Imprecise vector: Membership Surface and its arithmetic

Abstract

In this article, a method has been developed to perform the arithmetic operations of imprecise vector and its membership surface based on Randomness -Impreciseness Consistency Principle which states that Dubois-Prade left reference function is a distribution function and the right reference function is a complementary distribution function. Using the proposed method one can easily perform the arithmetic operations of imprecise vector and can construct the membership surface. Here, we have shown how to perform the arithmetic operations of imprecise vectors using the proposed method, explained its application in real life situation and compared with existing method. In numerical examples discussed here, we have performed the arithmetic operations only for two dimensional vectors, but there is no restriction on dimensions to perform the arithmetic operations and to obtain the membership surface by the proposed method.