - IAEA report STR-314 (May 1999). [2] L. A. Zadeh, The concept of a linguistic variable and its applications to approximate reasoning, Part I, II, III, Information Sciences 8 (1975) , 8 (1975) , 9 (1975) [3] R.R. Yager, An approach to ordinal decision making, Int. Journal of Approximate Reasoning 12 (1993) [4] R.R. Yager, Applications and extension of OWA aggregation, Int. Journal of Man-Machine Studies 37 (1992) [5] D. Dubois and H. Prade, A review of fuzzy sets aggregation connectives, Information Sciences 36 (1985) [6] R.R. Yager, A new methodology for ordinal multiple aspect decision based on fuzzy sets, Decision Sciences 12 (1981) [7] D. Ruan, R. Carchon, and E.E. Kerre, Aggregation operators: properties and applications, SCK CEN Internal Report R-3331 (1999). [8] R. Carchon, D. Ruan, J. Liu, M. Bruggeman, Application of Logical Computing Methods, The 22nd ESARDA Symposium on Safeguards and Nuclear Material Management, Dresden, Germany, May, [9] R. Carchon, D. Ruan, J. Liu, A linguistic evaluation model for strength safeguard relevant information, The 23rd ESARDA Symposium on Safeguards and Nuclear Material Management 2001, May, Bruges, Belgium. [10] J. Liu, D. Ruan and R. Carchon, A New Decision Model for nuclear Safeguards Applications Based on Linguistic Expressions, SCK CEN Report BLG-873, March,

9 [11] J. Liu, R. Carchon, and D. Ruan, Synthesis and Evaluation Analysis of the Physical Model Indicator Information if Considered in Combination, SCK CEN Report R-3463, May, [12] R.E. Bellman and L.A. Zadeh, Decision making in a fuzzy environment, Management Science 17 (1970) [13] M. Delgado, J.L. Verdegay and M.A. Vila, On aggregation operations of linguistic labels, Int. Journal of Intelligent Systems 8 (1993)