A Consensus Support System Model for Group Decision-Making Problems With Multigranular Linguistic Preference Relations

The group decision-making framework with linguistic preference relations is studied. In this context, we assume that there exist several experts who may have different background and knowledge to solve a particular problem and, therefore, different linguistic term sets (multigranular linguistic information) could be used to express their opinions. The aim of this paper is to present a model of consensus support system to assist the experts in all phases of the consensus reaching process of group decision-making problems with multigranular linguistic preference relations. This consensus support system model is based on i) a multigranular linguistic methodology, ii) two consensus criteria, consensus degrees and proximity measures, and iii) a guidance advice system. The multigranular linguistic methodology permits the unification of the different linguistic domains to facilitate the calculus of consensus degrees and proximity measures on the basis of experts' opinions. The consensus degrees assess the agreement amongst all the experts' opinions, while the proximity measures are used to find out how far the individual opinions are from the group opinion. The guidance advice system integrated in the consensus support system model acts as a feedback mechanism, and it is based on a set of advice rules to help the experts change their opinions and to find out which direction that change should follow in order to obtain the highest degree of consensus possible. There are two main advantages provided by this model of consensus support system. Firstly, its ability to cope with group decision-making problems with multigranular linguistic preference relations, and, secondly, the figure of the moderator, traditionally presents in the consensus reaching process, is replaced by the guidance advice system, and in such a way, the whole group decision-making process is automated     

Consensus reaching models of linguistic preference relations based on distance functions

In group decision making (GDM) using linguistic preference relations to obtain the maximum degree of agreement, it is desirable to develop a consensus process prior to the selection process. This paper proposes two consensus models with linguistic information to support the GDM consensus reaching process. Two different distance functions between linguistic preference relations are introduced to measure both individual consistency and group consensus. Based on these measures, the consensus reaching models are developed. The two models presented have the same concept that the expert whose preference is farthest from the group preference needs to update their opinion according to the group preference relation. In addition, the convergence of the models is proved. After achieving the predefined consensus level, each expert’s consistency indexes are still acceptable under the condition that the initial preference relations are of satisfactory consistency. Finally, an example is given to show the effectiveness of the models and to verify the theoretical results.     

A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations

Two processes are necessary to solve group decision making problems: A consensus process and a selection process. The consensus reaching process is necessary to obtain a final solution with a certain level of agreement between the experts; and the selection process is necessary to obtain such a final solution. In a previous paper, we present a selection process to deal with group decision making problems with incomplete fuzzy preference relations, which uses consistency measures to estimate the incomplete fuzzy preference relations. In this paper we present a consensus model. The main novelty of this consensus model is that of being guided by both consensus and consistency measures. Also, the consensus reaching process is guided automatically, without moderator, through both consensus and consistency criteria. To do that, a feedback mechanism is developed to generate advice on how experts should change or complete their preferences in order to reach a solution with high consensus and consistency degrees. In each consensus round, experts are given information on how to change their preferences, and to estimate missing values if their corresponding preference relation is incomplete. Additionally, a consensus and consistency based induced ordered weighted averaging operator to aggregate the experts' preferences is introduced, which can be used in consensus models as well as in selection processes. The main improvement of this consensus model is that it supports the management of incomplete information and it allows to achieve consistent solutions with a great level of agreement.     

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.     

Consistency and consensus reaching process for group decision making based on complete interval distributed preference relations under social network analysis

Group decision-making (GDM) problems often consist of many indeterminacy factors in realistic situation. How to cope with consistency and consensus under uncertain circumstance are two critical issues in pairwise comparison based GDM problems. In this paper, we firstly propose the model of complete interval distributed preference relation (CIDPR) based on the concept of linguistic distribution with interval symbolic proportions, distribution linguistic preference relation (DLPR) and IDPR. Secondly, the additive consistency index of CIDPR is defined to measure the consistency level of expert's judgment, and an adjustment algorithm is proposed for converting inconsistent CIDPR to an acceptable consistent level. Thirdly, since trust relation is a critical factor in the generation of experts’ weights and the adjustment of experts’ opinions, consensus reaching process (CRP) is designed to take into account distributed linguistic trust relations under social network analysis (SNA). In the proposed adjustment mechanism, non-consensus individual should modify opinion towards his/her trusted and highly weighted expert. The advantage of the proposed inconsistent CIDPR adjustment model can maximally retain the information in the original distribution, while the CRP has a relatively fast convergent speed and good practicality. An illustrative example of strategic new product selection is conducted to demonstrate the applicability of the proposed method and its potential in supporting realistic GDM problems.     

