An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: Taxonomy and future directions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The reciprocal preference relation (RPR) is a powerful tool to represent decision makers’ preferences in decision making problems. In recent years, various types of RPRs have been reported and investigated, some of them being the ‘classical’ RPRs, interval-valued RPRs and hesitant RPRs. Additive consistency is one of the most commonly used property to measure the consistency of RPRs, with many methods developed to manage additive consistency of RPRs. To provide a clear perspective on additive consistency issues of RPRs, this paper reviews the consistency measurements of the different types of RPRs. Then, consistency-driven decision making and information fusion methods are also reviewed and classified into four main types: consistency improving methods; consistency-based methods to manage incomplete RPRs; consistency control in consensus decision making methods; and consistency-driven linguistic decision making methods. Finally, with respect to insights gained from prior researches, further directions for the research are proposed

Granular computing and optimization model-based method for large-scale group decision-making and its application

In large-scale group decision-making process, some decision makers hesitate among several linguistic terms and cannot compare some alternatives, so they often express evaluation information with incomplete hesitant fuzzy linguistic preference relations. How to obtain suitable large-scale group decision-making results from incomplete preference information is an important and interesting issue to concern about. After analyzing the existing researches, we find that: i) the premise that complete preference relation is perfectly consistent is too strict, ii) deleting all incomplete linguistic preference relations that cannot be fully completed will lose valid assessment information, iii) semantics given by decision makers are greatly possible to be changed during the consistency improving process. In order to solve these issues, this work proposes a novel method based on Granular computing and optimization model for large-scale group decision-making, considering the original consistency of incomplete hesitant fuzzy linguistic preference relation and improving its consistency without changing semantics during the completion process. An illustrative example and simulation experiments demonstrate the rationality and advantages of the proposed method: i) semantics are not changed during the consistency improving process, ii) completion process does not significantly alter the inherent quality of information, iii) complete preference relations are globally consistent, iv) final large-scale group decision-making result is acquired by fusing complete preference relations with different weights

Consistency and Consensus Driven for Hesitant Fuzzy Linguistic Decision Making with Pairwise Comparisons

Hesitant fuzzy linguistic preference relation (HFLPR) is of interest because it provides an efficient way for opinion expression under uncertainty. For enhancing the theory of decision making with HFLPR, the paper introduces an algorithm for group decision making with HFLPRs based on the acceptable consistency and consensus measurements, which involves (1) defining a hesitant fuzzy linguistic geometric consistency index (HFLGCI) and proposing a procedure for consistency checking and inconsistency improving for HFLPR; (2) measuring the group consensus based on the similarity between the original individual HFLPRs and the overall perfect HFLPR, then establishing a procedure for consensus ensuring including the determination of decision-makers weights. The convergence and monotonicity of the proposed two procedures have been proved. Some experiments are furtherly performed to investigate the critical values of the defined HFLGCI, and comparative analyses are conducted to show the effectiveness of the proposed algorithm. A case concerning the performance evaluation of venture capital guiding funds is given to illustrate the availability of the proposed algorithm. As an application of our work, an online decision-making portal is finally provided for decision-makers to utilize the proposed algorithms to solve decision-making problems.Comment: Pulished by Expert Systems with Applications (ISSN: 0957-4174

A systematic review on multi-criteria group decision-making methods based on weights: analysis and classification scheme

Interest in group decision-making (GDM) has been increasing prominently over the last decade. Access to global databases, sophisticated sensors which can obtain multiple inputs or complex problems requiring opinions from several experts have driven interest in data aggregation. Consequently, the field has been widely studied from several viewpoints and multiple approaches have been proposed. Nevertheless, there is a lack of general framework. Moreover, this problem is exacerbated in the case of experts’ weighting methods, one of the most widely-used techniques to deal with multiple source aggregation. This lack of general classification scheme, or a guide to assist expert knowledge, leads to ambiguity or misreading for readers, who may be overwhelmed by the large amount of unclassified information currently available. To invert this situation, a general GDM framework is presented which divides and classifies all data aggregation techniques, focusing on and expanding the classification of experts’ weighting methods in terms of analysis type by carrying out an in-depth literature review. Results are not only classified but analysed and discussed regarding multiple characteristics, such as MCDMs in which they are applied, type of data used, ideal solutions considered or when they are applied. Furthermore, general requirements supplement this analysis such as initial influence, or component division considerations. As a result, this paper provides not only a general classification scheme and a detailed analysis of experts’ weighting methods but also a road map for researchers working on GDM topics or a guide for experts who use these methods. Furthermore, six significant contributions for future research pathways are provided in the conclusions.The first author acknowledges support from the Spanish Ministry of Universities [grant number FPU18/01471]. The second and third author wish to recognize their support from the Serra Hunter program. Finally, this work was supported by the Catalan agency AGAUR through its research group support program (2017SGR00227). This research is part of the R&D project IAQ4EDU, reference no. PID2020-117366RB-I00, funded by MCIN/AEI/10.13039/ 501100011033.Peer ReviewedPostprint (published version

Multiplicative Consistency Ascertaining, Inconsistency Repairing, and Weights Derivation of Hesitant Multiplicative Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant multiplicative preference relations (HMPRs). First, the completely multiplicative consistency and weakly multiplicative consistency of HMPRs are defined. Based on them, 0-1 mixed programming models and simple algebraic operations are proposed to ascertain the multiplicative consistency of HMPRs. Then, some goal programming models are developed to generate the weights from consistent HMPRs and to revise inconsistent HMPRs. An integrated procedure to manage the multiplicative consistencies of HMPRs is designed. The proposed methods are also extended to accommodate incomplete HMPRs, and to estimate missing values. Finally, some numerical examples, a comparative analysis with existent approaches, and a simulation analysis are included to illustrate the practicality and effectiveness of the developed models

