Due to the fact that basic uncertain information provides a simple form for decision information with certainty degree, it has been developed to reflect the quality of observed or subjective assessments. In order to study the algebra structure and preference relation of basic uncertain information, we develop some algebra operations for basic uncertain information. The order relation of such type of information has also been considered. Finally, to apply the developed algebra operations and order relations, a generalized TODIM method for multi-attribute decision making with basic uncertain information is given. The numerical example shows that the developed decision procedure is valid.
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