Elsevier

Information Sciences

Volume 180, Issue 23, 1 December 2010, Pages 4477-4495
Information Sciences

A web based consensus support system for group decision making problems and incomplete preferences

https://doi.org/10.1016/j.ins.2010.08.005Get rights and content

Abstract

Reaching a high level of consensus among experts is critical in group decision making problems. Usually, it is the moderator task to assure that the consensus process is carried out properly and, if possible, to offer recommendations to the expert in order to change their opinions and narrow their differences.

In this paper we present an implemented web based consensus support system that is able to help, or even replace, the moderator in a consensus process where experts are allowed to provide their preferences using one of many types (fuzzy, linguistic and multi-granular linguistic) of incomplete preference relations.

This system is based on both consistency and consensus measures and it has been designed to provide advice to the experts to increase group consensus level while maintaining the individual consistency of each expert. The consistency measures are characterized by and computed using uninorm operators. When appropriate, the system also helps experts to reduce the incompleteness of their preference relations. The web interface allows to carry out distributed consensus processes and thus, experts do not necessarily need to physically meet together.

Introduction

In group decision making (GDM) problems there are two processes to carry out before obtaining a final solution [21], [24], [31], [35]: the selection process and the consensus process. The former [26], [48] refers to how to obtain a solution set of alternatives from the opinions on the alternatives given by the experts, while the latter deals with the achievement of the maximum degree of consensus or agreement between the set of experts on the solution set of alternatives. Usually, this process is guided by the figure of a moderator [17], [24], [34], [35] and it is carried out before the selection process. Clearly, the consensus process is an important step in solving GDM problems because it aids to obtain solutions with high level of consensus among experts, which is usually a desirable property.

Good GDM processes require, before their application, the specification of several aspects about the problem to solve as well as the methodology to follow. This includes, but is not restricted to, the definition of the representation format(s) [45] available for the experts to express their preferences about the possible alternatives in the problem: linguistic [2], [19], [53] or fuzzy [32], [33], [51], [62], [63] formats. Many GDM approaches assume an homogeneous representation of the preference information provided by experts and therefore are based on the availability of one single representation format. However, it may well be the case that experts might feel more comfortable if different representation formats are available to express their preferences [8], [31]. Thus, the use of multiple representation formats has become a major area of research in GDM.

In [8] an approach with three different preference representation formats was proposed. In that approach, preference orderings and utility values are transformed into fuzzy preference relations in order to be able to operate with them. In [9], another preference representation format (multiplicative preference relations) was incorporated to the previous model to enhance it. Additionally, in [31] a consensus model for GDM problems with these four representation formats was presented. Fan et al. [18] proposed a goal programming approach where the preference information on alternatives provided by decision makers is represented in two different formats, multiplicative preference relations and fuzzy preference relations. In [42] an approach that deals with preference information represented in four different formats was also presented. These two approaches differ from the previous ones in that the ranking of alternatives or selection of the most desirable alternative(s) is obtained in a direct way, i.e. no unify process or aggregation of individual preferences are required. In [28] a model that tackles GDM situations with information expressed using 2-tuple linguistic values and interval valued preferences is presented. In [58] an interactive method for multiple attribute GDM dealing with exact numerical values and triangular fuzzy numbers was developed. Finally, in [64] some experimental results that validate the necessity of using multiple preference formats in decision making were presented.

A different issue that needs attention when dealing with real GDM problems is the lack of complete information [44], [55]. There might be situations where some of the experts might not not be able to efficiently express any kind of preference degree between two or more of the available options. Indeed, this may be due to an expert not possessing a precise or sufficient level of knowledge of part of the problem to be solved, or because that expert is unable to discriminate the degree to which some options are better than others. In such situations experts may prefer not to guess some values and thus, not to give part of the required information, that is, they would provide incomplete information [3], [16], [30], [37], [38], [56], [57], [59], [54].

Current decision support models and systems incorporate mechanisms to maximize the consensus in the decision process [5], [6], [4], [17], [25], [24], [34], [35], [36], [65]. For example, in [14] a consensus driven model is used in the selection of advanced technology field; in [22] some consensus reaching ideas are included as part of a decision support system for water resource management; while in [29] the authors developed a consensus model for GDM and incomplete information.

The aim of this paper is to present a new web based consensus support system (WBCSS) to deal with GDM problems under incomplete information situations and with experts’ preferences represented with different representation formats: fuzzy preference relations, linguistic preference relations and multi-granular linguistic preference relations. This consensus support system is based on the use of several consensus and consistency measures which are interactively computed when the experts provide their preferences. One of the main novelties in this contribution is the use of uninorms [40] to define the consistency measures as well as to tackle missing information. The consensus support system uses both kinds of measures to offer advice to the experts by means of easy to follow rules, thus providing a feedback mechanism to help experts to change their preferences in order to obtain solutions with a high level of consensus. The system also aims to help experts to maintain a high consistency level in their preferences to avoid self contradiction and, when that is the case, to reduce as much as possible incomplete information situations. This system is designed to help the moderator to carry out his duties during the different steps of the consensus process, but it could takeover the role of the moderator once the initialization steps have been completed. The system has been fully implemented and the experts can use it via a web interface which allows to carry out consensus processes in distributed environments. This means that the usual imperative condition of experts to physically meet together is eliminated and therefore the decision making process for group of experts, living for example in different countries, is facilitated.

