This paper elaborates the different methods to generate normalized weight vector in multi-criteria decision-making where the given information of both criteria and inputs are uncertain and can be expressed by basic uncertain information. Some general weight allocation paradigms are proposed in view of their convenience in expression. In multi-criteria decision-making, the given importance for each considered criterion may have different extents of uncertainty. Accordingly, we propose some special induced weight-allocation methods. The inputs can be also associated with varying uncertainty extents, and then we develop several induced weight-generation methods for consideration. In addition, we present some suggested and prescriptive weight allocation rules and analyze their reasonability.

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.