In multiple attribute decision making (MADM), strategic weight manipulation is understood as a deliberate manipulation of attribute weight setting to achieve a desired ranking of alternatives. In this paper, we study the strategic weight manipulation in a group decision making (GDM) context with interval attribute weight information. In GDM, the revision of the decision makers' original attribute weight information implies a cost. Driven by a desire to minimize the cost, we propose the minimum cost strategic weight manipulation model, which is achieved via optimization approach, with the mixed 0-1 linear programming model being proved appropriate in this context. Meanwhile, some desired properties to manipulate a strategic attribute weight based on the ranking range under interval attribute weight information are proposed. Finally, numerical analysis and simulation experiments are provided with a twofold aim: 1) to verify the validity of the proposed models and 2) to show the effects of interval attribute weights information and the unit cost, respectively, on the cost to manipulate strategic weights in the MADM in a group decision context.

Different feedback mechanisms have been developed in large-scale group decision-making (GDM) to provide the decision-makers with advices for preference adjustment with the aim of improving the group consensus level. However, the willingness of the decision-makers to accept these advices is rarely considered in the extant feedback mechanisms. In the field of opinion dynamics, this issue is studied by the bounded confidence model, which shows that the decision-makers only consider the preferences that differ from their own preferences not more than a certain confidence level. Following this idea, this article proposes a large-scale consensus model with a bounded confidence-based feedback mechanism to promote the consensus level among decision-makers with bounded confidences. Specifically, this feedback mechanism classifies the decision-makers into different clusters and provides the corresponding clusters with more acceptable advices based on a bounded confidence-based optimization approach. Finally, through the numerical example and the simulation analysis, the use of the model is introduced, and the effectiveness of the model is justified.

Nowadays, online social networks, such as ``Facebook'' and ``WeChat,'' facilitate the expression, diffusion, and interactions of individuals' opinions regarding various issues. In this environment, individuals' opinions are liable to be influenced by others and then evolve over the time. In this paper, we propose an approach based on minimum adjustments to manage the consensus in the group decision making (GDM) with opinions evolution. First, inspired by the idea proposed in DeGroot model, we establish a novel GDM model with opinions evolution, and then discuss its consensus conditions. Based on this, we propose an algorithm to achieve the network partition, and then provide a consensus model with minimum adjustments to obtain the optimal adjusted initial opinions and collective consensus opinion. Finally, we provide a numerical example to demonstrate the feasibility and effectiveness of the proposed theoretical results, and design comparative simulations to explore the effects of the opinions evolution on the final consensus solution.

Managing comparative linguistic expressions (CLEs) information is a key issue in group decision-making (GDM). A transformation approach has been previously defined to convert CLEs into hesitant fuzzy linguistic terms sets (HFLTSs). However, it is noted that the occurring possibilities of the linguistic terms in the HFLTSs are assumed equal. This assumption might sometimes not capture the real opinions of the decision makers. Linguistic distribution assessments (LDAs) are an effective way to deal with this issue. This paper develops a linguistic distribution-based optimization approach for converting CLEs into LDAs, in which we assume that decision makers provide their opinions using preference relations with CLEs. Particularly, the proposed optimization approach is based on the use of a consistency-driven methodology, which seeks to minimize the inconsistency level of LDA preference relations obtained by transforming the original CLE preference relations elicited from decision makers. The linguistic distribution-based optimization approach is further developed to transform CLEs into interval LDAs to increase their flexibility. Moreover, society and technology trends make it possible to involve and manage large groups of decision makers in GDM environment. So, a large-scale GDM framework with CLE information is designed based on the linguistic distribution-based optimization approach. To justify the effectiveness and applicability of the proposed methodology, it is applied to solve a real large-scale GDM problem, pertaining the selection of best sustainable disinfection technique for wastewater reuse projects. A comparison against a baseline method is likewise provided to highlight the advantages and innovations of our proposal.

In the bounded confidence model it is widely known that individuals rely on the opinions of their close friends or people with similar interests. Meanwhile, the decision maker always hopes that the opinions of individuals can reach a consensus in a required time. Therefore, with this idea in mind, this paper develops a consensus reaching model with time constraints and minimum adjustments in a group with bounded confidence effects. In the proposed consensus approach, the minimum adjustments rule is used to modify the initial opinions of individuals with bounded confidence, which can further influence the opinion evolutions of individuals to reach a consensus in a required time. The properties of the model are studied, and detailed numerical examples and comparative simulation analysis are provided to justify its feasibility.

Opinion dynamics are investigated extensively to describe the process of opinion formation in groups of individuals. Most of the existing opinion dynamics models assume that the individuals express the numerical opinions. However, this assumption does not consider the fact that people often express their opinions in a linguistic way. Particularly, for the linguistic opinions, an important point to be highlighted in computing with words (CW) is that words mean different things to different people. In this paper, following the idea of personalized individual semantics (PIS) model, we propose the PIS based linguistic opinions dynamics model (PIS-LOD model) in the framework of bounded confidence effects. Then, some desired properties in the PIS-LOD model are discussed in details. Furthermore, we design the detailed simulation experiments to show that the individuals' familiarity (which refers to the knowledge on others' semantics) and the PISs' differences have great influence on the stabilized time, distributions of the extreme and moderate opinions, linguistic opinions distribution, semantics distribution, number of clusters, consensus reaching and the extremely small clusters. The results in this paper are very helpful for us to understand the process of group opinion formation in a linguistic context.