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Linguistic distribution, as a flexible representation structure, is often used in linguistic decision-making. Several approaches have been proposed for managing the missing elements in incomplete preference relations when decision makers cannot provide all the linguistic comparisons between alternatives in preference relations. However, in linguistic decision-making, words can mean different things to different people, which implies the necessity of personalizing individual semantics. This study proposes a two-stage method, including a personalized individual semantics (PIS)-based consistency model and a PIS-based consensus model, to manage PIS and missing elements in incomplete distributed linguistic preference relations (DLPRs). The proposed method combines the characteristics of the personalization of linguistic expression and estimates the missing values, guaranteeing optimum consistency and consensus at the same time in group decision-making with incomplete DLPRs. Numerical and comparison analyses were performed to illustrate the use of the two-stage method, and demonstrates the various numerical meanings of words and the features of the obtained complete DLPRs from the proposed model. [ABSTRACT FROM AUTHOR]

Consensus reaching process (CRP) is important and present in a wide range of application areas. In practical CRP, the managers (e.g., enterprise) often hire some informed individuals (e.g., persuaders) to promote the efficiency of consensus reaching. This article proposes a CRP with minimum cost of informed individuals and time constraint in large-scale group decision-making (LSGDM) with bounded confidence effects. The consensus model with bounded confidence effects (CBC model) is formulated. Then, desirable properties of the CBC model are discussed to facilitate its resolution. Next, an extended particle swarm optimization algorithm is designed to solve the CBC model. Finally, a numerical analysis, a comparison analysis, and a simulation analysis are provided to illustrate the feasibility and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Linguistic distribution expressions provide a flexible way for decision makers to express their opinions in linguistic decision making. When working with a linguistic distribution, words mean different things for different people, i.e., decision makers have personalized individual semantics (PISs) regarding words. Therefore, in this paper, we propose a consistency-driven methodology to manage distribution linguistic preference relations (DLPRs) with PISs. This methodology can not only estimate the ignorance elements in incomplete DLPRs but also obtain the personalized numerical meanings of linguistic expressions to decision makers. In this way, we can combine the characteristics of the personalized representation in linguistic decision making and guarantee the optimum consistency of incomplete DLPRs with ignorance elements. Detailed numerical and comparison analyses have been proposed to justify our proposal. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The consistency test is a vital basis of the pairwise comparison method, which is performed to ensure that the decision maker is being logical in his/her pairwise comparisons. In the analytic hierarchy process, the pairwise comparison method with a fixed numerical scale has been employed. In this study, we provide a systematic review analysis regarding the inconsistency causes in the pairwise comparison method with a fixed numerical scale, and propose the paradoxes on Saaty’s consistency test in this pairwise comparison method. Meanwhile, based on the use of the consistency-driven linguistic methodology, we propose a novel approach from a perspective of the linguistic and numerical scale to deal with the inconsistency in the pairwise comparison method. [ABSTRACT FROM AUTHOR]

The consensus model with the minimum cost (or minimum adjustments or minimum information loss) is a powerful decision tool for consensus building in the group decision making (GDM). In the extant consensus models with the minimum cost, the unit adjustment cost of each expert is assumed to be exactly known, and an optimization-based consensus model is utilized to support the consensus building. In the practical GDM, however, it is difficult to obtain the exact unit adjustment costs, and the unit adjustment costs of experts are often uncertain. Moreover, we argue that the consensus cannot be achieved directly using the established optimization-based consensus model, because the consensus building is an interactive process that needs the participation of experts. This paper proposes an interactive consensus reaching process with the minimum and uncertain cost. In the consensus reaching process, an optimization-based consensus model with the uncertain unit cost is constructed to obtain the optimal adjusted opinions of experts. Then, the costs/resources are provided for experts to modify their opinions, and the obtained optimal adjusted opinions are used as a reference for the opinions-modifying in the consensus reaching process. Meanwhile, the unit adjustment costs of experts can be estimated according to the actual situation of the opinions-modifying in the consensus reaching process. The detailed numerical and simulation analysis are conducted to demonstrate the validity of the proposed consensus reaching model. [ABSTRACT FROM AUTHOR]

