Yucheng Dong

Consensus models for AHP group decision making under row geometric mean prioritization method

The consistency measure is a vital basis for consensus models of group decision making using preference relations, and includes two subproblems: individual consistency measure and consensus measure. In the analytic hierarchy process (AHP), the decision makers express their preferences using judgement matrices (i.e., multiplicative preference relations). Also, the geometric consistency index is suggested to measure the individual consistency of judgement matrices, when using row geometric mean prioritization method (RGMM), one of the most extended AHP prioritization procedures. This paper further defines the consensus indexes to measure consensus degree among judgement matrices (or decision makers) for the AHP group decision making using RGMM. By using Chiclana et al.s consensus framework, and by extending Xu and Weis individual consistency improving method, we present two AHP consensus models under RGMM. Simulation experiments show that the proposed two consensus models can improve the consensus indexes of judgement matrices to help AHP decision makers reach consensus. Moreover, our proposal has two desired features: (1) in reaching consensus, the adjusted judgement matrix has a better individual consistency index (i.e., geometric consistency index) than the corresponding original judgement matrix; (2) this proposal satisfies the Pareto principle of social choice theory.

The OWA-based consensus operator under linguistic representation models using position indexes

When using linguistic approaches to solve decision problems, we need linguistic representation models. The symbolic model, the 2-tuple fuzzy linguistic representation model and the continuous linguistic model are three existing linguistic representation models based on position indexes. Together with these three linguistic models, the corresponding ordered weighted averaging operators, such as the linguistic ordered weighted averaging operator, the 2-tuple ordered weighted averaging operator and the extended ordered weighted averaging operator, have been developed, respectively. In this paper, we analyze the internal relationship among these operators, and propose a consensus operator under the continuous linguistic model (or the 2-tuple fuzzy linguistic representation model). The proposed consensus operator is based on the use of the ordered weighted averaging operator and the deviation measures. Some desired properties of the consensus operator are also presented. In particular, the consensus operator provides an alternative consensus model for group decision making. This consensus model preserves the original preference information given by the decision makers as much as possible, and supports consensus process automatically, without moderator.

On consistency measures of linguistic preference relations

Inspired by the concept of deviation measure between two linguistic preference relations, this paper further defines the deviation measure of a linguistic preference relation to the set of consistent linguistic preference relations. Based on this, we present a consistency index of linguistic preference relations and develop a consistency measure method for linguistic preference relations. This method is performed to ensure that the decision maker is being neither random nor illogical in his or her pairwise comparisons using the linguistic label set. Using this consistency measure, we discuss how to deal with inconsistency in linguistic preference relations, and also investigate the consistency properties of collective linguistic preference relations. These results are of vital importance for group decision making with linguistic preference relations.

A comparative study of the numerical scales and the prioritization methods in AHP

Abstract In the analytic hierarchy process (AHP), a decision maker first gives linguistic pairwise comparisons, then obtains numerical pairwise comparisons by selecting certain numerical scale to quantify them, and finally derives a priority vector from the numerical pairwise comparisons. In particular, the validity of this decision-making tool relies on the choice of numerical scale and the design of prioritization method. By introducing a set of concepts regarding the linguistic variables and linguistic pairwise comparison matrices (LPCMs), and by defining the deviation measures of LPCMs, we present two performance measure algorithms to evaluate the numerical scales and the prioritization methods. Using these performance measure algorithms, we compare the most common numerical scales (the Saaty scale, the geometrical scale, the Ma–Zheng scale and the Salo–Hamalainen scale) and the prioritization methods (the eigenvalue method and the logarithmic least squares method). In addition, we also discuss the parameter of the geometrical scale, develop a new prioritization method, and construct an optimization model to select the appropriate numerical scales for the AHP decision makers. The findings in this paper can help the AHP decision makers select suitable numerical scales and prioritization methods.

Computing the Numerical Scale of the Linguistic Term Set for the 2-Tuple Fuzzy Linguistic Representation Model

When using linguistic approaches to solve decision problems, we need the techniques for computing with words (CW). Together with the 2-tuple fuzzy linguistic representation models (i.e., the Herrera and Martinez model and the Wang and Hao model), some computational techniques for CW are also developed. In this paper, we define the concept of numerical scale and extend the 2-tuple fuzzy linguistic representation models under the numerical scale. We find that the key of computational techniques based on linguistic 2-tuples is to set suitable numerical scale with the purpose of making transformations between linguistic 2-tuples and numerical values. By defining the concept of the transitive calibration matrix and its consistent index, this paper develops an optimization model to compute the numerical scale of the linguistic term set. The desired properties of the optimization model are also presented. Furthermore, we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations. The results in this paper are pretty helpful to complete the fuzzy 2-tuple representation models for CW.

