An Outline of New Approach to Computation with Z-Numbers Based on the Concept of Lower Prevision

The concept of the Z-number was introduced to formalize partially reliable information. A Z-number represents linguistic evaluations of a random variable’s value and the associated reliability degree. The latter is defined as a fuzzy restriction on the value of a probability measure since the actual probability distribution is unknown. Lotfi Zadeh formalized an extension principle for computation with Z-numbers based on fuzzy and probabilistic arithmetic and noted that the problem of computing with Z-numbers is easy to formulate but difficult to solve. Since then, a series of theoretical studies and practical applications of Z-numbers has been proposed. However, the computational complexity of Z-numbers remains a challenge. Because the actual probability distribution is unknown, a set of probability distributions is considered, which is the main source of computational complexity. In this study, we outline a new approach to computation with Z-numbers that relies on the concept of imprecise probability. Specifically, we use a lower prevision measure (the lower envelope of a set of probability measures) as the basis for computation. The reason is a one-to-one correspondence between lower previsions and convex sets of probability measures. Experimental results show that the proposed approach reduces computational complexity compared with existing methods.