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Merging Fuzzy Information

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Fuzzy Sets in Approximate Reasoning and Information Systems

Part of the book series: The Handbooks of Fuzzy Sets Series ((FSHS,volume 5))

Abstract

This chapter deals with an important issue pertaining to intelligent information processing systems, that of managing information coming from several sources. Possibility theory and the body of aggregation operations from fuzzy set theory provide some tools to address this problem. The fusion of imprecise information is carefully distinguished from the estimation problem. The approach to fusion is set-theoretic and the choice of conjunctive versus disjunctive fusion modes depends on assumptions on whether all sources are reliable or not. Quantified, prioritized and weighted and fusion rules are described. Fuzzy extensions of estimation processes are also discussed. The approach, based on conflict analysis, applies to sensor fusion, aggregation of expert opinions as well as the merging of databases.

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References

  • Abidi M. A. and Gonzalez R. C., eds. (1992). Data Fusion in Robotics and Machine Intelligence Academic Press, New York.

    MATH  Google Scholar 

  • Arbuckle T. D., Lange E., Iwamoto T., Otsu N. and Kyuma K. (1995). Fuzzy information fusion in a face regognition system, Int. J. Uncertainty, Fuzziness and Knowledge-based Systems, 3, 217–246.

    Article  Google Scholar 

  • Baral C., Kraus S., Minker J. and Subrahmanian (1992). Combining knowledge bases consisting in first order theories, Computational Intelligence, 8(1), 45–71.

    Article  Google Scholar 

  • Bardossy A., Duckstein L. and Bogardi I. (1993). Combination of fuzzy numbers representing expert opinions, Fuzzy Sets and Systems, 57, 173–181.

    Article  MathSciNet  Google Scholar 

  • Bar-Shalom Y. and Fortmann T. E. (1988). Tracking and Data Association, Academic Press, New York.

    MATH  Google Scholar 

  • Benferhat S., Dubois D. and Prade H. (1997a). Some syntactic approaches to the handling of inconsistent knowledge bases — Part 1: The flat case, Studia Logica, 58, 1997, 17–45.

    Article  MathSciNet  MATH  Google Scholar 

  • Benferhat S., Dubois D. and Prade H. (1997b). From semantic to syntactic approaches to information combination in possibilistic logic, Aggregation and Fusion of Imperfect Information (Bouchon-Meunier B., Ed.), Physica-Verlag, Heidelberg, Germany, 141–161.

    Google Scholar 

  • Benferhat S., Dubois D. and Prade H. (1997c). Nonmonotonic reasoning, conditional objects and possibility theory, Artificial Intelligence, 92(1/2), 259–276.

    Article  MathSciNet  MATH  Google Scholar 

  • Bezdek J., Keller J., Krishnapuram R. and Pal N. R. (1999). Fuzzy Models and Algorithms for Pattern Recognition and Image Processing, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, The Netherlands.

    MATH  Google Scholar 

  • Bezdek J. and Sutton M. A. (1999). Image processing in medicine, Applications of Fuzzy Sets (Zimmermann H.-J., Ed.), The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

  • Biacino L., Gerla G. (1999). Closure operators in fuzzy set theory. This volume, chapter 3.

    Google Scholar 

  • Bloch I. (1996). Information combination operation for data fusion: A comparative review with classification, IEEE Trans. on Systems, Man and Cybernetics, 26, 52–67.

    Article  Google Scholar 

  • Bloch I. and Maitre H. (1997). Fusion of image information under imprecision, Aggregation and Fusion of Imperfect Information (Bouchon-Meunier B., Ed.) Physica-Verlag, Heidelberg, Germany, 141–161.

    Google Scholar 

  • Bloch I., Sureda F., Pellot C. and Herment A. (1997). Fuzzy modelling and fuzzy mathematical morphology applied to 3D reconstruction of blood vessels by multimodality data fusion, Fuzzy Information Engineering (Dubois D., Prade H. and Yager R.R., eds.), John Wiley, New York, 93–110.

    Google Scholar 

  • Boldrin L. (1995). A substructural connective for possibilistic logic, Symbolic and Quantitative Approaches to Reasoning and Uncertainty (Proc. of Europ. Conf. ECSQARU’95) (Froidevaux C. and Kohlas J., eds.), Springer Verlag, Fribourg, 60–68.

