Theory of Imprecise Sets: Imprecise Matrix

Imprecise vector: Membership Surface and its arithmetic

“…The Randomness-Impreciseness Consistency Principle states that two laws of randomness are necessary and sufficient to define a normal imprecise number. Based on this principle Das and Baruah ([7], [8], [9], [10], [11]) have already shown the construction of the membership surface or presence level indicator surface of a normal imprecise vector. An imprecise vector (X,Y ), where X and Y are imprecise numbers represented by X = [a, b, c] and Y = [p, q, r] respectively and if the membership function of X and Y be…”

“…According to Randomness-Impreciseness Consistency Principle L(x), a ≤ x ≤ b, p ≤ y ≤ r and L(y), a ≤ x ≤ c, p ≤ y ≤ q are distribution functions and R(x), b ≤ x ≤ c, p ≤ y ≤ r and R(y), a ≤ x ≤ c, q ≤ y ≤ r are complementary distribution functions. Then Das and Baruah ([7], [8]) have established that the membership surface of the imprecise vector (X,Y ) can be obtained as follows…”