Evidential Reasoning Approach for Multiattribute Decision Analysis Under Both Fuzzy and Interval Uncertainty

Many multiple attribute decision analysis (MADA) problems are characterized by both quantitative and qualitative attributes with various types of uncertainties. Incompleteness (or ignorance) and vagueness (or fuzziness) are among the most common uncertainties in decision analysis. The evidential reasoning (ER) and the interval grade ER (IER) approaches have been developed in recent years to support the solution of MADA problems with interval uncertainties and local ignorance in decision analysis. In this paper, the ER approach is enhanced to deal with both interval uncertainty and fuzzy beliefs in assessing alternatives on an attribute. In this newly developed fuzzy IER (FIER) approach, local ignorance and grade fuzziness are modeled under the integrated framework of a distributed fuzzy belief structure, leading to a fuzzy belief decision matrix. A numerical example is provided to illustrate the detailed implementation process of the FIER approach and its validity and applicability.