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Hi everyone, I have been struggling with this problem since a while now with no luck in solving it. I find it very challenging, but also, I don't consider myself as an expert in probability and statistics. I really hope and appreciate very much if someone can help me with a hint or a solution for it. It is problem summarised below. Many thanks Etienne **************************************************************************** ********** We need to classify the risk of some computer processes Pi (where i in [1..n], where n is an integer of finite value, say 20), in risk levels. As the risk level of every Pi is not known in advance, we choose to classify them those Pi in a maximum of n risk levels, in case every one of those processes turned out was in a different risk level. I informally call a risk level as a risk band, or simply a band. Band goes from 1 to n, also. The data about the risks of those processes is available in the following forms: (Pi<Pj, 0.6) meaning that the risk level of Pi is lower than that of Pj with a degree of confidence of 60%. Informally, the risk analyst is 60% sure of this statement (a kind of fuzziness). Also, for the same i and j, we have: (Pi=Pj, 0.3) and (Pi>Pj, 0.1). The sum of the assertion of the 3 different statements about every relation between two permissions is always 1 (0.6+0.3+0.1). So we are provided with such statements about processes in the system in the way shown. Not every relation between Pi and Pj (for all i and j) has risk data available, but we have a good subset of relations between many of the system's processes. Since there is no total assertion of the relations between the risk level of processes, there isn't also a total assertion about which risk level every process lies in. There is a kind of distribution of the membership of every process within the risk levels (bands). For instance, Pi can be found to be in band j with a membership value of 0.25, and in band k with a membership value of 0.46. A fact is, since every Pi can be in any of those n bands mean that for j=1 to n: Sum(membership (Pi in band j) =1 The goal is to calculate the degree of memberships of every Pi (i=1 to n) in every Band k (k=1 to n). To be more concrete, I consider n=20. For this I have adopted a probabilistic style approach, because the degree of membership of a process in a band is similar to the idea of the likelihood of the process to be in this band. I have tried many solutions, but I couldn't get anywhere. Also the number of scenarios to consider is very large and impossible to calculate on a PC. So, I have tried to do some simulations, with no luck, because the conditions for the simulation technique I used (Monte Carlo) were not met. ------ -------------------------------------------------------------------------------- The information contained herein is confidential and is intended solely for the addressee. Access by any other party is unauthorised without the express written permission of the sender. If you are not the intended recipient, please contact the sender either via the company switchboard on +44 (0)20 7623 8000, or via e-mail return. If you have received this e-mail in error or wish to read our e-mail disclaimer statement and monitoring policy, please refer to http://www.drkw.com/disc/email/ or contact the sender. 3167 --------------------------------------------------------------------------------