    Chapter  Google Scholar 

  • Boldrin L. and Sossai C. (1995). An algebraic semantics for possibilistic logic, Proc of the 11th Conf. Uncertainty in Artifucial Intelligence (Besnard P. and Hank S., eds.) Morgan Kaufmann, San Francisco, CA, 27–35.

    Google Scholar 

  • Bouchon-Meunier B., Ed. (1997). Aggregation and Fusion of Imperfect Information, Physica-Verlag, Heidelberg, Germany.

    MATH  Google Scholar 

  • Bouchon-Meunier, B., Dubois, D., Godo L. and Prade H. (1999) Fuzzy sets and possibility theory in approximate and plausible reasoning. Chapter 1, this volume.

    Google Scholar 

  • Buchanan B. G. and Shortliffe E. H. (1984). Rule-Based Expert Systems — The MYCIN Experiments of the Stanford Heuristic Programming Project, Addison-Wesley, Reading.

    Google Scholar 

  • Brown C., Durrant-Whyte H., Rao L. B. and Steer B. (1992). Distributed data fusion using Kaiman filtering: a robotics application, Data Fusion in Robotics and Machine Intelligence (Abidi M.A. and Gonzalez R.C., eds.). Academic Press, New York, 267–310.

    Google Scholar 

  • Cheng Y. Z. and Kashyap R. L. (1989). A study of associative evidential reasoning, IEEE Trans. on Pattern Analysis and Machine Intelligence, 11(6), 623–631.

    Article  MATH  Google Scholar 

  • Cholvy L. (1993). Proving theorems in a multi-source environment, Proc. of the 13th Inter. Joint Conf. on Artificial Intelligence (IJCAI’93), Chambéry, France, Aug. 28-Sept. 3, 66–71.

    Google Scholar 

  • Cholvy L. (1998). Reasoning about merged information, Belief Change (Dubois D. and Prade H., Eds), Vol. 3 in the Handbook of Defeasible Reasoning and Uncertainty Management Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 233–265.

    Chapter  Google Scholar 

  • Cooke R. M. (1988). Uncertainty in risk assessment: A probabilist’s manifesto, Reliability Engineering and Systems Safety, 23, 277–283.

    Article  Google Scholar 

  • Cooke R. M. (1991). Experts in Uncertainty, Oxford University Press, Oxford, UK.

    Google Scholar 

  • Coolen F. P. A. (1994). Statistical Modeling of Expert Opinions Using Imprecise Probabilities, PhD Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.

    MATH  Google Scholar 

  • Czogala E. and Hirota K. (1986). Probabilistic Sets: Fuzzy and Stochastic Approach to Decision, Control and Recognition Processes, ISR 91, Verlag TÜV Rheinland, Köln, Germany.

    MATH  Google Scholar 

  • De Cooman G. (1997). Possibility theory — Part I: Measure-and integral-theoretics groundwork; Part II: Conditional possibility; Part III: Possibilistic independence, Int. J. of General Systems, 25(4), 291–371.

    Article  MATH  Google Scholar 

  • De Kleer J. (1986). An assumption-based TMS, Artificial Intelligence, 28, 127–162.

    Article  Google Scholar 

  • Delmotte F. and Borne P. (1998). Modeling of reliability with possibility theory, IEEE Trans. On Systems Man & Cybern.A, 28, 78–88.

    Article  Google Scholar 

  • Delplanque M., Desodt-Jolly A. M., Jolly D. and Jamin J. (1997). Fusion dissymétrique d’informations incomplètes pour la classification d’objets sousmarins, Traitement du Signal, 14, 511–522.

    MATH  Google Scholar 

  • Deveughèle S. and Dubuisson B. (1993). Using possibility theory in perception: An application in artificial vision, Proc. of the 2nd IEEE Inter. Conf. on Fuzzy Systems (FUZZ-IEEE’93), San Francisco, CA, March 28-April 1st, 821–826.

    Google Scholar 

  • Deveughèle S. and Dubuisson B. (1995). Adaptive aggregation: decomposing before combining, Proc. of the 4th IEEE Inter. Conf. on Fuzzy Systems (FUZZ-IEEE’95), Yokohama, Japan, 1589–1596.

