An optimization model of the acceptable consensus and its economic significance

Purpose – The purpose of this paper is to construct an optimal resource reallocation model of the limited resource by a moderator for reaching the greatest consensus, and show how to reallocate the limited resources by using optimization methodology once the consensus opinion is reached. Moreover, this paper also devotes to theoretically exploring when or what is the condition that the group decision-making (GDM) system is stable; and when new opinions enter into the GDM, how the level of consensus changes. Design/methodology/approach – By minimizing the differences between the individuals’ opinions and the collective consensus opinion, this paper constructs a consensus optimization model and shows that the objective weights of the individuals are actually the optimal solution to this model. Findings – If all individual deviations of the decision makers (DMs) from the consensus balance each other out, the information entropy theorem shows this GDM is most stable, and economically each individual DM gets the same optimal unit of compensation. Once the consensus opinion is determined and each individual opinion of the DMs is under an acceptable consensus level, the consensus is still acceptable even if additional DMs are added, and the moderator’s cost is still no more than a fixed upper limitation. Originality/value – The optimization model based on acceptable consensus is constructed in this paper, and its economic significance, including the theoretical and practical significance, is emphatically analyzed: it is shown that the weight information of the optimization model carries important economic significance. Besides, some properties of the proposed model are discussed by analyzing its particular solutions: the stability of the consensus system is explored by introducing information entropy theory and variance distribution; in addition, the effect of adding new DMs on the stability of the acceptable consensus system is discussed by analyzing the convergence of consensus level: it is also built up the condition that once the consensus opinion is determined, the consensus degree will not decrease even when additional DMs are added to the GDM

The dynamics of consensus in group decision making: investigating the pairwise interactions between fuzzy preferences.

In this paper we present an overview of the soft consensus model in group decision making and we investigate the dynamical patterns generated by the fundamental pairwise preference interactions on which the model is based. The dynamical mechanism of the soft consensus model is driven by the minimization of a cost function combining a collective measure of dissensus with an individual mechanism of opinion changing aversion. The dissensus measure plays a key role in the model and induces a network of pairwise interactions between the individual preferences. The structure of fuzzy relations is present at both the individual and the collective levels of description of the soft consensus model: pairwise preference intensities between alternatives at the individual level, and pairwise interaction coefficients between decision makers at the collective level. The collective measure of dissensus is based on non linear scaling functions of the linguistic quantifier type and expresses the degree to which most of the decision makers disagree with respect to their preferences regarding the most relevant alternatives. The graded notion of consensus underlying the dissensus measure is central to the dynamical unfolding of the model. The original formulation of the soft consensus model in terms of standard numerical preferences has been recently extended in order to allow decision makers to express their preferences by means of triangular fuzzy numbers. An appropriate notion of distance between triangular fuzzy numbers has been chosen for the construction of the collective dissensus measure. In the extended formulation of the soft consensus model the extra degrees of freedom associated with the triangular fuzzy preferences, combined with non linear nature of the pairwise preference interactions, generate various interesting and suggestive dynamical patterns. In the present paper we investigate these dynamical patterns which are illustrated by means of a number of computer simulations.

Distance-based consensus models for fuzzy and multiplicative 3 preference relations

This paper proposes a distance-based consensus model for fuzzy preference relations where the weights of fuzzy preference relations are automatically determined. Two indices, an individual to group consensus index (ICI) and a group consensus index (GCI), are introduced. An iterative consensus reaching algorithm is presented and the process terminates until both the ICI and GCI are controlled within predefined thresholds. The model and algorithm are then extended to handle multiplicative preference relations. Finally, two examples are illustrated and comparative analyses demonstrate the effectiveness of the proposed methods

Supporting Complex Business Decisions with a Fuzzy Mobile Assistant

Researchers have recognized the importance of semantic expressiveness in understanding and solving complex problems and have identified a need to incorporate reasoning about uncertainty into decision tools that assist business managers. This study extends current approaches and develops new tools to allow artificial mobile assistants to manage rule-driven consultations by capturing and recommending problem solutions through natural language interfaces. A prototype assistant is described to support fuzzy knowledge representations and fuzzy rule-based consultations. The prototype’s application is implemented in a Windows 8 mobile device and applied in a case study of business outsourcing decisions

Fuzzy Rating Framework for Knowledge Management

Abstract In this work we deploy five phases of the Case-based Reasoning in a fuzzy rating framework, which illustrates a holistic knowledge management method including eliciting expert's experience into case base, validating the expert's expertise in knowledge-consistency level, aggregating the judgments of weighted experts into final ratings, solving new problem by retrieving the relevant cases, and retaining the adapted case into case base once the experience had been learned. The main contribution of this framework is to explore a novel measure of knowledge-consistency level (KC ratio) for identifying experts in performance-rating domain. The would-be experts' own judgments were used to validate their knowledge qualities. Moreover, the framework results in an optimal consensus for the performance rating with the help of experts

