Imprecise Vector: The Case of Subnormality

Abstract

Imprecise vector is a vector containing imprecise elements. An array or a vector $$X=(X_{1}, X_{2},\ldots,X_{n})$$ is an imprecise vector if the elements $$X_{i}, i=1,2,\ldots,n,$$ are imprecise numbers. Two laws of randomness are necessary and sufficient to define a normal law of impreciseness. Based on the method of superimposition of sets, the construction of the membership surface of normal imprecise vector has been developed with reference to probability measure. A normal imprecise vector is a special case of a subnormal imprecise vector in the sense that a subnormal imprecise vector is nothing but a generalized imprecise vector. The method of construction of the membership surface of subnormal imprecise vector with reference to Lebesgue–Stieltjes measure is explained in this paper.