    Google Scholar 

  • Domotor Z. (1985). Probability kinematics, conditionals and entropy principle, Synthèse, 63, 75–114.

    Article  MathSciNet  Google Scholar 

  • Dubois D. (1986). Generalized probabilistic independence, and its implications for utility, Operations Research Letters, 5, 255–260.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D., Fargier H. and Prade H. (1996) Possibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty, Applied Intelligence, 6, 287–309.

    Article  Google Scholar 

  • Dubois D., Fodor J., Prade H. and Roubens M. (1996). Aggregation of decomposable measures with application to utility theory, Theory and Decision, 41, 59–95.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D. and Kalfsbeek H. W. (1990). Elicitation, assessment and pooling of expert judgments using possibility theory, Proc. of the 8th Inter. Congress of Cybernetics and Systems (Manikopoulos C.N., Ed.), New York, June 11-15, 360–367. Published by New Jersey Institute of Technology Press.

    Google Scholar 

  • Dubois, D., Kerre E., Mesiar R. and Prade H. (1999). Fuzzy intervals, Fundamentals of Fuzzy Sets, The Handbook of Fuzzy Sets Series, Kluwer Academic Publ., Dordrecht, to appear.

    Google Scholar 

  • Dubois D., Nguyen H.T. and Prade H. (1999). Possibility theory, probability and fuzzy sets: Misunderstandings, bridges and gaps. Fundamentals of Fuzzy Sets, The Handbook of Fuzzy Sets Series, Kluwer Academic Publ., Dordrecht, to appear.

    Google Scholar 

  • Dubois D. and Koning J.L. (1991). Social choice axioms for fuzzy set aggregation, Fuzzy Sets and Systems, 49(3), 257–274.

    Article  MathSciNet  Google Scholar 

  • Dubois D., Lang J. and Prade H. (1992). Dealing with multi-source information in possibilistic logic, Proc. of the 10th Europ. Conf. on Artificial Intelligence (ECAI’92) (B. Neumann, Ed.), Vienna, Austria, Aug. 3–7, 1992, 38–42. Wiley, New York.

    Google Scholar 

  • Dubois D., Lang J. and Prade H. (1994a). Automated reasoning using possibilistic logic: Semantics, belief revision and variable certainty weights, IEEE Trans. on Knowledge and Data Engineering, 6(1), 64–71.

    Article  Google Scholar 

  • Dubois D., Lang J. and Prade H. (1994b). Possibilistic logic, Handbook of Logic in Artificial Intelligence and Logic Programming — Vol 3: Nonmonotonic Reasoning and Uncertain Reasoning (Gabbay D.M., Hogger C.J., Robinson J.A. and Nute D., eds.), Oxford Univ. Press, 439–513.

    Google Scholar 

  • Dubois D., Moral S. and Prade H. (1997). A semantics for possibility theory based on likelihoods, J. of Mathematical Analysis and Applications, 205, 359–380.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D., Moral S. and Prade H. (1998). Belief change rules in ordinal and numerical uncertainty theories, Belief Change (Dubois D. and Prade H., Eds), Vol. 3 in the Handbook of Defeasible Reasoning and Uncertainty Management Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 311–392.

    Chapter  Google Scholar 

  • Dubois D. and Prade H. (1980). Fuzzy Sets and Systems — Theory and Applications, Academic Press, New York.

    MATH  Google Scholar 

  • Dubois D. and Prade H. (1981). Additions of interactive fuzzy numbers, IEEE Trans. on Automatic Control, 26, 926–936

    Article  MathSciNet  Google Scholar 

  • Dubois D. and Prade H. (1985). A review of fuzzy set aggregation connectives, Information Sciences, 36, pp. 85–121.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D. and Prade H. (1986). Weighted minimum and maximum operations in fuzzy set theory, Information Sciences, 39, 205–210.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D. and Prade H. (1987a). Fuzzy Numbers: An Overview, Analysis of Fuzzy Information, Vol. I (Bezdek J., Ed.), CRC Press, Boca Raton, FL, 3–39.

    Google Scholar 

  • Dubois D. and Prade H. (1987b). The mean value of a fuzzy number, Fuzzy Sets and Systems, 24, 279–300.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D. and Prade H. (1987c). Une approche ensembliste de 1a combination d’informations incertaines, Revue d’Intelligence Artificielle, 1(4), 23–42.

