With the increase of technological and societal demands, more and more decision makers are involved in the process of group decision making, which is called large-scale group decision making (LGDM). For an LGDM problem with linguistic information, it is common that different decision makers tend to provide linguistic assessments defined on multigranular linguistic term sets due to the difference in knowledge and culture background, and that hesitant fuzzy linguistic term sets (HFLTSs) are used by decision makers to model the hesitancy of their assessments. This article proposes first an algorithm to represent a linguistic distribution assessment (LDA) using a hesitant linguistic distribution (HLD). Two other algorithms are then proposed to transform an unbalanced HFLTS into a balanced LDA and to transform a balanced LDA into an unbalanced LDA, respectively. An approach is then proposed to deal with multiattribute LGDM problems with multigranular unbalanced hesitant fuzzy linguistic information based on these algorithms. In the proposed approach, all unbalanced hesitant fuzzy linguistic information is transformed into LDAs defined on a balanced linguistic term set, and then an LDA-based clustering algorithm is devised to cluster decision makers. Based on the clustering result, decision makers' linguistic distribution decision matrices are further fused to obtain collective assessments of alternatives. In order to provide easy-to-understand linguistic results for decision makers, all LDAs of alternatives are represented by HLDs defined on each decision maker's initial linguistic term set. Finally, an example for the selection of subway lines is used to demonstrate the proposed approach.

The fuzzy preference relation with self-confidence (FPR-SC), whose elements are composed of the degree to which an alternative is preferred to another and the self-confidence level about the preference degree, is a useful tool for decision makers to express their preference information over alternatives. In this paper, an extended logarithmic least squares method (LLSM) is first proposed to derive a priority weight vector from an FPR-SC, based on which the multiplicative consistency of an FPR-SC is further defined and two algorithms are devised to improve the multiplicative consistency of an unacceptably consistent FPR-SC. Furthermore, we develop a novel approach to two-sided matching decision making with FPRs-SC based on the LLSM and the proposed consistency improving algorithms. Eventually, the feasibility and effectiveness of the two-sided matching decision making approach are demonstrated by an example for the matching of knowledge suppliers and knowledge demanders.

In group decision making (GDM), there may exist some problems that need to assign alternatives to some predefined ordered categories, which are called ordinal classification-based GDM problems. To obtain classification results that can be accepted by most decision makers (DMs), it is necessary to implement a consensus reaching process for ordinal classification-based GDM problems. In this paper, we study consensus reaching models for a new type of ordinal classification-based GDM problem, in which DMs do not provide criteria weights and category cardinalities but provide indirect and imprecise heterogeneous preference information. To do so, a consistency verification method is first proposed to check whether each DM’s preference information is consistent and then a minimum adjustment optimization model is developed to modify DMs’ inconsistent preference information. Afterwards, we establish some optimization models to obtain each DM’s possible categories for alternatives. Followed by this, we define the consensus levels of DMs and devise some optimization models to assist DMs in adjusting alternatives’ classification results and DMs’ preference information at the same time. Furthermore, a maximum support degree-based method is provided to determine the consensual classification result for alternatives. Finally, a numerical application and some sensitivity analysis are provided to justify the proposed models.

Traditional group decision making (GDM) problems typically aim to obtain a complete ranking of all considered alternatives from best to worst. However, in numerous real-life scenarios, there are instances where it is imperative to assign each alternative into one of two rank levels, creating a ranking where one subset of alternatives is prioritized above the other subset of alternatives. These scenarios are known as 2-rank GDM problems. While a range of methods exist for addressing 2-rank GDM problems, most are specifically tailored to multiattribute decision making situations, thereby limiting their applicability in scenarios involving preference relations. The linguistic preference relation (LPR) is an effective representation tool of decision makers’ (DMs’) preferences for pairwise comparisons of alternatives using linguistic terms. Since words may have different meanings for different DMs, a phenomenon known as personalized individual semantics (PISs), the modeling of linguistic PISs in 2-rank GDM problems with LPRs is worth investigating and challenging to address. Consequently, this article develops models to support consensus reaching for 2-rank linguistic GDM problems with PISs and consistency of DMs. Specifically, PIS consistency-driven models are initially employed to measure and improve the consistency of the LPRs of the individual DMs with unacceptable consistency level. Based on this foundation, the 2-rank vectors for both individuals and the group are determined. Subsequently, a 2-rank consensus measurement method is proposed on which a 2-rank consensus reaching process is designed to support DMs in improving their consensus levels. This involves the development of a PISs-based minimum adjustment consensus optimization model and a PISs-based individual consensus level maximization model. An algorithm to implement the proposed consensus reaching framework is also provided. Finally, numerical experiments and simulation results are reported to demonstrate the effectiveness of the proposed method.