Preference Representation Structures Research Articles

Managing consensus reaching process with self-confident double hierarchy linguistic preference relations in group decision making

Group decision making (GDM) can be defined as an environment where there exist a set of possible alternatives and a set of individuals (experts, judgements, etc.). Preference relation is one of the most widely used preference representation structures in GDM. Considering that the self-confidence degree is an important part to express preference information, and double hierarchy linguistic preference relation (DHLPR) is a cognitive complex linguistic information representation tool to express complex linguistic information, this paper presents a novel preference relation named as self-confident DHLPR. In addition, a weight-determining method is developed, which considers three kinds of information including the subjective weights and two kinds of objective weights. Furthermore, a consensus model is set up to manage the GDM problems with self-confident DHLPRs based on the priority ordering theory. The effectiveness of the proposed consensus model is illustrated by a case study concerning the selection of optimal hospitals in the field of Telemedicine. Finally, a simulation experiment is devised to testify the proposed consensus model and then some comparisons with other consensus reaching models are provided from three different angles including the number of iterations, the consensus success ratio and the distance between the original and adjusted preferences.

Adaptive Consensus-Based Model for Heterogeneous Large-Scale Group Decision-Making: Detecting and Managing Noncooperative Behaviors

Large-scale group decision-making (LSGDM), which involves dozens to hundreds of decision-makers (DMs), is attracting extensive attention and has become an interesting and hot topic in recent years. Because of various backgrounds and expression habits, DMs tend to elicit preferences with different preference representation structures. Moreover, due to various attitudes and interests, some DMs may adopt noncooperative behaviors to further benefit themselves in LSGDM. To cope with these issues, this study develops an adaptive consensus framework to support heterogeneous LSGDM. A cosine similarity based optimization model is constructed and its analytical solution is derived to directly obtain the collective priority vector of the group using heterogeneous preferences. An extended k-means algorithm is then used to classify DMs. Subsequently, a two-stage uninorm-based behavior management method is developed to generate personalized weight feedback to each DM and subcluster according to their cooperative and noncooperative degrees in the consensus-reaching process. Finally, an illustrative example followed by simulation and comparative analyses is provided to reveal the advantages and features of the proposed approach.

A New Two-Stage Approach for a Bi-Objective Facility Layout Problem Considering Input/ Output Points Under Fuzzy Environment

Facility layout problem is one of the most important problems in a huge range of industries and services organizations. Simultaneous study of some qualitative and quantitative parameters like closeness relationship between facilities, physical constraints such as input/output points and how to arrange facilities can play a key role to determine the facility layout. Considering these parameters can lead to reduce production costs, increase production capacity, and remove additional displacements. A two-stage approach is proposed to achieve these goals. In the first stage, a goal programming model is proposed to determine weights of the attributes based on the experts' opinions with different preference representation structures. Afterwards, the closeness ratings of the facilities are calculated using weights of attributes. In the second stage, an efficient layout is designed by determining facilities placement sequence, location of the next facility adjacent to the previous one, location of input/output points, and rectilinear feasible shortest path between facilities. Two meta-heuristic algorithms including particle swarm optimization and genetic algorithm are designed due to computational complexity. The objective function is to minimize the sum of products distance between facilities and closeness rating and also to minimize the dead space. A case study of an Auto Body Parts company is demonstrated to verify the efficiency of the proposed two-stage approach. Furthermore, in order to assess the performance of the proposed approach, a comparison is drawn between the proposed approach and five existing approaches in the literature to solve different problems by using the two meta-heuristic algorithms.

A novel consensus reaching framework for heterogeneous group decision making based on cumulative prospect theory

This paper examines decision makers’ bounded rationality in consensus building, and proposes a direct consensus framework based on cumulative prospect theory to solve group decision making problem with eight kinds of preference representation structures. This framework consists of two processes: selection process and consensus process. In selection process, we first transform different preference structures into uniform individual preference vectors using different transformation functions. Then, according to the individual preference vectors and gain and loss matrices, we determine reference points using preference-approval structures and the prospect value matrix. Third, we design an optimization model to obtain decision weights, and further get the prospect values of alternatives. In consensus process, we define a consensus measure by applying cumulative prospect theory, design a feedback adjustment to make consensus better, and output satisfying comprehensive prospect value after several iterations if necessary; then, the final optimal solution is obtained. At last, an example is provided to illustrate the effectiveness of framework.