    Google Scholar 

  • Dubois D. and Prade H. (1988a). Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, 4, 244–264.

    Article  Google Scholar 

  • Dubois D. and Prade H. (1988b). Possibility Theory — An Approach to the Computerized Processing of Uncertainty, Plenum Press, New York.

    MATH  Google Scholar 

  • Dubois D. and Prade H. (1988c). Default reasoning and possibility theory, Artificial Intelligence, 35, 243–257.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D. and Prade H. (1988d). On the combination of uncertain or imprecise pieces of information in rule-based systems — A discussion in the framework of possibility theory, Int. J. of Approximate Reasoning, 2, 65–87.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D. and Prade H. (1989a), Order-of-magnitude reasoning with fuzzy relations, Revue d—Intelligence Artificielle, 3, 69–94.

    Google Scholar 

  • Dubois D. and Prade H. (1989b). Fuzzy sets, probability and measurement, Europ. J. of Operations Research, 40, 135–154.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D. and Prade H. (1990). Aggregation of possibility measures, Multiperson Decision Making using Fuzzy Sets and Possibility Theory (Kacprzyk J. and Fedrizzi M., eds.), Kluwer, Dordrecht, 55–63.

    Chapter  Google Scholar 

  • Dubois D. and Prade H. (1991). Updating with belief functions, ordinal conditional functions and possibility measures, Uncertainty in Artificial Intelligence 6 (Bonissone P.P., Henrion M., Kanal L.N. Lemmer J.F., eds.), North-Holland, Amsterdam, 311–329.

    Google Scholar 

  • Dubois D. and Prade H. (1992a). On the relevance of non-standard theories of uncertainty in modeling and pooling expert opinions, Reliability Engineering and Systems Safety, 36, 95–107.

    Article  Google Scholar 

  • Dubois D. and Prade H. (1992b). Combination of fuzzy information in the framework of possibility theory, Data Fusion in Robotics and Machine Intelligence (Abidi M.A. and Gonzalez R.C., eds.), 481–505. Academic Press, New York.

    Google Scholar 

  • Dubois D. and Prade H. (1992c). When upper probabilities are possibility measures, Fuzzy Sets and Systems, 49, 65–74.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D. and Prade H. (1992d). On the combination of evidence in various mathematical frameworks, Reliability Data Collection and analysis (Flamm J. and Luisi T., eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 213–242.

    Chapter  Google Scholar 

  • Dubois D. and Prade H. (1992e). Belief change and possibility theory, Belief Revision (Gärdenfors P., ed.), Cambridge University Press, Cambridge, UK, 142–182.

    Chapter  Google Scholar 

  • Dubois D. and Prade H. (1994). Possibility theory and data fusion in poorly informed environments, Control Engineering Practice, 2(5), 811–823.

    Article  Google Scholar 

  • Dubois D. and Prade H. (1997). A synthetic view of belief revision with uncertain inputs in the framework of possibility theory, Int. J. of Approximate Reasoning, 17(2/3), 295–324

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D. and Prade H. (1998). Possibility theory: qualitative and quantitative aspects, Handbook on Defeasible Reasoning and Uncertainty Management Systems — Volume 1: Quantified Representation of Uncertainty and Imprecision. (Smets P., ed.) Kluwer Academic Publ., Dordrecht, The Netherlands, 1997.

    Google Scholar 

  • Dubois D., Prade H. and Nguyen H. T. (1999). Possibility theory, probability and fuzzy sets: Misunderstandings, bridges and gaps, Fundamentals of Fuzzy Sets (Dubois D. and Prade H., eds.), The Handbook of Fuzzy Sets Series, Kluwer Academic Publ., Dordrecht, to appear.

    Google Scholar 

  • Dubois D., Prade H. and Sandri S. (1993). On possibility/probability transformations, Fuzzy Logic: State of the Art (Lowen R. and Lowen M., eds.), Kluwer Academic Publ., 103–112.

    Google Scholar 

  • Dubois D., Prade H. and Testemale C. (1988). Weighted fuzzy pattern matching, Fuzzy Sets and Systems, 28, 313–331.

