8. Determine the a-cuts of the fuzzy relation à in Exercise 7 above for a = 0.4, 0.8, 1.0, as well as the equivalence classes induced by the fuzzy equivalence relation à in each of these a-cuts.
8. Determine the a-cuts of the fuzzy relation à in Exercise 7 above for a = 0.4, 0.8, 1.0, as well as the equivalence classes induced by the fuzzy equivalence relation à in each of these a-cuts.
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Please answer number 8
Transcribed Image Text:7. Prove that the relation à on the universe X = {a, b, c, d, e, f, g) represented by the following matrix.
à =
2A
1
0.8
0
0.4
0
0
0
0.8 0
1
0
0
1
0.4
0
0
0
0
0.4
0.4
0
1
1
0.9
0
0.5 0
0
0
0
0
0
0.9
0.5
0
0
1
0.9 0.5
0.9
1 0.5
0.5 0.5 1
0
0
1
0
is a fuzzy equivalence relation as well
8. Determine the a-cuts of the fuzzy relation à in Exercise 7 above for a = 0.4, 0.8, 1.0, as well as the
equivalence classes induced by the fuzzy equivalence relation à in each of these a-cuts.
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