Beyond Your Doubts

  1. Consider a fuzzy set A defined in the interval x = [0,10] of integers by the membership function images. Find α‐cut corresponding to α = 0.4.
  2. For two fuzzy sets: A = {(2,0.4), (4,0.5), (6,0.1)}, B = {(3,0.3), (7,0.5)}, compute the product A × B.
  3. Consider two fuzzy relations:

    images and images.

    Compute the following: (i) images, (ii) images, and (iii) images.

  4. For the relation, images,

    compute first projection, second projection, and total projection.

  5. For the two fuzzy relations:

    images, images,

    compute max‐average, max‐prod, and max‐min composition.

  6. Consider a fuzzy relation .

    Find the transitive closure of the relation.

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