Mario Fedrizzi

Group decision making and consensus under fuzzy preferences and fuzzy majority

Abstract We present how fuzzy logic with linguistic quantifiers, mainly its calculi of linguistically quantified propositions, can be used in group decision making. The fuzzy linguistic quantifiers (exemplified by most, almost all,...) are employed to represent a fuzzy majority which is in many cases closer to a real human perception of the very essence of majority. Fuzzy logic provides here means for a formal handling of such a fuzzy majority which was not possible by using traditional formal apparata. Assuming fuzzy individual and social preference relations, as it is commonly done, and employing in addition a fuzzy majority expressed by a fuzzy linguistic quantifier, we redefine solution concepts in group decision making, and present new ‘soft’ degrees of consensus.

A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences

Abstract Consensus, as traditionally meant to be a full and unanimous agreement, is often not reachable in practice. A degree of consensus for indicating how far a particular group of individuals is from consensus may be therefore very useful. We propose a new measure (degree) of consensus which is more human-consistent in the sense that it better reflects a real human perception of the essence of consensus in practice. Basically, our consensus measure expresses the degree to which, say, ‘most of the important individuals agree as to (their testimonies concerning) almost all of the relevant options’. The point of departure is the set of individual testimonies which are here the individual fuzzy preference relations. As a formal tool we use a fuzzy-logic-based calculus of linguistically quantified propositions.

An interactive multi-user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers

Abstract We present an interactive user-friendly microcomputer-based decision support system for consensus reaching processes. The point of departure is a group of individuals (experts, decision makers,…) who present their testimonies (opinions) in the form of individual fuzzy preference relations. Initially, these opinions are usually quite different, i.e., the group is far from consensus. Then, in a multistage session a moderator, who is supervising the session, tries to make the individuals change their testimonies by, e.g., rational argument, bargaining, etc. to eventually get closer to consensus. For gauging and monitoring the process a new ‘soft’ degree (measure) of consensus is used whose essence is the determination to what degree, e.g., ‘most of the individuals agree as to almost all of the relevant options’. A fuzzy-logic-based calculus of linguistically quantified propositions is employed.

A ‘human-consistent’ degree of consensus based on fuzzy login with linguistic quantifiers

Abstract A traditional meaning of consensus as a full and unanimous agreement is, first, often unrealistic in practice, since it is not reachable, and, second, often contradicts a human perception of its very essence which clearly indicates that consensus may be a matter of degree. To capture and reflect the latter, a new ‘humanly-consistent’ degree of consensus has been proposed by the authors which is basically meant as a degree to which, say, ‘most of the important individuals agree (as to their testimonies which are assumed to be individual fuzzy preference relations) as to almost all the relevant options’. To handle the linguistic quantifiers (most, almost all, …), which are a natural human perception of majority, a fuzzy-logic-based calculus of linguistically quantified propositions, in its classic Zadehs form, has been used. In this paper we redefine those degrees of consensus using an alternative, more sophisticated calculus due to Yager.

Probabilistic, fuzzy and rough concepts in social choice

Abstract We discuss how intrinsic inconsistencies and negative results (concerning opinion aggregation) in social choice may be alleviated by plausible modifications of underlying assumptions and problem formulations, basically by the introduction of some impreciseness of a probabilistic, fuzzy and rough type. First, we discuss briefly probabilistic voting, and the use of fuzzy preference relations and fuzzy majorities. Then, in the main part, we proceed to the use of Pawlaks rough sets theory in the analysis of crucial properties of voting schemes. In this framework we also discuss the concept of a distance between two voting schemes. Finally, we further explore difficult issues of how diverse types of impreciseness can be combined, and we consider in particular the combination of roughness with randomness and fuzziness in the context of spatial voting games.

On Measuring Consensus in the Setting of Fuzzy Preference Relations

Consensus, traditionally understood as a full and unanimous agreement, is a utopia in virtually all practical cases. A degree of consensus to indicate how far one is from complete agreement does therefore make sense. We present a ‘soft’ consensus measure which is basically a degree to which, say, “most pairs of individuals agree as to their preferences between almost all relevant options”. The point of departure is the set of individual preference relations. A fuzzy-logic-based calculus of linguistically quantified proposition is employed.

Soft consensus and network dynamics in group decision making

We propose a dynamical network model for consensus reaching in group decision making. The model combines the minimization of a soft measure of collective dissensus and an individual inertial mechanism which emulates opinion changing aversion. Both components of the dynamics are nonlinear. The collective consensual trend corresponds to a process of anisotropic diffusion among the various individual preference structures. The anisotropy is designed so as to outline and enhance the natural group segmentation into homogeneous preference subgroups (weak consensus). The individual inertial mechanism, on the other hand, opposes changes from the original preferences and provides an appropriate framework to deal with preference outliers. We examine in detail the simple case in which each decision maker must choose between only two alternatives. Finally we comment on the possibility of incorporating in the dynamics a form of transitivity constraint regarding the group segmentation. ©1999 John Wiley & Sons, Inc.

Consensus reaching via a GDSS with fuzzy majority and clustering of preference profiles

An interactive DSS for consensus reaching is presented. Experts provide their testimonies as fuzzy preference relations. The consensus reaching process is supervised by a moderator (“super-expert”). A degree of consensus, based on the concept of a fuzzy majority given as a linguistic quantifier is employed. Algorithms of cluster analysis are used to find groups of experts having similar preferences.

GROUP DECISION MAKING WITH FUZZY MAJORITIES REPRESENTED BY LINGUISTIC QUANTIFIERS

ABSTRACT New solution concepts in group decision making under fuzzy individual preference relations and a fuzzy majority expressed by a fuzzy linguistic quantifier (e.g., most, almost all, …) are presented. Two fuzzy – logic – based calculi of linguistically quantified proposition, underlying Zadehs representation of commonsense knowledge as a collection of dispositions (propositions with implicit linguistic quantifiers), are used. These new solution concepts seem to be more human – consistent, hence should be more acceptable and implementable. Moreover, the use of a similar approach to develop some “soft” degrees of consensus is outlined.

Approximate Reasoning in the Modeling of Consensus in Group Decisions

In this paper we propose an approach to consensus reaching based on linguistically expressed individual opinions and on so-called opinion changing aversion. We operate within this basic context: there is a group of experts which must choose a preferred alternative from a finite set of admissible ones according to several criteria. Each expert is called upon evaluate linguistically the alternatives in terms of their performance with respect to each criterion. The task of the experts is to reach some agreement during a consensus reaching process directed by a third person called the moderator. The experts are expected subsequently to change their testimonies until sufficient agreement (consensus) has been reached. The measure of consensus depends on a function estimated for each expert according to his/her aversion to opinion change.