# Suppose that the state of “fast speed” of a machine is denoted by the fuzzy set F with membership…

Suppose that the state of “fast speed” of a machine is denoted by the fuzzy set F with membership function mF (n ). Then the state of “very fast speed,” where the linguistic hedge “very” has been incorporated, may be represented by mF (n ? n0 ) with n0 > 0. Also, the state “presumably fast speed,” where the linguistic hedge “presumably” has been incorporated, may be represented by mF 2 (n ).

(a) Discuss the appropriateness of the use of these membership functions to represent the respective linguistic hedges.

(b) In particular,

in the discrete universe V = {0, 10, 20, . . . , 190, 200} rev/s and v0 = 50 rev/s, determine the membership functions of “very fast speed” and “presumably fast speed.”

(c) Suppose that power p is given by the relation (crisp)

p = v2

For the given fast speed (fuzzy) F, determine the corresponding membership function for power. Compare/contrast this with “presumably fast speed.”

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