Consensus Building for the Heterogeneous Large-Scale GDM With the Individual Concerns and Satisfactions

Nowadays, societal and technological trends demand the management of large scale of decision makers in group decision-making (GDM) contexts. In a large-scale GDM, decision makers often have individual concerns and satisfactions, and also they will use heterogeneous preference representation structures to express their preferences. Meanwhile, it is difficult to set the numerical consensus threshold to judge whether a consensus degree can be acceptable or not in the consensus reaching process in a large-scale GDM. This study proposes a novel consensus reaching model for the heterogeneous large-scale GDM with the individual concerns and satisfactions. In this consensus reaching model, a selection process is proposed to obtain the individual preference vectors, to divide decision makers into different clusters, and to yield the preference vector of the large group. Following this, a consensus measure method that considers the individual concerns on alternatives is defined for measuring the consensus degree, and a linguistic approach is developed to measure the individual and collective satisfactions regarding the consensus degree. Finally, a feedback adjustment process is proposed and utilized to help decision makers adjust their preferences. A practical example and a simulation analysis are presented to demonstrate the validity of the proposed consensus reaching model.

A direct consensus framework based on extended MCCM for multiperson decision making problem with different preference representation structures

A direct consensus framework based on extended MCCM for multiperson decision making problem with different preference representation structures

Consensus building in multiperson decision making with heterogeneous preference representation structures: A perspective based on prospect theory

Multiperson decision making (MPDM) models with heterogeneous preference representation structures have initiated by Chiclana et al. In this study, we propose a novel framework for MPDM problems with heterogeneous preference representation structures. This framework takes the decision makers’ psychological behaviors into consideration and is based on the prospect theory, which is one of the most influential psychological behavior decision theories. In this framework, the heterogeneous preference representation structures are all transformed into preference orderings. The preference-approval structures are introduced to determine the reference points in prospect theory, and then the prospect value function is used to obtain individual and collective prospect values. Finally, based on the prospect values and preference-approval structures, we propose the two-step feedback adjustment rules, which will adjust both the preference evaluations and the preference-approval information, to help the decision makers reach higher consensus degree. Further, we find that there are two significant observations in this framework: (1) the uses of different reference points will yield different outputs of the selection process in MPDM; (2) compared with only adjusting the preference evaluations in the existing studies, the pace of consensus reaching will be accelerated in adjusting both the preference evaluations and the preference-approval information.

An Analysis of Several Novel Frameworks and Models in the Consensus Reaching Process

Usually, at the beginning of the group decision making (GDM) problem, experts’ opinions may differ substantially. Therefore, the consensus reaching process is often a necessity in GDM, and numerous approaches for modeling the consensus process have been proposed. This paper provides an analysis for several novel consensus frameworks and models, investigated by our group. They are the consensus models with minimum adjustments, the consensus models based on consistency and consensus measures, and the direct consensus framework for GDM with different preference representation structures. The advantages of these consensus frameworks and models are analyzed. Meanwhile, the drawbacks and future researches are discussed.

Multiperson decision making with different preference representation structures: A direct consensus framework and its properties

This study proposes a direct consensus framework for multiperson decision making (MPDM) with different preference representation structures (preference orderings, utility functions, multiplicative preference relations and fuzzy preference relations). In this framework, the individual selection methods, associated with different preference representation structures, are used to obtain individual preference vectors of alternatives. Then, the standardized individual preference vectors are aggregated into a collective preference vector. Finally, based on the collective preference vector, the feedback adjustment rules, associated with different preference representation structures, are presented to help the decision makers reach consensus. This study shows that the proposed framework satisfies two desirable properties: (i) the proposed framework can avoid internal inconsistency issue when using the transformation functions among different preference representation structures; (ii) it satisfies the Pareto principle of social choice theory. The results in this study are helpful to complete Chiclana et al.’s MPDM with different preference representation structures.

Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations

The aim of this paper is to study the integration of multiplicative preference relation as a preference representation structure in fuzzy multipurpose decision-making problems. Assuming fuzzy multipurpose decision-making problems under different preference representation structures (ordering, utilities and fuzzy preference relations) and using the fuzzy preference relations as uniform representation elements, the multiplicative preference relations are incorporated in the decision problem by means of a transformation function between multiplicative and fuzzy preference relations. A consistency study of this transformation function, which demonstrates that it does not change the informative content of multiplicative preference relation, is shown. As a consequence, a selection process based on fuzzy majority for multipurpose decision-making problems under multiplicative preference relations is presented. To design it, an aggregation operator of information, called ordered weighted geometric operator, is introduced, and two choice degrees, the quantifier-guided dominance degree and the quantifier-guided non-dominance degree, are defined for multiplicative preference relations.

Multiperson decision-making based on multiplicative preference relations

A multiperson decision-making problem, where the information about the alternatives provided by the experts can be presented by means of different preference representation structures (preference orderings, utility functions and multiplicative preference relations) is studied. Assuming the multiplicative preference relation as the uniform element of the preference representation, a multiplicative decision model based on fuzzy majority is presented to choose the best alternatives. In this decision model, several transformation functions are obtained to relate preference orderings and utility functions with multiplicative preference relations. The decision model uses the ordered weighted geometric operator to aggregate information and two choice degrees to rank the alternatives, quantifier guided dominance degree and quantifier guided non-dominance degree. The consistency of the model is analysed to prove that it acts coherently.