Question: In the field of computer networking there is an imprecise relationship between the level of use of a network communication bandwidth and the latency

In the field of computer networking there is an imprecise relationship between the level of use of a network

In the field of computer networking there is an imprecise relationship between the level of use of a network communication bandwidth and the latency experienced in peer-to-peer communication. Let X~ be a fuzzy set of use levels (in terms of the percentage of full bandwidth used) and Y~ be a fuzzy set of latencies (in milliseconds) with the following membership function: X~= (0.2 0.5 0.8 10 20 0.3 0.6 0.5 1 Y~= + 40 60 0.9 1.5 1.0 0.6 80 + 1.0 4 + + 0.6 8 + 0.1 100, 0.3 20 Find the Cartesian product represented by the relation R~= XxY. Now, suppose we have second fuzzy set of bandwidth usage given by (0.3 0.6 0.7 0.9 1 0.5 + 60 80 20 40 Find S=X~.R using (1) Max-min composition and (2) Using max-product composition.

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