A maximizing consensus approach for alternative selection based on uncertain linguistic preference relations

In alternative selection problems managed by multiple experts in uncertain situations achieving consensus is a desirable objective as incorrect selection may adversely affect stakeholder outcomes. This paper develops an approach to solve consensus problems when expert preference information is in the form of uncertain linguistic preference relations. First, definitions for aggregation operators and group consensus level based on a 2-tuple linguistic representation model are provided. Then, in order to obtain the weights of the experts under the assumption of incomplete weights information, an optimization model is developed which seeks maximum consensus from the current expert preferences in the group. If the consensus level reached does not meet predefined requirements, a consensus reaching algorithm is presented which can automatically achieve the goal. To determine the parameters for the proposed algorithm, a simulation procedure is presented. Finally, an investment company optimal selection example is provided to show the properties of the proposed approach. A comparative study and discussion of the proposed approach are also conducted.     

Group prioritisation with unknown expert weights in incomplete linguistic context

In this paper, we study a group prioritisation problem in situations when the expert weights are completely unknown and their judgement preferences are linguistic and incomplete. Starting from the theory of relative entropy (RE) and multiplicative consistency, an optimisation model is provided for deriving an individual priority vector without estimating the missing value(s) of an incomplete linguistic preference relation. In order to address the unknown expert weights in the group aggregating process, we define two new kinds of expert weight indicators based on RE: proximity entropy weight and similarity entropy weight. Furthermore, a dynamic-adjusting algorithm (DAA) is proposed to obtain an objective expert weight vector and capture the dynamic properties involved in it. Unlike the extant literature of group prioritisation, the proposed RE approach does not require pre-allocation of expert weights and can solve incomplete preference relations. An interesting finding is that once all the experts express their preference relations, the final expert weight vector derived from the DAA is fixed irrespective of the initial settings of expert weights. Finally, an application example is conducted to validate the effectiveness and robustness of the RE approach.     

Linguistic-labels aggregation and consensus measure for autocratic decision making using group recommendations

Group decision making is a common and important activity in everyday life. In many cases, due to inherent uncertainty, experts cannot express their score or preference using exact numbers. The use of linguistic labels makes expert judgment more reliable and informative for decision-making. One of the problems of group decision making in fuzzy domains is aggregating experts' opinions, expressed using linguistic labels, into a group opinion. This aggregation allows the group to select the most "preferred" alternative from a finite set of candidates. The aggregation of individual judgments into a group opinion requires a measured level of consensus. In this paper, by introducing a new linguistic-labels aggregation operation, we present a procedure for handling an autocratic group decision-making process under linguistic assessments. The methodology presented results in two consequent outcomes: a group-based recommendation, and a score for each expert, reflecting the expert's contribution towards the group recommendation. By changing the weights of the experts based on their contributions, we increase the consensus and reinforce the common decision, without forcing the experts to modify their opinions. This methodology allows an autocratic decision maker to use a diversified group of consultants for a succession of decisions reaching a high level of consensus.     

Multiplicative consistency-based decision support system for incomplete linguistic preference relations

The experts may have difficulty in expressing all their preferences over alternatives or criteria, and produce the incomplete linguistic preference relation. Consistency plays an important role in estimating unknown values from an incomplete linguistic preference relation. Many methods have been developed to obtain a complete linguistic preference relation based on additive consistency, but some unreasonable values may be produced in the estimation process. To overcome this issue, we propose a new characterisation about multiplicative consistency of the linguistic preference relation, present an algorithm to estimate missing values from an incomplete linguistic preference relation, and establish a decision support system for aiding the experts to complete their linguistic preference relations in a more consistent way. Some examples are also given to illustrate the proposed methods.     

A consensus model for multiperson decision making with different preference structures

In this paper, we present a consensus model for multiperson decision making (MPDM) problems with different preference structures based on two consensus criteria: 1) a consensus measure which indicates the agreement between experts' opinions and 2) a measure of proximity to find out how far the individual opinions are from the group opinion. These measures are calculated by comparing the positions of the alternatives between the individual solutions and collective solution. In such a way, the consensus situation is evaluated in each moment in a more realistic way. With these measures, we design a consensus support system that is able to substitute the actions of the moderator. In this system, the consensus measure is used to guide the consensus process until the final solution is achieved while the proximity measure is used to guide the discussion phases of the consensus process. The consensus support system has a feedback mechanism to guide the discussion phases based on the proximity measure. This feedback mechanism is based on simple and easy rules to help experts change their opinions in order to obtain a degree of consensus as high as possible. The main improvement of this consensus model is that it supports consensus process automatically, without moderator, and, in such a way, the possible subjectivity that the moderator can introduce in the consensus process is avoided.