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D., Prade H. and Yager R. R. (1998). Computation of intelligent fusion operations based on constrained fuzzy arithmetics, Proc IEEE Int. Conf. on Fuzzy Systems, Anchorage, Alaska, 767–772.

    Google Scholar 

  • Dubois D. and Yager R. R. (1992). Fuzzy set connectives as combinations of belief structures, Information Sciences, 66, 245–275.

    Article  MathSciNet  MATH  Google Scholar 

  • Edwards W. F. (1972). Likelihood, Cambridge University Press, Cambridge, U.K.

    MATH  Google Scholar 

  • Fodor J. and Yager R. (1999). Fuzzy set-theoretic operators and quantifiers, Fundamentals of Fuzzy Sets (Dubois D. and Prade H., eds.), The Handbook of Fuzzy Sets Series, Kluwer Academic Publ., Dordrecht, to appear.

    Google Scholar 

  • Fortemps P. and Roubens M. (1996). Ranking and defuzzification methods based on area compensation, Fuzzy Sets and Systems, 82, 319–330.

    Article  MathSciNet  MATH  Google Scholar 

  • French S. (1985). Group consensus probability distributions: a critical survey, Bayesian Statistics (Bernardo J. et al., Eds), Elsevier, The Netherlands, 183–201.

    Google Scholar 

  • Fukuda T., Shimojida K., Fumihito A. and Matsuura H. (1993). Multisensor integration systems based on fuzzy inference and neural network, Information Sciences, 71, 27–41

    Article  Google Scholar 

  • Gebhardt J. and Kruse R. (1998). Parallel combination of information sources, Belief Change (Dubois D. and Prade H., Eds), Vol. 3 in the Handbook of Defeasible Reasoning and Uncertainty Management Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 393–440.

    Chapter  Google Scholar 

  • Goodman I. R. (1982), Fuzzy sets as equivalence classes of random sets, Fuzzy Sets and Possibility Theory (Yager R., ed.), Pergamon Press, Oxford, 327–342.

    Google Scholar 

  • Grabisch M., Murofushi T. and Sugeno M. (1992). Fuzzy measure of fuzzy events defined by fuzzy integrals, Fuzzy Sets and Systems, 50, 293–313.

    Article  MathSciNet  MATH  Google Scholar 

  • Grabisch M., Orlovski S. and Yager R. R. (1998). Fuzzy aggregations of numerical preferences, Fuzzy Sets in Decision Analysis, Operations Research and Statistics, (Slowinski R., Ed.), The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, The Netherlands, 31–68.

    Chapter  Google Scholar 

  • Hajek P. (1985). Combining functions for certainty degrees in consulting systems, Int. J. of Man-Machine Studies, 22, 59–76.

    Article  MATH  Google Scholar 

  • Hirota K. (1981). Concepts of probabilistic sets, Fuzzy Sets and Systems, 5, 31–46.

    Article  MathSciNet  MATH  Google Scholar 

  • Hirota K., Pedrycz W. and Yuda M. (1991). Fuzzy set-based models of sensor fusion, Proc. International Fuzzy Engineering Symposium, Yokohama, Japan, World Scientific, Singapore, 623–633.

    Google Scholar 

  • Hisdal E. (1978). Conditional possibilities — Independence and non-interactivity, Fuzzy Sets and Systems, 1, 283–297.

    Article  MATH  Google Scholar 

  • Jeffrey R. (1965). The Logic of Decision, McGraw-Hill, New York.

    Google Scholar 

  • Kacprzyk J. and Nurmi H. (1998). Group decision-making under fuzziness, Fuzzy Sets in Decision Analysis, Operations Research and Statistics, (Slowinski R., Ed.), The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, The Netherlands, 103–136.

    Chapter  Google Scholar 

  • Kalfsbeek H. (1989), Elicitation, assessment and pooling of expert judgment using possibility theory, Working Paper PERI 829/89 (revised version), Joint Research Center of the EEC, Ispra, Italy.

    Google Scholar 

  • Kaufmann A. (1988). Theory of expertons and fuzzy logic. Fuzzy Sets and Systems, 28, 295–304.

    Article  MathSciNet  MATH  Google Scholar 

  • Klir G. J. and Folger T. (1988). Fuzzy Sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, NJ.