Consistency-Driven Automatic Methodology to Set Interval Numerical Scales of 2-Tuple Linguistic Term Sets and Its Use in the Linguistic GDM With Preference Relation

The 2-tuple linguistic modeling is a popular tool for computing with words in decision making. In order to deal with the linguistic term sets that are not uniformly and symmetrically distributed, the numerical scale model has been developed to generalize the 2-tuple linguistic modeling. In the numerical scale model, the key task of the 2-tuple based models is the definition of a numerical scale function that establishes a one to one mapping between the linguistic information and numerical values. In this paper, we propose a consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets in the decision making problems with linguistic preference relations. This consistency-driven methodology is based on a natural premise regarding the consistency of preference relations. If linguistic preference relations provided by experts are of acceptable consistency, the corresponding transformed numerical preference relations by the established interval numerical scale are also consistent. Compared with the existing approach based on canonical characteristic values, the consistency-driven methodology provides a new way to set the interval numerical scale without the need of the semantics defined by interval type-2 fuzzy sets. Meanwhile, interval multiplicative preference relations are used in the pairwise comparisons method and the presented theory can be utilized in the pairwise comparisons method as it provides a novel approach to automatic construct interval multiplicative preference relations. Finally, we present the framework for the use of the consistency-driven automatic methodology in linguistic group decision making problems and two numerical examples are given to illustrate the feasibility and validity of this proposal.

Consistency and consensus measures for linguistic preference relations based on distribution assessments

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.

A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress

This position paper studies the necessity of hesitant fuzzy sets.A discussion about current proposals are introduced.Some challenges of hesitant fuzzy sets are proposed. The necessity of dealing with uncertainty in real world problems has been a long-term research challenge which has originated different methodologies and theories. Recently, the concept of Hesitant Fuzzy Sets (HFSs) has been introduced to model the uncertainty that often appears when it is necessary to establish the membership degree of an element and there are some possible values that make to hesitate about which one would be the right one. Many researchers have paid attention on this concept who have proposed diverse extensions, relationships with other types of fuzzy sets, different types of operators to compute with this type of information, applications on information fusion and decision-making, etc.Nevertheless, some of these proposals are questionable, because they are straightforward extensions of previous works or they do not use the concept of HFSs in a suitable way. Therefore, this position paper studies the necessity of HFSs and provides a discussion about current proposals including a guideline that the proposals should follow and some challenges of HFSs.

SVR with hybrid chaotic genetic algorithms for tourism demand forecasting

Accurate tourist demand forecasting systems are essential in tourism planning, particularly in tourism-based countries. Artificial neural networks are attracting attention to forecast tourism demands due to their general non-linear mapping capabilities. Unlike most conventional neural network models, which are based on the empirical risk minimization principle, support vector regression (SVR) applies the structural risk minimization principle to minimize an upper bound of the generalization error, rather than minimizing the training error. This investigation presents a SVR model with chaotic genetic algorithm (CGA), namely SVRCGA, to forecast the tourism demands. With the increase of the complexity and the larger problem scale of tourism demands, genetic algorithms (GAs) are often faced with the problems of premature convergence, slowly reaching the global optimal solution or trapping into a local optimum. The proposed CGA based on the chaos optimization algorithm and GAs, which employs internal randomness of chaos iterations, is used to overcome premature local optimum in determining three parameters of a SVR model. Empirical results that involve tourism demands data from existed paper reveal the proposed SVRCGA model outperforms other approaches in the literature.

Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making

In some real-world decision processes, decision makers may prefer to provide their opinions using linguistic expressions instead of a single linguistic term. Particularly, they may hesitate between several linguistic terms. In this paper, we deal with the consensus issue in the hesitant linguistic group decision making (GDM) problem. Firstly, a novel distance-based consensus measure is proposed. Then, using this consensus measure we develop an optimization-based consensus model in the hesitant linguistic GDM, which minimizes the number of adjusted simple terms in the consensus building. Furthermore, a two-stage model is displayed to further optimize the solutions to the proposed consensus model, through which we obtain the unique optimal adjustment suggestion to support the consensus reaching process in the hesitant linguistic GDM. Finally, several desirable properties are proposed to justify the proposal, and two examples are used to demonstrate the validity of the models.