Abstract
Possibility theory was coined by L.A. Zadeh in the late seventies as an approach to model flexible restrictions constructed from vague pieces of information, described by means of fuzzy sets. Possibility theory is also a basic non-classical theory of uncertainty, different from but related to probability theory. This chapter discusses the basic elements of the theory: possibility and necessity measures (as well as two other set functions associated with a possibility distribution), the minimal specificity principle which underlies the whole theory, the notions of possibilitic conditioning and possibilistic independence, the combination, and projection of joint possibility distributions, as well as the possibilistic counterparts to integration. The relations and differences between this approach and other uncertainty frameworks, and especially probability theory, are pointed out. The difference between probability theory and fuzzy set theory is thus tentatively clarified. Lastly, decision-theoretic justifications of possibility theory are given.
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References
Agbeko K. (1991). Optimal average, Ann, Univ. Sci. Budapest, Sect Comp., 16, 5–10 (Full version: Report 73/1990, Mathematical Institute, Hungarian Academy of Sciences, Budapest).
Akian M., Quadrat J.P. and Viot M. (1994). Bellman processes, Proc. 11th Conf. on Analysis and Optimization of Systems, L.N. in Control and Inf. Sci. n°199, Springer Verlag.
Akian M., Quadrat J.P. and Viot M. (1996). Duality between probability and optimization, Idempotency, (Gunawardena J., ed.), Cambridge University Press
Anger B. (1977). Representation of capacities, Math, Annalen, 229, 245–258.
Banon G. (1995). Constructive decomposition of fuzzy measures in terms of possibility and necessity measures, Proc. 6th IFSA World Congress, Sao Paulo, 217–220.
Banon G. and Barrera J. (1993). Decomposition of mappings between complete lattices by mathematical morphology, Signal Processing, 30, 299–327.
Barnett V. (1973). Comparative Statistical Inference, J. Wiley, New York
Bellman R.E. and Giertz M. (1973). On the analytic formalism of the theory of fuzzy sets, Information Sciences, 5, 149–157.
Bellman R.E. and Zadeh L.A. (1970). Decision making in a fuzzy environment, Management Science, 17, B141–B164.
Benferhat S., Dubois D. and Prade H. (1997a), Nonmonotonic reasoning, conditional objects and possibility theory, Artificial Intelligence, 92, 259–276.
Benferhat S., Dubois D. and Prade H. (1997b), Possibilistic and standard probabilistic semantics of conditional knowledge, Proc. of the 14th National Conf on Artificial Intelligence (AAAI’97), 70–75. Extended version to appear in J. Logic & Comput.
Benferhat S., Dubois D. and Prade H. (1998). Practical handling of exception-tainted rules and independence information in possibilistic logic, Applied Intelligence, 9, 101–127.
Bennett B.M., Hoffman D.D. and Murthy P. (1992). Lebesgue order on probabilities and some applications to perception, J. of Mathematical Psychology.
Berstein L.S., Bronevitch A.G., Karkishchenko A.N. and Zakharevitch V.G. (1996). Statistical classes and possibilistic models of classifying probability distributions, BUSEFAL, 65, 19–26.
Bezdek J.C. (Ed.) (1994). Special issue: Fuzziness v. probability-the n-th round, IEEE Trans, on Fuzzy Systems, 2, 1–42.
Bezdek J.G., Dubois D., and Prade H. (Eds.) (1999). Fuzzy Sets in Approximate Reasoning and Information Systems. The Handbooks of Fuzzy Sets Series (Dubois D. and Prade H., eds.), Kluwer Acad. Publ., Boston.
Biacino L. and Gerla G. (1992). Generated necessities and possibilities, Int. J. Intelligent Systems, 7, 445–454.
Bilgic T. and Türksen I.B. (1999). Measurement of membership functions: Theoretical and empirical work, Fundamentals of Fuzzy Sets (Dubois D. and Prade H. eds,), Kluwer Acad. Pub!., 1999. This volume.
Blockley D.I. (1985). Fuzziness and probability: A discussion of Gaines’ axioms, Civ. Engng Syst., 2, 195–200.
Bouchon-Meunier B., Dubois D., Godo L. and Prade H. (1999). Fuzzy sets and possibility theory in approximate and plausible reasoning, Fuzzy Sets in Approximate Reasoning and Information Systems (Bezdek J.C., Dubois D. and Prade H., eds.), The Handbooks of Fuzzy Sets Series, Kluwer Academic Publ., Boston, 15–190.
Boutilier C. (1994). Modal logics for qualitative possibility theory, Int. J. Approximate Reasoning, 10, 173–201.
Cayrol M., Farreny H. and Prade H. (1982). Fuzzy pattern matching, Kybernetes, 11, 103–116.
Ghanas S. and Nowakowski M. (1988). Single value simulation of fuzzy variable. Fuzzy Sets and Systems, 25, 43–57.