    MATH  Google Scholar 

  • Kosko B. (1986a). Fuzzy knowkedge combination, Int. J. Intelligent Systems, 1, 293–330.

    Article  MATH  Google Scholar 

  • Kosko B. (1986b). Fuzzy entropy and conditioning, Information Sciences, 40, 165–174.

    Article  MathSciNet  MATH  Google Scholar 

  • Kuncheva L. and Krishnapuram R. (1996). A fuzzy consensus operator, Fuzzy Sets and Systems, 79, 347–356.

    Article  MathSciNet  Google Scholar 

  • Lasserre V., Mauris G. and Foulloy L. (1998). A simple modelisation of measurement uncertainty: the truncated triangular possibility distribution, Proc 7th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU’98), Paris, Editions Medicales et Scientifiques, 10–17.

    Google Scholar 

  • Lopez-Sanchez M., Lopez de Mantaras R. and Sierra C. Incremental map generation by low-cost robots based on possibility/necessity grids, Proc of the 13th Conf. Uncertainty in Artificial Intelligence (Geiger D. and Shenoy P., eds.), Morgan Kaufmann, San Francisco, CA, 351–357.

    Google Scholar 

  • Lotan T. (1997). Integration of fuzzy numbers corresponding to static knowledge and dynamic information, Fuzzy Sets and Systems, 86, 335–344

    Article  MathSciNet  Google Scholar 

  • Mahler R. P. (1995). Comining ambiguous evidence with respect to ambiguous a priori knowledge — Part II: Fuzzy Logic, Fuzzy Sets and Systems, 75, 319–354.

    Article  MathSciNet  MATH  Google Scholar 

  • Marichal J. L. (1998). On Sugeno integral as an aggregation function, Tech. Rep. 9710, GEMME, Fac. d’Ecomomie, Université de Liège, Belgium. Proceedings of EUFIT’98 (Vol. I), Aachen, Germany, September 7-10,. 540–544

    Google Scholar 

  • Mauris G., Benoit E. and Foulloy L. Fuzzy linguistic methods for the aggregation of complementary sensor information, Aggregation and Fusion of Imperfect Information (Bouchon-Meunier B., Ed.) Physica-Verlag, Heidelberg, Germany, 214–230.

    Google Scholar 

  • Meizel D. and Piat E. (1997). Proposition d’un cadre probabiliste de fusion de croyances, Traitement du Signal, 14, 485–498.

    MATH  Google Scholar 

  • Mosleh A. and Apostolakis G. (1984). Models for the use of expert opinions, Low Probability/ High Consequence Risk Analysis (Waller R.A. and Covello V. T., Eds.). Plenum Press, New York.

    Google Scholar 

  • Mundici D. (1992). The logic of Ulam games with lies, Knowledge, Belief and Strategic Interaction (Bicchieri C. and Dalla Chiara M., eds.), Cambridge University Press, 275–284.

    Google Scholar 

  • Nifle A. and Reynaud R. (1997). Classification de comportements fondée sur l’occurrence d’événements en théorie des possibilités, Traitement du Signal, 14, 523–534.

    MATH  Google Scholar 

  • Novak V. (1999). Weighted inference systems. Chapter 2 in this volume.

    Google Scholar 

  • Ovchinnikov S. (1998). An analytic characterization of some aggregation operators, Int. J. Intell. Systems, 13, 3–10.

    Article  MathSciNet  Google Scholar 

  • Pannerec T., Oussalah M., Maaref H. and Barret. C. (1998). Absolute localization of a miniature mobile robot using heterogeneous sensors: comparison between Kaiman filter and possibility theory method, Proc. IEEE Symposium on Robotics and Cybernetics, CESA’98, Tunis.

    Google Scholar 

  • Park S. and Lee C. S. G. (1993). Uncertainty fusion of sensory information using fuzzy numbers, Proc. 5th IFSA Congress, Seoul, Korea, 1001–1004.

    Google Scholar 

  • Parratt L. G. (1961). Probability and Experimental Errors in Science, Dover, New York.

    MATH  Google Scholar 

  • Poloni M. (1994). Sensor data fusion using fuzzy decision-making techniques, Proc 2d Europ. Congress on Intelligent Techniques and Soft Computing. (EUFIT’94), Aachen, Germany, 35–41.

