Aggregation of monotone reciprocal relations with application to group decision making

Authors:
MichaëL Rademaker;Bernard De Baets
Affiliations:
KERMIT, Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure Links 653, B-9000 Gent, Belgium;KERMIT, Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure Links 653, B-9000 Gent, Belgium
Venue:
Fuzzy Sets and Systems
Year:
2011

Citing 12
Cited 4

A new approach to the maximum-flow problem

Journal of the ACM (JACM)
A model of consensus in group decision making under linguistic assessments

Fuzzy Sets and Systems
Fuzzy preference modeling

Fuzzy sets in decision analysis, operations research and statistics
A stochastic dominance method for incorporating yield monitor data into the hybrid and variety decisions of Argentinean farmers

Computers and Electronics in Agriculture
Consistent models of transitivity for reciprocal preferences on a finite ordinal scale

Information Sciences: an International Journal
Improving tractability of group decision making on environmental problems through the use of social intensities of preferences

Environmental Modelling & Software
Loss optimal monotone relabeling of noisy multi-criteria data sets

Information Sciences: an International Journal
Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity

Fuzzy Sets and Systems
Modeling the concept of majority opinion in group decision making

Information Sciences: an International Journal
Supervised ranking in the weka environment

Information Sciences: an International Journal
Optimal restoration of stochastic monotonicity with respect to cumulative label frequency loss functions

Information Sciences: an International Journal
Supervised learning algorithms for multi-class classification problems with partial class memberships

Fuzzy Sets and Systems

Order compatible fuzzy relations and their elicitation from general fuzzy partitions

ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Algorithms for improving consistency or consensus of reciprocal [0,1]-valued preference relations

Fuzzy Sets and Systems
Full Length Article: A ranking procedure based on a natural monotonicity constraint

Information Fusion
A method for deriving order compatible fuzzy relations from convex fuzzy partitions

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.20

Visualization

Abstract

This paper is composed of two complementary parts. The first part is a formal investigation into the interplay of properties of reciprocal relations, how monotonicity relates to some natural and intuitive properties, including stochastic transitivity. The goal is to aggregate monotone reciprocal relations on a given set of alternatives. Monotonicity is expressed w.r.t. a linear order on the set of alternatives. The second part is a practical protocol to both determine the best fitting linear order underlying the alternatives, and construct a reciprocal relation monotone w.r.t. it. We formulate the problem as an optimization problem, where the aggregated linear order is that for which the implied stochastic monotonicity conditions are closest to being satisfied by the distribution of the input monotone reciprocal relations. We show that if stochastic monotonicity conditions are satisfied, a monotone reciprocal relation is easily found on the basis of the (possibly constructed) stochastically monotone reciprocal distributional relation.