Cheeseman P. (1988). Probabilistic versus fuzzy reasoning, Uncertainty in Artificial Intelligence I (Kanal L. and Lemmer J., Eds.), North-Holland, Amsterdam, 85–102.
Choquet G. (1953). Theory of capacities, Ann. hist. Fourier (Grenoble), 5, 131–295.
Civanlar M.R. and Trussell HJ. (1986). Constructing membership functions using statistical data. Fuzzy Sets and Systems, 18, 1–13.
Cooke R. (1990). Experts in Uncertainty, Oxford University Press, Oxford.
Darwiche A. and Pearl J. (1997). On the logic of iterated revision, Artificial Intelligence, 89, 1–29.
De Baets B., De Cooman G. and Kerre E. (1998). The construction of possibility measures from samples on T-semi-partitions, Information Sciences, 106, 3–24.
De Baets B., Tsiporkova E. and Mesiar R. (1999). Conditioning in possibility with strict order norms, Fuzzy Sets and Systems, 106, 221–229.
De Campos L.M. (1995). Independence relationships in possibility theory and their application to learning belief networks, Mathematical end Statistical Methods in Artificial Intelligence (Delia Riccia R., Kruse R. and Viertl R., Eds.), CISM Courses and Lectures Vol. 363, Springer Verlag, Berlin, 119–130.
De Campos L.M., Gebhardt J. and Kruse R. (1995). Axiomatic treatment of possibilistic independence, Symbolic and Quantitative Approaches to Reasoning and Uncertainty (Froidevaux C. and Kohlas J.,, Lecture Notes in AI Vol. 946, Springer Verlag, 77–88.
De Campos L.M. and Huete J.F. (1999), Independence concepts in possibility theory, Part I: Fuzzy Sets and Systems, 103, 127–152; Part II: Fuzzy Sets and Systems.
De Campos L.M., Lamata M.T. and Moral S. (1990). The concept of conditional fuzzy measure, Int. J. of Intelligent Systems, 5, 237–246.
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.
De Cooman G. and Aeyels D. (1996). On the coherence of supremum preserving upper previsions, Proc. of the 6th Inter. Conf Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU’96), Granada, 1405–1410. Extended version to appear in Information Sciences.
De Cooman G. and Kerre E. (1996). Possibility and necessity integrals, Fuzzy Sets and Systems, 77, 207–229.
De Cooman G., Kerre E. and Vanmassenhove F.R. (1992). Possibility theory and integral-theoretic approach, Fuzzy Sets and Systems, 46, 287–300.
De Cooman G., Ruan D. and Kerre E.E. (Eds.) (1995). Foundations & Applications of Possibility Theory (Proceedings of the FAPT’95, Ghent, Belgium, Dec. 13–15, 1995), World Scientific, Singapore.
De Finetti B. (1974). Theory of Probability — A Critical Introductory Treatment — Vol. 1, John Wiley & Sons, Chichester, UK.
De Finetti B. (1975). Theory of Probability — A Critical Introductory Treatment — Vol. 2, John Wiley & Sons, Chichester, UK.
De lgado M. and Moral S. (1987). On the concept of possibility-probability consistency, Fuzzy Sets and Systems, 21, 311–318.
Dellacherie C. (1971). Quelques commentaires sur les prolongements de capacités, Séminaire de Probabilité (1969/70), Lecture Notes in Mathematics Vol. 191, Springer Verlag, Berlin, 77–81.
De mpster A.P. (1967). Upper and lower probabilities induced by a multivalued-mapping, Ann. Math. Statist, 38, 325–339.
Denneberg D. (1994). Non-Additive Measure and Integral, Kluwer Academic Publ., Dordrecht.
Diamond P. and Tanaka H. (1998). Fuzzy regression analysis, Fuzzy Sets in Decision Analysis, Operations Research and Statistics (Slowinski R., ed.), The Handbooks of Fuzzy Sets Series, Kluwer Academic Publ., Boston, 349–387.
Drakopoulos J.A. (1995). Probabilities, possibilities and fuzzy sets, Fuzzy Sets and Systems, 75, 1–15.
Dubois D. (1986). Belief structures, possibility theory and decomposable confidence measures on finite sets, Computers and Artificial Intelligence (Bratislava), 5, 403–416.
Dubois D., Fargier H., Fortemps P. and Prade H. (1997). Leximin optimality and fuzzy set-theoretic operations, Proc. of the 7th World Congress of the Inter, Fuzzy Systems Assoc. (IFSA’97), Prague.
Dubois D., Fargier H. and Prade H. (1994). Propagation and satisfaction of flexible constraints, Fuzzy Sets, Neural Networks and Soft Computing (Yager R.R. and Zadeh L.A., Eds.), Van Nostrand Reinhold, New York, 166–187.
