Ambiguity Measures for preference-based decision viwewpoints

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This paper examines the ambiguity of subjective judgments, which are represented by a system of pairwise preferences over a given set of alternatives. Such preferences are valued with respect to a set of reasons, in favor and against the alternatives, establishing a complete judgment, or viewpoint, on how to solve the decision problem. Hence, viewpoints entail particular decisions coming from the system of preferences, where the preference-based reasoning of a given viewpoint holds according to its soundness or coherence. Here we explore such a coherence under the frame of ambiguity measures, aiming at learning viewpoints with highest preference-score and minimum ambiguity. We extend existing measures of ambiguity into a multi-dimensional fuzzy setting, and suggest some future lines of research towards measuring the coherence or (ir)rationality of viewpoints, exploring the use of information measures in the context of preference learning.
1. D. Bouyssou, T. Marchant, M. Pirlot, A. Tsoukiàs, Ph. Vincke. Evaluation and Decision Models with Multiple Criteria. Springer, Heidelberg, 2006. 2. H. Bustince, M. Pagola, R. Mesiar, E. Hullermeier, F. Herrera. Grouping, overlap, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Transactions on Fuzzy Systems 20, 405-415, 2012. 3. V. Cutello, J. Montero. Fuzzy rationality measures. Fuzzy Sets and Systems 62, 39-54, 1994. 4. G. Debreu, Theory of Value. An Axiomatic Approach of Economic Equilibrium. Yale University Press, New York, 1959. 5. L. De Miguel, D. Gómez, J.T. Rodríguez, J. Montero, H. Bustince, G. Dimuro, J. Sanz. General overlap functions. Fuzzy Sets and Systems. DOI: 10.1016/j.fss.2018.08.003. 6. D. Ellsberg. Risk ambiguity and the savage axioms. Quarterly Journal of Economics 75, 643-669, 1961. 7. P. Fishburn. The axioms and algebra of ambiguity. Theory and Decision 34, 119-137, 1993. 8. J. Fodor, M. Roubens. Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht, 1994. 9. C. Franco, J. Montero, J.T. Rodríguez. A fuzzy and bipolar approach to preference modelling with application to need and desire. Fuzzy Sets and Systems 214, 2013, 20-34. 10. C. Franco, J.T. Rodríguez, J. Montero. Building the meaning of preference from logical paired structures. Knowledge-Based Systems 83, 2015, 32-41. 11. C. Franco, J.T. Rodríguez, J. Montero. Learning preferences from paired opposite-based semantics. International Journal of Approximate Reasoning 86, 2017, 80-91. 12. C. Franco, J.T. Rodriguez, J. Montero, D. Gomez. Modeling opposition with restricted paired structures. Journal of Multi-Valued Logic & Soft Computing 30, 2018, 239-262. 13. N. Georgescu-Roegen. The pure theory of consumers behavior. Quarterly Journal of Economics 50, 545593, 1936. 14. J.M. Keynes. A Treatise on Probability. MacMillan, London, 1963. 15. F. Knight. Risk, Uncertainty, and Profit. University of Chicago Press, Chicago, 1971. 16. J. Montero, H. Bustince, C. Franco, J.T. Rodríguez, D. Gomez, M. Pagola, J. Fernández, E. Barrenechea. Paired structures in knowledge representation, Knowledge Based Systems 100, 2016, 50-58. 17. J. Montero, J. Tejada, C. Cutello. A general model for deriving preference structures from data. European Journal of Operational Research 98, 98-110, 1997. 18. B. Van der Walle, B. de Baets, E. Kerre. Characterizable fuzzy preference struc- tures. Annals of Operational Research 80 105136, 1998. 19. R.R. Yager. On a measure of ambiguity. International Journal of Intelligent Systems 10, 1001-1019, 1995.