    Google Scholar 

  • Poloni M., Ulivi G. and Vendittelli M. (1995). Fuzzy logic and autonomous vehicles: Experiments in data fusion, Fuzzy Sets and Systems, 69, 15–27.

    Article  MATH  Google Scholar 

  • Poole D. L. (1985). On the comparison of theories: preferring the most specific explanation, Proc. 9th Int. Joint Conf. on Artificial Intelligence, Los Angeles, 465–474.

    Google Scholar 

  • Prade H. (1985). Reasoning with fuzzy default values, Proc. of the 5th Inter. Symp. on Multiple-Valued Logic, Kingston, Ont., May 28-30, 191–197.

    Google Scholar 

  • Rescher N. and Manor R. (1970). On inference from inconsistent premises, Theory and Decision, 1, 179–219.

    Article  MATH  Google Scholar 

  • Roux L. and Desachy J. (1997). Multisources information fusion application for satellite image classification, Fuzzy Information Engineering (Dubois D., Prade H. and Yager R.R., eds.), John Wiley, New York, 111–121.

    Google Scholar 

  • Sandri S. (1991). La combinaison de l’information incertaine et ses aspects algorithmiques, Thèse de Doctorat de l’Université Paul Sabatier, Toulouse, France.

    Google Scholar 

  • Sandri S., Besi A., Dubois D., Mancini G., Prade H. and Testemale C. (1989). Data fusion problems in an intelligent data base interface, Reliability Data Collection and Use in Risk and Availability Assessment (Colombari U., Ed.), 655–670. Springer Verlag, Berlin.

    Chapter  Google Scholar 

  • Sandri S., Dubois D. and Kalfsbeek H. (1995). Elicitation, assessment and pooling of expert judgement using possibility theory, IEEE Trans. on Fuzzy Systems, 3, 313–335

    Article  Google Scholar 

  • Schweizer B. and Sklar A. (1983). Probabilistic Metric Spaces, North-Holland, New York.

    MATH  Google Scholar 

  • Shafer G. (1976). A Mathematical Theory of Evidence, Princeton Univ. Press, Princeton, NJ.

    MATH  Google Scholar 

  • Shafer G. (1978). Non-additive probabilities in the works of Bernoulli and Lambert, Archives for the History of Exact Sciences, 19, 309–370

    Article  MathSciNet  MATH  Google Scholar 

  • Shafer G. (1986). The combination of evidence, Int. J. Intelligent Systems, 1, 155–179.

    Article  MathSciNet  MATH  Google Scholar 

  • Silvert W. (1979). Symmetric summation: A class of operations on fuzzy sets, IEEE Trans. on Systems, Man and Cybernetics, 9(10), 657–659.

    Article  MathSciNet  MATH  Google Scholar 

  • Smets P. (1982). Possibilistic inference from statistical data, Proc. of the 2nd World Conf. on Math. at the Service of Man, Las Palmas, Spain, June 28-July 3, 611–613

    Google Scholar 

  • Smets P. (1988). Belief functions, Non-Standard Logics for Automated Reasoning (Smets P., Mamdani A., Dubois D. and Prade H., eds.), Academic Press, London, 253–286.

    Google Scholar 

  • Spohn W. (1988). Ordinal conditional functions: A dynamic theory of epistemic states, Causation in Decision, Belief Change, and Statistics, Vol. 2 (Harper W.L. and Skyrms B., eds.), D. Reidel, Dordrecht, 105–134.

    Chapter  Google Scholar 

  • Sugeno M. (1974). Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokyo Inst. of Technology.

    Google Scholar 

  • Sugeno, M. (1977). Fuzzy measures and fuzzy integrals — A survey, Fuzzy Automata and Decision Processes (Gupta M.M., Saridis G.N. and BGaines B.R., eds.), North-Holland, Amsterdam, 89–102.

    Google Scholar 

  • Tahani H. and Keller J. (1990). Information fusion in computer vision using fuzzy integrals, IEEE Trans. on Systems, Man and Cybernetics, 20, 733–741.

    Article  Google Scholar 

  • Tang Y. C. and Lee C. S.G (1992). Optimal strategic recognition of objects based on candidate discriminating graphs with coordinated sensors, IEEE Trans. on Systems, Man and Cybernetics, 22, 647–661.

