Operations on hybrid linguistic representations

To reflect the personalized cognition and expression in qualitative multiple criteria decision-making, this paper proposes unified operations for hybrid linguistic representations. To do so, the expected values of ten linguistic representation models are respectively defined based on the characteristic values of linguistic terms calculated by linguistic scale functions. Then, methods to compute the uncertainty degrees for ten models are developed to reflect the inherent hesitation and uncertainty of linguistic evaluations. Based on the expectation values and uncertainty degrees, hybrid linguistic operations are unified. An expectation value and uncertainty degree-based (EVUDB) method is developed for multiple criteria decision-making problems based on the proposed operations on hybrid linguistic representations. The advantages of the hybrid linguistic representations are highlighted by comparing with single linguistic representation model in solving a practical problem.