Multiple attribute consensus rules with minimum adjustments to support consensus reachingKnowledge-Based Systems


Bowen Zhang, Yucheng Dong, Yinfeng Xu
Artificial Intelligence / Information Systems and Management / Software / Management Information Systems


iConsensus rules ovel ) pro th ract nsen stm analysis is conducted to show the advantage of the proposed consensus rules. ome m for a ecisio ing (M

GDM problems [1,2,6–8,13,16,19,20,23,24,33,35,36,38,37,40].

Herrera et al. [19,20] presented the consensus models for GDM problems with linguistic assessments. Herrera-Viedma [24] and

Mata et al. [33] developed the consensus reaching processes to solve

GDM problems with multigranular linguistic preference relations.

Meanwhile, Herrera-Viedma [23] and Dong and Zhang [16] so presented a upport con

Besides, th s have als investigated [29,41]. Kim et al. [29] presented an interactive dure for solving a MAGDM problem with incomplete inform

Xu and Wu [41] also presented a discrete model to supp consensus process for MAGDM problems.

In the consensus model, one of the most significant issues is how to design an effective feedback mechanism to guide decision makers reach consensus with minimum adjustments. Dong et al. [15] provided an alternative consensus model, which preserves the individuals’ original opinions as much as possible. Ben-Arieh and Easton [3] and Ben-Arieh et al. [4] defined the concept of ⇑ Corresponding author. Tel.: +86 2982673492.

E-mail address: (Y. Dong).

Knowledge-Based Systems 67 (2014) 35–48

Contents lists availab

Knowledge-Ba .e lagreement in GDMproblem is hard to reach and often not necessary in real life, so ‘‘soft’’ consensus degree is widely presented and used in the consensus process [22,21,25–28]. Over the past few decades, more and more studies pay attention to the consensus models in paradigm, Palomares and Martínez [35] al semi-supervised consensus support system to s reaching processes for large scale GDMproblems. active consensus processes for MAGDM problem 0950-7051/ 2014 Elsevier B.V. All rights reserved.sensus e intero been proceation. ort thereceived increasing attention in the field of decision science [9,10,17,31,32,39,45,49].

Generally, disagreement among decision makers blocks the process of reaching consensus in group decision making (GDM) problems. Consensus process in GDM models is defined as a dynamic and iterative group discussion process, which can help decision makers to bring their opinions closer [7,11]. Meanwhile, a complete port system for GDM problems under dynamic decision environments. Recently, with consideration of the characteristics of Web 2.0 communities, Alonso et al. [2] further proposed a new consensus model to solve GDM problems with linguistic preference relations.

In order to solve large-scale GDM problems, Palomares et al. [36] proposed a consensus model for GDM problems with large groups of decision makers. Meanwhile, based on the multi-agent systemMinimum adjustments

Consensus reaching process

Consensus model 1. Introduction

Nowadays, decision problems bec and uncertain, and it is very hard to evaluate all relevant aspects of a d ple attribute group decision mak 2014 Elsevier B.V. All rights reserved. ore and more complex single decision maker n problem. Thus, multiAGDM) problem has introduced the consensus model for the GDM problems with different preference structures. Furthermore, Alonso et al. [1] presented a new web based consensus support system for GDM problems with incomplete preferences. An important issue which merits our attention is the dynamic change of decision environment in GDM problems. Pérez et al. [38] presented amobile decision sup-Keywords:

Multiple attribute group decision making

Furthermore, we provide the convergence proof of the consensus reaching process, and present one example to show the application of the consensus reaching process. Finally, a detailed comparisonMultiple attribute consensus rules with m to support consensus reaching

Bowen Zhang a, Yucheng Dong b,⇑, Yinfeng Xu a a School of Management, Xi’an Jiaotong University, Xi’an 710049, China bBusiness School, Sichuan University, Chengdu 610065, China a r t i c l e i n f o

Article history:

Received 31 March 2014

Received in revised form 7 June 2014

Accepted 8 June 2014

Available online 17 June 2014 a b s t r a c t

This paper presents two n decision making (MAGDM and adjusted opinions, and

Then, we develop an inte consensus rules. In the co within the suggested adju journal homepage: wwwnimum adjustments consensus rules with minimum adjustments for multiple attribute group blems. One rule is to minimize the distance between the original opinions e other one seeks to minimize the number of adjusted preference values. ive consensus reaching process for MAGDM problems based on the two sus reaching process, decision makers can adjust their opinions flexibly ent intervals guided by the consensus rules with minimum adjustments. le at ScienceDirect sed Systems sevier .com/ locate /knosys (3) aseconsensus cost and further presented the minimum cost consensus and maximum expert consensus models. Subsequently, Zhang et al. [48] extended the minimum cost consensus models and proposed a novel framework to achieve minimum cost consensus under aggregation operators. Zhang et al. [47] incorporated aggregation operators into the maximum expert consensus model, and proposed the maximum expert consensus model with aggregation operators to maximize the number of experts within consensus under the given cost budget. In this study, we will present multiple attribute consensus rules with minimum adjustments to support consensus reaching. Comparison with the previous researches regarding the consensus models with minimum adjustments, our proposal can mainly fill three gaps: (1) The existing consensus models with minimum adjustments, such as Ben-Arieh and Easton [3], Ben-Arieh et al. [4], Dong et al. [13],Zhang et al. [48], Zhang et al. [47] and Liu et al. [30], mainly focus on the GDM problems with single attribute (or single alternative). In this paper, the consensus rules with minimum adjustments are proposed for decision problems with multiple attributes and alternatives. (2) All consensus models with minimum adjustments focus on minimizing the distance between the original opinions and adjusted opinions. However, in the consensus reaching process, the decision makers not only hope to minimize the deviation in the sense of distance criterion, but also seek to minimize the number of adjusted preference values.