Multi Attribute Decision Making Using Optimistic/Pessimistic Z-Numbers

This paper presents a novel approach for multi attribute decision making (MADM). It proposes the concept of optimistic/pessimistic Z-number, which is defined as a tuple
$(Z_{x},\delta)$
where
$Z_{x}$
is a Z-number, and
$\delta \in \{+,-\}$
determines if the evaluator is optimistic (+) or pessimistic (−) regarding the provided Z-valuation. Optimistic Z-valuation shows that the hesitation of the evaluator is toward increasing the value of the evaluated object. Pessimistic Z-valuation shows that the hesitation of the evaluator is toward decreasing the value of the evaluated object. Using optimistic/pessimistic Z-number in MADM process involves asking the decision maker to evaluate a set of alternatives with respect to a set of weighted criteria using optimistic/pessimistic Z-numbers. After that the provided evaluations are converted to crisp values using the proposed
$RANKING$
function, which considers the linguistic meaning of the components of Z-numbers. In the last stage, weighted sum model is used to find the best alternative. The proposed
$RANKING$
function shows realistic results when it is compared with a well-known method from the literature.