Francisco Mata

COMAS: A Multi-agent System for Performing Consensus Processes

The need for achieving consensus in group decision making problems is a common and sometimes necessary task in a myriad of social and business environments. Different consensus reaching processes have been proposed in the literature to achieve agreement among a group of experts. Initially, such processes were guided by a human moderator, but afterwards, some proposals to facilitate such a process arose by automating the moderator tasks. However, not many consensus support systems have been developed so far, due to the difficulty to manage intelligent tasks and cope with the negotiation process involved in consensus. This paper aims to present an initial prototype of an automatic consensus support system, developed by using the multi-agent paradigm that provides intelligent tools and capacities to tackle the inherent complexity found in this problem. To do so, we focus on the consensus model considered, the multi-agent architecture designed to develop such a system, and the ontology used for reasoning and communication tasks.

Modelling influence in group decision making

Group decision making has been widely studied since group decision making processes are very common in many fields. Formal representation of the experts’ opinions, aggregation of assessments or selection of the best alternatives has been some of main areas addressed by scientists and researchers. In this paper, we focus on another promising area, the study of group decision making processes from the concept of influence and social networks. In order to do so, we present a novel model that gathers the experts’ initial opinions and provides a framework to represent the influence of a given expert over the other(s). With this proposal it is feasible to estimate both the evolution of the group decision making process and the final solution before carrying out the group discussion process and consequently foreseeing possible actions.

Measurements of Consensus in Multi-granular Linguistic Group Decision-Making

The reaching of consensus in group decision-making (GDM) problems is a common task in group decision processes. In this contribution, we consider GDM with linguistic information. Different experts may have different levels of knowledge about a problem and, therefore, different linguistic term sets (multi-granular linguistic information) can be used to express their opinions.

A Multi-granular Linguistic Decision Model for Evaluating the Quality of Network Services

The fuzzy linguistic approach has been applied successfully to many problems dealing with qualitative aspects that are assessed by means of linguistic terms. The use of linguistic information implies in most cases the need for using fusion processes to obtain aggregated values that summarize the input information. One important limitation of the fuzzy linguistic approach appears when fusion processes are applied to problems in which the linguistic information is assessed in linguistic term sets with different granularity of uncertainty, i.e., different cardinality; this type of information is denoted as multi-granular linguistic information. This limitation consists of the difficulty in dealing with this type of information in fusion processes due to the fact that there is no standard normalization process for this type of information, as in the numerical domain.

COMAS: A consensus multi-agent based system

In group decision making problems is common the necessity of achieving a consensus before making a decision. Many consensus reaching processes have been introduced in the literature but not many intelligent systems have finally been implemented to deal with such processes. In this contribution an initial prototype of a consensus support system supported on a multi-agent paradigm is presented, showing the system architecture (set of agents, behaviours and relationships) and a preliminary ontology to represent the problem knowledge and used for the agent communication.

A Consensus Support System for Group Decision Making Problems with Heterogeneous Information

Summary. A group decision making (GDM) problem is a decision process where several decision makers (experts, judges, etc.) participate and try to reach a common solution. In the literature these problems have been solved carrying out a selection process that returns the solution set of alternatives from the preferences given by the experts. In order to achieve an agreement on the solution set of alternatives among the experts, it would be adequate to carry out a consensus process before the selection process. In the consensus process the experts discuss and change their preferences in order to achieve a big agreement. Due to the fact that the experts may belong to different research areas, they may express their preferences in different information domains. In this contribution we focus on the consensus process in GDM problems defined in heterogeneous contexts where the experts express their preferences by means of numerical, linguistic and interval-valued assessments. We propose a consensus support system model to automate the consensus reaching process, which provides two main advantages: (1) firstly, its ability to cope with GDM problems with heterogeneous information by means of the Fuzzy Sets Theory, and, (2) secondly, it assumes the moderator’s tasks, figure traditionally presents in the consensus reaching process.

