ABSTRACT
In traditional preference modeling approaches, agents can express preferences among a pair of alternatives in three distinct ways: either an agent has a strict preference of one alternative compared to the other, or is indifferent between both alternatives, or considers the two alternatives as incomparable. These three preference relations are disjunct, and take the crisp binary values of 0 and 1 only. We propose in this paper a fuzzy preference model to relax these dichotomous conditions: an agent can have at the same time a degree of preference, indifference and incomparability among any pair of alternatives, taking values in the interval [0,1]. This increased preference modeling flexibility allows for a far more detailed analysis of the agents' (partial) preference orderings, which can now be analyzed at different degrees of precision. We illustrate how this analysis can be performed on the preference relations of an individual agent, as well as in the case of two interacting agents. While incomparabilities are inherent to our preference model, it may be useful to resolve these incomparabilities to transform the partial orderings into linear orders. We therefore also present a model of reasoning for the resolution of such incomparabilities by an agent who forms beliefs over the expected orderings.
- L. Amgoud, S. Parsons and N. Maudet, "Arguments, Dialogue and Negotiation", Proceedings of the 14th European Conference on Artificial Intelligence, Berlin, 2000.Google ScholarDigital Library
- K. J. Arrow, "Social Choice and Individual Values", Wiley New York, 1951 (2nd Edition 1963).Google Scholar
- W. Bandler and L. Kohout, "Fuzzy relational products as a tool for analysis and synthesis of the behavior of complex natural and artificial systems", in Fuzzy Sets: Theory and Application to Policy Analysis and Information Systems (Wang, S.K. and Wang, P.P., eds.), Plenum Press, New York and London 1980, pp. 341--367.Google ScholarCross Ref
- B. De Baets and J. Fodor, "Twenty years of fuzzy preference structures (1978-1997)", Belgian J. of Op. Research, Statistics and Computational Science.Google Scholar
- B. De Baets and B. Van de Walle, "Fuzzy preference structures without incomparability", Fuzzy Sets and Systems 76 (1995), 333--348. Google ScholarDigital Library
- B. De Baets and B. Van de Walle, "Minimal definitions of classical and fuzzy preference structures", Proceedings of the Annual Meeting of the North American Fuzzy Information Processing Society (Syracuse, New York), 1997, 299--304.Google Scholar
- K.P. Corfman and S. Gupta, "Mathematical Models of Group Choice and Negotiation", Handbook of OR and MS, 5 (1993), 83--142.Google Scholar
- P. Faratin, C. Sierra and N. Jennings (1997): Negotiation Decision Functions for Autonomous Agents <pubs/RAS.ps> in Int. Journal of Robotics and Autonomous Systems, 24(3-4):159--182.Google Scholar
- P. Faratin, C. Sierra and N. Jennings (2000): Using Similarity Criteria to Make Negotiation Trade-Offs <pubs/ICMAS00-peyman.ps>International Conference on Multiagent Systems (ICMAS-2000), Boston, MA, 119--126. Google ScholarDigital Library
- M. Fedrizzi, M. Fedrizzi and R.A. Marques Pereira, "Soft consensus and network dynamics in group decision making", Intl. Journal of Intelligent Systems 14 (1999), 63--77.Google ScholarCross Ref
- J. Fodor and M. Roubens, "Fuzzy Preference Modeling and Multicriteria Decision Support", Kluwer Academic, Dordrecht, 1994.Google Scholar
- T. Gal, T. Stewart and T. Hanne, "MultiCriteria Decision Making: advances in MCDM models, algorithms, theory and applications", Kluwer Academic, Boston, 1999.Google Scholar
- M. Fedrizzi, M. Fedrizzi and R.A. Marques Pereira, "Soft consensus and network dynamics in group decision making", Intl. Journal of Intelligent Systems 14 (1999), 63--77.Google ScholarCross Ref
- J. Kacprzyck and M. Fedrizzi, "A soft measure of consensus in the setting of partial (fuzzy) preferences", European Journal of Operational Research 34 (1988), 316--325.Google ScholarCross Ref
- J. Kacprzyck and H. Nurmi, "Group decision making under fuzziness", in R. Sowiski (Ed.), Fuzzy Sets in Decision Analysis, Operations Research and Statistics, Kluwer, Boston, 1998, 103--136. Google ScholarDigital Library
- A. Kaufmann, "The Science of Decision-Making", World University Library, 1968.Google Scholar
- H. Kwon, I. Im and B. Van de Walle (2002): Are you Thinking What I am Thinking? A Comparison of Decision makers" Cognitive Maps by Means of a New Similarity Measure. Hawaii International Conference on Systems Science (HICSS-2002), (to appear). Google ScholarDigital Library
- J. Liu and Y. Ye, "E-Commerce Agents", Springer Verlag Lecture Notes in Artificial Intelligence, Berlin, 2001.Google ScholarCross Ref
- R. Luce and H. Raiffa, "Games and Decisions", Dover Publications, 1957.Google Scholar
- J. Montero, "Social welfare functions in a fuzzy environment", Kybernetes 16 (1987), 241--245.Google ScholarCross Ref
- M. Roubens and Ph. Vincke, "Preference Modeling", Lecture Notes in Economics and Mathematical Systems 250, Springer, Berlin, 1985.Google Scholar
- R. A. Ribeiro, "Fuzzy multiple-attribute decision making: a review and new preference elicitation techniques", Fuzzy Sets and Systems 78 (1996), 155--181. Google ScholarDigital Library
- B. Van de Walle, B. De Baets and E. E. Kerre, "Fuzzy multi-criteria analysis of cutting techniques in a nuclear reactor dismantling project", Fuzzy Sets and Systems 74 (1995), 115--126. Google ScholarDigital Library
- B. Van de Walle, B. De Baets and E. E. Kerre, "Characterizable Fuzzy Preference structures", Annals of Operations Research (special issue on Preference Modeling) 80 (1998), 105--136.Google ScholarCross Ref
- B. Van de Walle, S. Heitsch and P. Faratin, "Coping with one-to-many multi-criteria negotiations in an electronic marketplace", Proceedings of the eNegotiations Workshop at DEXIA'01 (Munchen, September 2001), in press. Google ScholarDigital Library
- B. Van de Walle and P. Faratin, "Fuzzy preferences for multi-criteria negotiation", Position Paper for the American Association of Artificial Intelligence Fall 2001 Symposium, Boston MA, November 2001.Google Scholar
- C.J. Watkins, "Models of Delayed Reinforcement Learning", phD Thesis, Psychology Department, Cambridge University, Cambridge, UK. 1989.Google Scholar
- R. R. Yager, "Penalizing Strategic Preference Manipulation in Multi-Agent Decision Making", IEEE Transactions on Fuzzy Systems 9--3 (2001), 393--4. Google ScholarDigital Library
Index Terms
- Agent preference relations: strict, indifferent and incomparable
Recommendations
Incomplete linguistic preference relations and their fusion
Various linguistic preference relations, including incomplete linguistic preference relation, consistent incomplete linguistic preference relation and acceptable incomplete linguistic preference relation, are introduced. Some desirable properties of the ...
On fuzzy strict preference, indifference, and incomparability relations
Special issue dedicated to Professor Claude PonsardThe Some of the MADM Method Behaviors Versus Incomparability
One of the advantages of the PROMETHEE I method is to bring out such incomparability's. Incomparability mostly means that the analysis of the decision problem does not permit to identify a relation of overall preference or indifference between two or ...
Comments