Application of Z-numbers in multi-criteria decision making

The Z-number contains both uncertain variable and its reliability, and it has stronger potential in applications in the fields of decision making, risk assessment etc. In this paper, a method of multi-criteria fuzzy decision making with Z-numbers is proposed, where the evaluation of each alternative with respect to each criterion is described as a Z-number, including both the evaluation and its reliability from evaluators. The reliability towards the evaluation is here regarded as the uncertain region of the fuzzy number of evaluation. Then the Z-number is converted to the interval-valued fuzzy set with footprint of uncertainty (FOU). By computing the centroid of the interval-valued fuzzy set with K-M algorithm, the Z-numbers in the decision making matrix are converted to the crisp numbers for decision making. A numerical example is given to illustrate the procedure and effectiveness of the method.