Type-1 OWA Unbalanced Fuzzy Linguistic Aggregation Methodology: Application to Eurobonds Credit Risk Evaluation

In decision making, a widely used methodology to manage unbalanced fuzzy linguistic information is the linguistic hierarchy (LH), which relies on a linguistic symbolic computational model based on ordinal 2‐tuple linguistic representation. However, the ordinal 2‐tuple linguistic approach does not exploit all advantages of Zadehs fuzzy linguistic approach to model uncertainty because the membership function shapes are ignored. Furthermore, the LH methodology is an indirect approach that relies on the uniform distribution of symmetric linguistic assessments. These drawbacks are overcome by applying a fuzzy methodology based on the implementation of the type‐1 ordered weighted average (T1OWA) operator. The T1OWA operator is not a symbolic operator and it allows to directly aggregate membership functions, which in practice means that the T1OWA methodology is suitable for both balanced and unbalanced linguistic contexts and with heterogeneous membership functions. Furthermore, the final output of the T1OWA methodology is always fuzzy and defined in the same domain of the original unbalanced fuzzy linguistic labels, which facilitates its interpretation via a visual joint representation. A case study is presented where the T1OWA operator methodology is used to assess the creditworthiness of European bonds based on real credit risk ratings of individual Eurozone member states modeled as unbalanced fuzzy linguistic labels.

Aggregation of unbalanced fuzzy linguistic information in decision problems based on Type-1 OWA operator

Information aggregation is a key task in any group decision making problem. In the fuzzy linguistic context, when comparing two alternatives, it is usually assumed that assessments belong to linguistic term sets of symmetrically distributed labels with respect to a central label that stands for the indifference state. However, in practice there are many situations whose nature recommends their modelling using not symmetric linguistic term sets, and therefore formal approaches to deal with sets of unbalanced linguistic labels in decision making are necessary to be appropriately developed. In literature, the linguistic hierarchy methodology has proved successful when modelling unbalanced linguistic labels using an ordinal approach in their representation. However, linguistic labels can be modelled using a cardinal approach, i.e. as fuzzy subsets represented by membership functions. Obviously, the linguistic hierarchy methodology is not appropriate in these cases. In this contribution, a Type-1 OWA approach is proposed to deal with the aggregation step of the resolution process of a group decision making problem with unbalanced linguistic information modelled using a cardinal approach. The Type-1 OWA operator aggregates fuzzy sets and uses whole membership functions to compute the aggregated output fuzzy sets. The application of the Type-1 OWA approach to an example where the linguistic hierarchy approach was applied before will provide us an opportunity to compare the aggregated results obtained in both cases. Following the defuzzification of the Type-1 OWA aggregated values, it can be concluded that both methodologies are equivalent. The use of the Type-1 OWA approach in this decision making context does not require building linguistic hierarchies while at the same time allows a fully exploitation of the fuzzy nature of linguistic information.

A Preliminary Study of the Effects of Different Aggregation Operators on Consensus Processes

Searching for consensus in group decision making is a process in which experts change their preferences in order to achieve a minimum agreement before making a decision. Computing the consensus degree among experts and the group collective opinion by aggregating experts’ opinions are two main tasks in a consensus reaching process. In this contribution we have studied the effects of different aggregation operators on the consensus processes. In particular, we have analyzed the obtained outcomes by three different aggregation operators: arithmetic mean, OWA with the linguistic quantifier “most” and Dependent OWA. Finally, some preliminary conclusions about the obtained results and the influence of these aggregation operations on consensus processes are drawn

Optimizing the Method for Building an Extended Linguistic Hierarchy

In those problems dealing with linguistic information and multiple sources of information may happen that the sources involved have different degree of knowledge about the problem and could be suitable and necessary the use of different linguistic term sets with different granularity defining a multi-granular linguistic context. Different approaches have been presented to deal with this type of context, being the linguistic hierarchies an approach quite interesting due to its accuracy in computational model but with a strong limitation about the term sets that can be used. We presented an extension of the linguistic hierarchies [2] to deal any linguistic term set in a precise way. This new approach presents initially a drawback, it needs a term set with a very high granularity, implying complexity in computing with words processes. Therefore, we propose an optimization to building an extended linguistic hierarchy in order to decrease the granularity of such a term set