Abstract
This study defines interval type basic uncertain information and BUI type basic uncertain information, which are two extensions of basic uncertain information and can model more types of uncertainties and uncertainty involved evaluation problems. Under rules based and linguistic decision making environments, we analyze and provide some classification rules with real values, interval values, BUI granules, interval type basic uncertain information and BUI type basic uncertain information. Using the proposed new concepts and decision making methods, an illustrative example in preference and uncertainty involved multi-source evaluation is presented.