Actual stochastic multicriteria decision‐making (MCDM) problems usually exhibit two forms of information loss: criteria value uncertainty and criteria weight uncertainty. In this paper, extended gray numbers (EGNs), integrated with discrete gray numbers and interval gray numbers are used to express the uncertainty of stochastic MCDM problems. Stochastic multicriteria acceptability analysis (SMAA) and ELECTRE III are combined to solve stochastic MCDM problems with uncertain weight information. First, the outranking relations on interval gray numbers and EGNs are defined. Then, a SMAA‐ELECTRE model for dealing with gray stochastic MCDM problems is constructed. Finally, an illustrative example and two comparative analyses are provided to verify the feasibility and usability of the proposed approach. The proposed approach provides recommendations for alternatives based on uncertain preference information. It therefore contributes a new way to solve stochastic MCDM problems with uncertain, imprecise, and/or missing preference information.

Linguistic hesitant fuzzy sets (LHFSs), which can be used to represent decision-makers' qualitative preferences as well as reflect their hesitancy and inconsistency, have attracted a great deal of attention due to their flexibility and efficiency. This paper focuses on a multi-criteria decision-making approach that combines LHFSs with the evidential reasoning (ER) method. After reviewing existing studies of LHFSs, a new order relationship and Hamming distance between LHFSs are introduced and some linguistic scale functions are applied. Then, the ER algorithm is used to aggregate the distributed assessment of each alternative. Subsequently, the set of aggregated alternatives on criteria are further aggregated to get the overall value of each alternative. Furthermore, a nonlinear programming model is developed and genetic algorithms are used to obtain the optimal weights of the criteria. Finally, two illustrative examples are provided to show the feasibility and usability of the method, and comparison analysis with the existing method is made.

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Linguistic hesitant fuzzy sets (LHFSs) are a very useful and appropriate means of expressing preferences of decision-makers; moreover their basic operations and comparison methods have been defined and applied to the solving of MCDM problems. However, there are a number of limitations in the related studies. In this paper, using information from existing studies, several new operations and a new order relationship are defined; moreover four linguistic hesitant fuzzy Heronian mean operators are proposed: the linguistic hesitant fuzzy arithmetic Heronian mean (LHFAHM) operator; the linguistic hesitant fuzzy weighted arithmetic Heronian mean (LHFWAHM) operator; the linguistic hesitant fuzzy geometric Heronian mean (LHFGHM) operator; and the linguistic hesitant fuzzy weighted geometric Heronian mean (LHFWGHM) operator. Furthermore, some useful and desirable properties of these operators are analyzed in some special cases, with respect to the different parameter values in these operators, are discussed. Additionally, an approach based on the LHFWAHM and LHFWGHM operators for solving MCDM problems is proposed. Finally, an illustrative example is provided to verify the validity and feasibility of the proposed approaches, and a comparison analysis is also presented to demonstrate the influences of different parameters on the results of decision-making.