    Article  Google Scholar 

  • Wagner C. and Lehrer K. (1981). Rational Consensus in Science and Society, D. Reidel, Dordrecht.

    MATH  Google Scholar 

  • Williams M. A. (1994). Transmutations of knowledge systems, Proc. of the 4th Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’94) (Doyle J., Sandewall E. and Torasso P., eds.), Bonn, Germany, May 24-27, 1994, Morgan & Kaufmann, San Mateo, CA, 619–629.

    Google Scholar 

  • Wu J. S., Apostolakis G. E. and Okrent D. (1990). Uncertainties in system analysis: probabilistic versus nonprobabilistic theories, Reliability Engineering and Systems Safety, 30, 163–181.

    Article  Google Scholar 

  • Yager R. R. (1981a). A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24, 143–161

    Article  MathSciNet  MATH  Google Scholar 

  • Yager R. R. (1981b). A new methodology for ordinal multiobjective decisions based on fuzzy sets, Decision Sciences, 12, 589–600

    Article  MathSciNet  Google Scholar 

  • Yager R. R. (1984). Approximate reasoning as a basis for rule-based expert systems, IEEE Trans. on Systems, Man and Cybernetics, 14, 636–643.

    Article  MathSciNet  MATH  Google Scholar 

  • Yager R. R. (1985). Aggregating evidence using quantified statements, Information Sciences, 36, 179–206.

    Article  MathSciNet  MATH  Google Scholar 

  • Yager R. R. (1987). Quasi-associative operations in the combination of evidence, Kybernetes, 16, 37–41.

    Article  MathSciNet  MATH  Google Scholar 

  • Yager R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. on Systems, Man and Cybernetics, 18, 183–190.

    Article  MathSciNet  MATH  Google Scholar 

  • Yager R. R. (1991). Non-monotonic set-theoretic operators, Fuzzy Sets and Systems, 42, 173–190.

    Article  MathSciNet  MATH  Google Scholar 

  • Yager R. R. (1992). On the specificity of a possibility distribution, Fuzzy Sets and Systems, 50, 279–292.

    Article  MathSciNet  MATH  Google Scholar 

  • Yager R. R. (1997). A general approach to the fusion of imprecise information, Int. J. of Intelligent Systems, 12, 1–29.

    Article  MATH  Google Scholar 

  • Yager R. R. and Filev D.P. (1994). Essentials of Fuzzy Modeling and Control, John Wiley, New York.

    Google Scholar 

  • Yager R. R. and Kelman A. (1996). Fusion of fuzzy information with considerations for compatibility, partial aggregation and reinforcement, Int. J. of Approximate Reasoning, 15, 93–122

    Article  MathSciNet  MATH  Google Scholar 

  • Yan B. and Keller J. (1996). A heuristic, simulated annealing algorithm of learning possibility measures for multisource decision-making, Fuzzy Sets and Systems, 77, 87–109

    Article  Google Scholar 

  • Yang M. S. and Liu M. C. (1998), On possibility analysis of fuzzy data, Fuzzy Sets and Systems, 94, 171–183.

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh L. A. (1965). Fuzzy sets, Information and Control, 8, 338–353.

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh L. A. (1971). Similarity relations and fuzzy orderings, Information Sciences, 3, 177–200.

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh L. A. (1978). Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3–28.

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh L. A. (1984). Review of “A Mathematical Theory of Evidence” (G. Shafer), The AI Magazine, 5(3), 81–83

    Google Scholar 

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Authors and Affiliations

  1. Institut de Recherche en Informatique de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 4, France

    Didier Dubois & Henri Prade

  2. Machine Intelligence Institute, Iona College, New Rochelle, NY, 10801, USA

    Ronald Yager

Authors
  1. Didier Dubois
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  2. Henri Prade
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  3. Ronald Yager
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Editors and Affiliations

  1. University of West Florida, USA

    James C. Bezdek

  2. IRIT, CNRS & University of Toulouse III, France

    Didier Dubois  & Henri Prade  & 

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Dubois, D., Prade, H., Yager, R. (1999). Merging Fuzzy Information. In: Bezdek, J.C., Dubois, D., Prade, H. (eds) Fuzzy Sets in Approximate Reasoning and Information Systems. The Handbooks of Fuzzy Sets Series, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5243-7_7

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