A dynamic feedback mechanism with attitudinal consensus threshold for minimum adjustment cost in group decision making

This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 71971135, Grant 71571166, Grant 72071056, and Grant 71910107002, in part by the Innovative Talent Training Project of Graduate Students in Shanghai Maritime University of China under Grant 2019YBR017, and in part by the Spanish State Research Agency under Project PID2019-103880RB-I00/AEI/10.13039/501100011033.This article presents a theoretical framework for a dynamic feedback mechanism in group decision making (GDM) by the implementation of an attitudinal consensus threshold (ACT) to generate recommendation advice for the identified inconsistent experts with the aim to increase consensus. The novelty of the approach resides in its ability to implement the ACT continuously, which allows the covering of all possible consensus states of the group from its minimum to maximum consensus degrees. Therefore, it can be flexibly applied to GDM problems with different consistency requirements. A sensitivity analysis method with visual simulation is proposed to support the checking of the numbers of experts involved in the feedback process and the minimum adjustment cost associated with the different ACT intervals. Experimental results show that an increase in the ACT value will lead to an increase in the number of experts and adjustment cost involved in the feedback process. Eventually, a numerical example is included to simulate the feedback process under various decision making scenarios with different ACT intervals.National Natural Science Foundation of China (NSFC) 71971135 71571166 72071056 71910107002Innovative Talent Training Project of Graduate Students in Shanghai Maritime University of China 2019YBR017Spanish Government PID2019-103880RB-I00/AEI/10.13039/50110001103

Integer programming modeling on group decision making with incomplete hesitant fuzzy linguistic preference relations

© 2013 IEEE. Complementing missing information and priority vector are of significance important aspects in group decision making (GDM) with incomplete hesitant fuzzy linguistic preference relations (HFLPRs). In this paper, an integer programming model is developed based on additive consistency to estimate missing values of incomplete HFLPRs by using additive consistency. Once the missing values are complemented, a mixed 0-1 programming model is established to derive the priority vectors from complete HFLPRs, in which the underlying idea of the mixed 0-1 programming model is the probability sampling in statistics and minimum deviation between the priority vector and HFLPR. In addition, we also propose a new GDM approach for incomplete HFLPRs by integrating the integer programming model and the mixed 0-1 programming model. Finally, two case studies and comparative analysis detail the application of the proposed models

Managing consensus by multi-stage optimization models with linguistic preference orderings and double hierarchy linguistic preferences

Preference ordering structures are useful and popular tools to represent experts’ preferences in the decision making process. In the existing preference orderings, they lack the research on the precise relationship between any two adjacent alternatives in the preference orderings, and the decision making methods are unreasonable. To overcome these issues, this paper establishes a novel concept of linguistic preference ordering (LPO) in which the ordering of alternatives and the relationships between two adjacent alternatives should be fused well, and develops two transformation models to transform each LPO into the corresponding double hierarchy linguistic preference relation with complete consistency. Additionally, to fully respect the experts’ expression habits and provide more refined solutions to experts, this paper establishes a multi-stage consensus optimization model by considering the suggested preferences represented in both the continuous scale and the discrete scale, and develops a multi-stage interactive consensus reaching algorithm to deal with multi-expert decision making problem with LPOs. Furthermore, some numerical examples are presented to illustrate the developed methods and models. Finally, some comparative analyses between the proposed methods and models and some existing methods have been made to show the advantages of the proposed methods and models. First published online 24 February 202

Reconciliation, Restoration and Reconstruction of a Conflict Ridden Country

Conflict has sadly been a constant part of history. Winning a conflict and making a lasting peace are often not the same thing. While a peace treaty ends a conflict and often dictates terms from the winners’ perspective, it may not create a lasting peace. Short of unconditional surrender, modern conflict ends with a negotiated cessation of hostilities. Such accords may have some initial reconstruction agreements, but Reconciliation, Restoration and Reconstruction (RRR) is a long term process. This study maintains that to achieve a lasting peace: 1) The culture and beliefs of the conflict nation must be continuously considered and 2) RRR is a long term effort which will occur over years not just in the immediate wake of signing a treaty or agreement. To assure the inclusion of all stakeholders and gain the best results in dealing with this “wicked problem”, an array of Operations Research techniques can be used to support the long term planning and execution of a RRR effort. The final decisions will always be political, but the analysis provided by an OR support team will guide the decision makers to better execute consensus decisions that consider all stakeholder needs. The development of the value hierarchy framework in this dissertation is a keystone of building a rational OR supported long term plan for a successful RRR. The primary aim of the research is to propose a framework and associated set of guidelines derived from appropriate techniques of OR, Decision Analysis and Project Management (right from development of a consensus based value hierarchy to its implementation, feedback and steering corrections) that may be applied to help RRR efforts in any conflict ridden country across the globe. The framework is applicable to any conflict ridden country after incorporating changes particular to any country witnessing a prolonged conflict

Consensus Reaching in Social Network Group Decision Making: Research Paradigms and Challenges

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In social network group decision making (SNGDM), the consensus reaching process (CRP) is used to help decision makers with social relationships reach consensus. Many CRP studies have been conducted in SNGDM until now. This paper provides a review of CRPs in SNGDM, and as a result it classifies them into two paradigms: (i) the CRP paradigm based on trust relationships, and (ii) the CRP paradigm based on opinion evolution. Furthermore, identified research challenges are put forward to advance this area of research