The rest of this paper is organized as follows. Section 2 presents the theoretical model on which the WBCSS is based. In Section 3 the WBCSS for GDM problems with different kinds of preference relations is presented, and some of the technical details regarding its implementation and use are discussed. In Section 4 a toy application example of the system is used to illustrate the solving a simple GDM problem. Finally, in Section 5 we draw our conclusions and future improvements to the system are highlighted.

Section snippets

Theoretical model for the consensus support system

In [29] a consistency and consensus measures based theoretical model to guide the GDM consensus process with incomplete fuzzy preference relations was developed. This section briefly describes the extension of that model and the necessary improvements needed to allow the use of multi-granular linguistic preference relations, the use of uninorms as a new characterization of consistency and their use to deal with incomplete information. In order for this paper to be as self-contained as possible,

Web based consensus support system

Nowadays, many decision and consensus support systems are being implemented in order to aid experts to solve decision problems efficiently [22], [49]. Web-based applications are increasingly being used for GDM and Decision Support environments [65] because they offer many advantages. An example of these advantages is the possibility of accessing them from all over the world and thus, the possibility of carrying out distributed decision making processes where experts cannot meet physically

Example of application

In this section we present an example of application of the consensus support system to solve a simple GDM problem. The problem is that of selecting the best car from a set of four different alternatives:

  • Black, economic and slow car: Black Car.

  • Red, very small, fast and comfortable car: Red Car.

  • White and very fast car. It consumes little but it is very expensive: White Car.

  • Blue, very small and very cheap car: Blue Car.

Four experts (e1, e2, e3, e4) will give their preferences using different kinds

Conclusions and future works

We have presented a web consensus support system to deal with GDM problems with different kinds of incomplete preference relations (fuzzy, linguistic and multi-granular linguistic preference relations). The consensus reaching process is guided by both consistency and consensus measures. Consistency has been modelled via the multiplicative consistency property also known as the Cross Ratio uninorm, and it has been used to estimate unknown values of incomplete preference relations as well as to

Acknowledgments

This paper has been developed with the Financing of FEDER funds in FUZZYLING project (TIN2007-61079), PETRI project (PET2007-0460), Andalucian Excellence project (TIC-5299) and project of Ministry of Public Works (90/07).

References (65)

  • R. Giordano et al.

    Integrating conflict analysis and consensus reaching in a decision support system for water resource management

    Journal of Environmental Management

    (2007)
  • F. Herrera et al.

    A fusion approach for managing multigranularity linguistic term sets in decision making

    Fuzzy Sets and Systems

    (2000)
  • F. Herrera et al.

    Linguistic measures based on fuzzy coincidence for reaching consensus in group decision making

    International Journal of Approximate Reasoning

    (1997)
  • F. Herrera et al.

    Choice processes for non-homogeneous group decision making in linguistic setting

    Fuzzy Sets and Systems

    (1998)
  • F. Herrera et al.

    Non-homogeneous information in group decision making

    European Journal of Operational Research

    (2005)
  • E. Herrera-Viedma et al.

    Some issues on consistency of fuzzy preference relations

    European Journal of Operational Research

    (2004)
  • J. Kacprzyk

    Group decision making with a fuzzy linguistic majority

    Fuzzy Sets and Systems

    (1986)
  • J. Kacprzyk et al.

    A “soft” measure of consensus in the setting of partial (fuzzy) preferences

    European Journal of Operational Research

    (1988)
  • J. Kacprzyk et al.

    Group decision making and consensus under fuzzy preferences and fuzzy majority

    Fuzzy Sets and Systems

    (1992)
  • I. Kaya et al.

    Development of fuzzy process accuracy index for decision making problems

    Information Sciences

    (2010)
  • S.H. Kim et al.

    Interactive group decision making procedure under incomplete information

    European Journal of Operational Research

    (1999)
  • S.H. Kim et al.

    An interactive procedure for multiple attribute group decision making with incomplete information: range-based approach

    European Journal of Operational Research

    (1999)
  • Y.-M. Li et al.

    Weak uninorm aggregation operators

    Information Sciences

    (2000)
  • Z. Meng et al.

    A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets

    Information Sciences

    (2009)
  • C. Mousset

    Families of relations modelling preferences under incomplete information

    European Journal of Operational Research

    (2009)
  • C. Porcel et al.

    A recommender system for research resources based on fuzzy linguistic modeling

    Expert Systems with Applications

    (2009)
  • M. Roubens

    Fuzzy sets and decision analysis

    Fuzzy Sets and Systems

    (1997)
  • J. Sancho et al.

    Design and implementation of a decision support system for competitive electricity markets

    Decision Support Systems

    (2008)
  • Z. Switalski

    General transitivity conditions for fuzzy reciprocal preference matrices

    Fuzzy Sets and Systems

    (2003)
  • T. Tanino

    Fuzzy preference orderings in group decision making

    Fuzzy Sets and Systems

    (1984)
  • T.-C. Wang et al.

    Incomplete fuzzy linguistic preference relations under uncertain environments

    Information Fusion

    (2010)
  • Z. Wang et al.

    An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights

    Information Sciences

    (2009)
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