Due to the complexity of problems in hand and the limitation of experts’ cognition, uncertainties are generally inevitable in decision information. In the fuzzy linguistic approach, linguistic variables enable a manner to represent uncertain information which is close to human’s cognition. It is necessary that, in the traditional way of computing with words, the experts have to represent decision information by means of a certain term. However, this is quite difficult when facing complex types of uncertainties. Uncertain linguistic expressions, which include more than one possible term in a direct or indirect way, are more consistent with people’s language convention.
On the basis of the existing models, this thesis presents some novel linguistic models to represent two types of uncertain linguistic expressions #ULEs# which conform to natural language conventions, and investigates the related fundamental theories and approaches for group decision making #GDM#. Specifically, the innovative works of this thesis are as follows:
#1# Theoretically, two types of ULE models are presented, which are extended hesitant fuzzy linguistic term sets #EHFLTSs# and linguistic terms with weakened hedges #LTWHs#. The former focuses on ULEs which contains multiple terms, and possesses some flexible properties than those of hesitant fuzzy linguistic term sets. The latter takes use of a weakened hedge to express the degree of uncertainty of using a specific term. After systematically defining the syntax and semantics of virtual terms, the representational and computational models of the two types of ULEs are developed and thus can serve as the basis of applications.
#2# A collection of GDM approaches are proposed based on the existing models and the novel models. When the decision information is expressed by EHFLTSs, a multi-groups decision making approach is presented at first based on the idea of information fusion. Then a two-stage GDM approach is developed on the basis of total orders of the set of EHFLTSs and how different orders affect final decisions is discussed. Moreover, a new category of linguistic preference relations #LPRs#, whose entries are EHFLTSs, are introduced. Some graph-based approaches are presented to measure the consistencies of the new category of LPRs and reduce them to the traditional LPRs. Furthermore, EHFLTSs are utilized to collect all the possible values of a missing entry of incomplete LPRs. Based on the consistency measures, some new algorithms for completing incomplete LPRs are developed. When the decision information takes the form of LTWHs, an approach for GDM with multi-granularity linguistic information is proposed at first, and then another category of LPRs, whose entries are LTWHs, are introduced. Based on fuzzy weighted graphs, the approaches for consistency checking and improving are investigated. Finally, the problems, whose information takes the form of multiple types of ULEs, are focused, and a linguistic aspiration-based approach and a stochastic approach are proposed for GDM.
#3# Several case studies are proposed to demonstrate the effectiveness and analyze the strengths and weaknesses of the proposed GDM approaches. Especially, the necessity of introducing Big Data into the audit realm is discussed and a hierarchical model for evaluating Big Data-based auditing platforms is developed. As there are many qualitative attributes in the hierarchical model, one of the proposed approach is employed to implement the evaluations.