Multiple attribute decision making with flexible linguistic expressions: A linguistic distribution-based approach with interval estimations

•We investigate the linguistic MADM with the data of flexible linguistic expressions.•We present a linguistic distribution-based approach with interval estimations.•We estimate the lower and upper bounds of linguistic distribution approximations.•We demonstrate the effectiveness of the flexible linguistic MADM methods. In linguistic multiple attribute decision making (MADM), flexible linguistic expressions can provide a general way to express complex preference data linguistically, which presents the challenge of handling such complex linguistic data. In this paper, we investigate the linguistic MADM with the concept of flexible linguistic expressions, and present a linguistic distribution-based approach with interval estimations to support the MADM with the data of flexible linguistic expressions. We first convert flexible linguistic expressions approximately to linguistic distributions through developing two models to estimate the lower and upper bounds of the approximated linguistic distributions’ expectations on the attribute level. Then, we generate the interval estimations of comprehensive values of approximated linguistic distributions on the alternative level, and propose the solution algorithm to support the linguistic MADM with flexible linguistic expressions. Finally, the numerical and comparative analysis is performed to illustrate and justify the flexible linguistic MADM methods.