This study put forwards a novel consensus framework to manage the consensus and weights (i.e., weights of the experts and attributes) in iterative multiple-attribute group decision making (MAGDM) problem. In this consensus framework, an optimization-based consensus model is devised to support the process of preferences-modifying, which seeks to minimize the adjustment amounts (in the sense of Manhattan distance) between the original and adjusted preferences. Then, the other two optimization-based consensus models are constructed to support the weights-updating, in which the consensus level among experts can be further improved. A numerical example is provided to show the application of the proposed consensus framework, and a detailed comparison analysis is presented to verify the effectiveness of the proposed consensus framework. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose the concept of distribution assessments in a linguistic term set, and study the operational laws of linguistic distribution assessments. The weighted averaging operator and the ordered weighted averaging operator for linguistic distribution assessments are presented. We also develop the concept of distribution linguistic preference relations, whose elements are linguistic distribution assessments. Further, we study the consistency and consensus measures for group decision making based on distribution linguistic preference relations. Two desirable properties of the proposed measures are shown. A consensus model also has been developed to help decision makers improve the consensus level among distribution linguistic preference relations. Finally, illustrative numerical examples are given. The results in this paper provide a theoretic basis for the application of linguistic distribution assessments in group decision making. [Copyright &y& Elsevier]

In group decision making, consensus models are decision aid tools and help experts modify their individual opinions to reach a closer agreement. Based on the concept of minimum-cost consensus, this paper proposes a novel framework to achieve minimum-cost consensus under aggregation operators. Analytical results indicate that the proposed framework reduces to the consensus model of Ben-Arieh when the selected aggregation operator is the ordered weighted averaging (OWA) operator with weight vector (1/2, \ldots, 0, \ldots, 1/2)^T. Furthermore, this paper closely examines the minimum-cost consensus models with a linear cost function under the common aggregation operators (e.g., the weighted averaging operator and the OWA operator). Linear-programming-based approaches are also developed to solve these models. The results of this paper significantly contribute to efforts to develop the consensus model of Ben-Arieh [ABSTRACT FROM PUBLISHER]

The validity of the priority vector used in the analytic hierarchy process (AHP) relies on two factors: the selection of a numerical scale and the selection of a prioritization method. The traditional AHP selects only one numerical scale (e.g., the Saaty scale) and one prioritization method (e.g., the eigenvector method) for each particular problem. For this traditional selection approach, there is disagreement on which numerical scale and prioritization method is better in deriving a priority vector. In fact, the best numerical scale and the best prioritization method both rely on the content of the pairwise comparison data provided by the AHP decision makers. By defining a set of concepts regarding the scale function and the linguistic pairwise comparison matrices (LPCMs) of the priority vector and by using LPCMs to unify the format of the input and output of AHP, this paper extends the AHP prioritization process under the 2-tuple fuzzy linguistic model. Based on the extended AHP prioritization process, we present two performance measure criteria to evaluate the effect of the numerical scales and prioritization methods. We also use the performance measure criteria to develop a 2-tuple fuzzy linguistic multicriteria approach to select the best numerical scales and the best prioritization methods for different LPCMs. In this paper, we call this type of selection the individual selection of the numerical scale and prioritization method. We also compare this individual selection with traditional selection by using both random and real data and show better results with individual selection. [ABSTRACT FROM AUTHOR]

The symbolic model based on the linguistic scale has been widely used to represent linguistic knowledge to deal with various linguistic decision problems. However, linguistic scales with different granularity may yield inconsistent decision outcomes in the linguistic decision making. Thus, this paper systematically studies the linguistic scale consistency issues in multi-granularity decision making contexts. We first define the concepts of the consistent multi-granularity representation, consistent multi-granularity aggregation and consistent multi-granularity ranking. After that, we analytically present a necessary and sufficient condition to guarantee the consistent multi-granularity representation and a sufficient condition to characterize the intrinsic mechanism of the consistent multi-granularity aggregation. Then, an attitude-based linguistic representation method (ALRM) is proposed to improve the consistent multi-granularity ranking. Finally, a detailed numerical analysis and simulation experiments are presented to show the advantages of the ALRM over the traditional linguistic approach. These results will provide new insights into the use of linguistic scales in the linguistic decision making. • A necessary and sufficient condition is presented to guarantee the consistent multi-granular representation. • A sufficient condition is presented to characterize the mechanism of the consistent multi-granular aggregation. • A novel linguistic approach is proposed to improve the consistent multi-granular ranking. • Simulation experiments are designed to analyze the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel opinion dynamics model that is based on bounded confidence and termed interval opinion dynamics with the dynamic bounded confidence. In this opinion dynamics model, the agents express their opinions in numerical intervals, and the bounded confidences vary in a specified interval as time varies (i.e., dynamic bounded confidence). Based on several theoretical analyses of the proposed opinion dynamics, we propose conditions that are sufficient to form a consensus or fragmentations among the agents. Moreover, we also design several simulation experiments to investigate the effects of the dynamic bounded confidence and interval widths on the proposed opinion dynamics and to illustrate the differences between the proposed model and the original opinion dynamics with bounded confidence. [ABSTRACT FROM AUTHOR]