Exact Construction of Liu Process

Credibility measure was created by Baoding Liu [5, 7] and his Chinese co workers [4] around 2004. Then, Baoding Liu designed a grand view of fuzzy process, hybrid process and uncertain process [6]. In response to his work, Dai [1] sketched how to create standard normal fuzzy process under credibility measure, which he called standard Liu process. Independently Kageyama and Iwamura [3] constructed discrete time credibilistic processes and studied some convergences of the processes. Then, Iwamura and Kageyama [2] showed the existence of fuzzy process called standard Liu process with non decreasing sample paths. In this paper, we show how to mathematically create Liu process. In section 2, we give preliminary facts on credibility measure, fuzzy process, Liu process and credibility extension theorem. In section 3, we state how to create standard Liu process. In section 4, we state how to create Liu process.