Visual information feedback mechanism and attitudinal prioritisation method for group decision making with triangular fuzzy complementary preference relations

A visual information feedback mechanism for group decision making (GDM) problems with triangular fuzzy complementary preference relations (TFCPRs) is investigated. The concepts of similarity degree (SD) between two experts as well as the proximity degree (PD) between an expert and the rest of experts in the group are developed for TFCPRs. The consensus level (CL) is defined by combining SD and PD, and a feedback mechanism is proposed to identify experts, alternatives and corresponding preference values that contribute less to consensus. The novelty of this feedback mechanism is that it will provide each expert with visual representations of his/her consensus status to easily ‘see’ his/her consensus position within the group as well as to identify the alternatives and preference values that he/she should be reconsidered for changing in the subsequent consensus round. The feedback mechanism also includes individualised recommendation to those identified experts on changing their identified preference values and visual graphical simulation of future consensus status if the recommended values were to be implemented. Based on the continuous ordered weighted average (COWA) operator, the triangular fuzzy COWA (TF-COWA) operator is defined, and a novel attitudinal expected score function for TFCPRs is developed. The advantage of this function is that the alternatives are ranked by taking into account the attitudinal character of the group of experts or its moderator if applicable. Additionally, a ranking sensitivity analysis of the attitudinal expected score function with respect to the attitudinal parameter is provided

Integrating experts’ weights generated dynamically into the consensus reaching process and its applications in managing non-cooperative behaviors

This work was supported in part by the NSF of China under grants 71171160 and 71571124, in part by the SSEM Key Research Center at Sichuan Province under grant xq15b01, in part by the FEDER funds under grant TIN2013-40658-P, and in part by Andalusian Excellence Project under grant TIC-5991.The consensus reaching process (CRP) is a dynamic and iterative process for improving the consensus level among experts in group decision making. A large number of non-cooperative behaviors exist in the CRP. For example, some experts will express their opinions dishonestly or refuse to change their opinions to further their own interests. In this study, we propose a novel consensus framework for managing non-cooperative behaviors. In the proposed framework, a self-management mechanism to generate experts' weights dynamically is presented and then integrated into the CRP. This self-management mechanism is based on multi-attribute mutual evaluation matrices (MMEMs). During the CRP, the experts can provide and update their MMEMs regarding the experts' performances (e.g., professional skill, cooperation, and fairness), and the experts' weights are dynamically derived from the MMEMs. Detailed simulation experiments and comparison analysis are presented to justify the validity of the proposed consensus framework in managing the non-cooperative behaviors.National Natural Science Foundation of China 71171160 71571124SSEM Key Research Center at Sichuan Province xq15b01European Union (EU) TIN2013-40658-PAndalusian Excellence Project TIC-599

Towards Designing Robo-Advisory to Promote Consensus Efficient Group Decision-Making in New Types of Economic Scenarios

Robo-advisors are a new type of FinTech increasingly used by millennials in place of traditional financial advice. Building on artificial intelligence, robo-advisors provide personalized asset and wealth management services. Their application and study have hitherto focused exclusively on individual advisory regarding asset management. We observe a pressing need to investigate robo- advisors’ application for complex artificial intelligence based recommendation tasks both, in context of group decision-making and in contexts beyond asset management, due to robo-advisors’ potential as a lever for integrating artificial intelligence in the entire decision-making process. Thus, we present a action design research in progress aimed at designing such a robo-advisor. More specifically, this study investigates whether and how robo-advisory promotes consensus-efficient group decision-making in new types of economic scenarios (after-sales). Based on a comprehensive problem formulation, we aim towards deriving a set of meta-requirements and design principles that are embodied in a preliminary prototypical instantiation of a robo-advisor

EXPERTISE-BASED EXPERTS IMPORTANCE WEIGHTS IN ADVERSE JUDGMENT

The objective of this research was to propose the use of expertise levels of experts to determine the experts’ importance weights since there has been no research that determines the 'importance weight' using the expertise level as a whole. The significance of this research was the integration of three concepts, namely: the expert’s expertise level, FPR’s Additive Consistency and the Induced-OWA operator to obtain the expert’s importance weight in adverse judgment situation. The Expertise level of an expert in adverse judgment situation is determined by his/her own assessment on a set of alternatives and defined as ‘the ability to differentiate consistently’ and expressed as the ratio between Discrimination and Inconsistency. The experts provided their preferences using FPR (Fuzzy Preference Relations) since FPR has Additive Consistency property to replicate each element of FPR matrix. Experts were sorted according to their expertise level and the experts’ importance weights followed the OWA (Ordered Weighted Averaging) operator’s weights which were determined by parameterization using Basic Unit-Interval Increasing Monotonic functions. The experts’ importance weights model illustrated by a numerical example, and it concluded that the higher the expert’s expertise level, the higher his/her importance weight

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