Dubois D., Fargier H. and Prade H. (1995). Fuzzy constraints in job-shop scheduling, J. of Intelligent Manufacturing, 6, 215–234.
Dubois D., Fargier H. and Prade H. (1996a). Refinements of the maximin approach to decision-making in fuzzy environment, Fuzzy Sets and Systems, 81, 103–122.
Dubois D., Fargier H; and Prade H. (1996b). Possibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty, Applied Intelligence, 6, 287–309.
Dubois D., Fargier H. and Prade H. (1998). Possibilistic likelihood relations, Proc. of the 7th Inter. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU’98), Paris, 1196–1203.
Dubois D., Farinas del Cerro L., Herzig A. and Prade H. (1994). An ordinal view of independence with application to plausible reasoning, Proc. of the 10th Conf on Uncertainty in Artificial Intelligence (Lopez de Mantaras R. and Poole D., eds.), Seattle, WA, July 29–31, 195–203
Dubois D., Fariñas del Cerro L., Herzig A., and Prade H. (1997). Qualitative relevance and independence: A roadmap, Proc. of the I5h Inter. Joint Conf on Artificial Intelligence (IJCAI’97), Nagoya, Japan, Aug. 23–29, 62–67.
Dubois D., Fodor J.C., Prade H. and Roubens M. (1996). Aggregation of decomposable measures with application to utility theory, Theory and Decision, 41, 59–95.
Dubois D. and Fortemps P. (1999). Computing improved optimal solutions to fuzzy constraint satisfaction problems, Eur. J, Operational Research., 118, 95–126.
Dubois D., Godo L., Prade H. and Zapico A. (1998). Making decision in a qualitative setting: From decision under uncertainty to case-based decision, Proc. of the 6th Inter. Conf on Principles of Knowledge Representation and Reasoning (KR’98) (Cohn A.G., Schubert L. and Shapiro S.C., eds.), Trento, Italy, 594–605.
Dubois D., Lang J. and Prade H. (1994). 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.), Clarendon Press, Oxford, 439–513.
Dubois D., Kerre E., Mesiar R. and Prade H. (1999). Fuzzy interval analysis, Fundamentals of Fuzzy Sets (Dubois D. and Prade H., eds.), Kluwer Acad. Publ., 1999. This volume.
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.
Dubois D. and Prade H. (1980), Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.
Dubois D. and Prade H. (1982a). A class of fuzzy measures based on triangular norms, Int. J. of General Systems, 8, 43–61.
Dubois D. and Prade H. (1982b). A unifying view of comparison indices in a fuzzy set-theoretic framework, Fuzzy Sets and Possibility Theory — Recent-De velopments (Yager R.R., Ed.), Pergamon Press, pp. 1–13.
Dubois and Prade H. (1982c). On several representations of an uncertain body of evidence, Fuzzy Information and Decision Processes (Gupta M.M. and Sanchez E., eds,), North-Holland, Amsterdam, 167–181.
Dubois D. and Prade H. (1983). Unfair coins and necessity measures: towards a possibilistic interpretation of histograms, Fuzzy Sets and Systems, 10, 15–20.
Dubois D. and Prade H. (1985a). Evidence measures based on fuzzy information, Automatica, 21, 547–562.
Dubois D. and Prade H. (1985b). The mean value of a fuzzy number, Fuzzy Sets and Systems, 24, 279–300.
Dubois D. and Prade H. (1986). Fuzzy sets and statistical data, Europ. J. Operations Research, 25, 345–356.
Dubois D. and Prade H. (1987). Twofold fuzzy sets and rough sets — Some issues in knowledge representation, Fuzzy Sets and Systems, 23, 3–18.
Dubois D. and Prade H. (1988a). Modelling uncertainty and inductive inference, Acta Psychologica, 68, 53–78.
Dubois D. and Prade H. (1988b). Possibility Theory, Plenum Press, New York.
Dubois D. and Prade H. (1988c). Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence, 4, 244–264.
Dubois D. and Prade H. (1988d). Weighted fuzzy pattern matching, Fuzzy Sets and Systems, 28, 313–331.
Dubois D. and Prade H. (1989). Fuzzy sets, probability and measurement, Europ. J. of Operations Research, 40, 135–154.
Dubois D. and Prade H. (1990a). Consonant approximations of belief functions, Int. J. Approximate Reasoning, 4, 419–449.
Dubois D. and Prade H. (1990b). Modelling uncertain and vague knowledge in possibility and evidence theories, Uncertainty in Artificial Intelligence 4 (Shachter R., et al., Eds.), North-Holland, Amsterdam, 303–318.
Dubois D. and Prade H. (1990c). Aggregation of possibility measures, Multiperson Decision Making Using Fuzzy Sets and Possibility Theory (Kacprzyk J. and Fedrizzi M., eds.), Kluwer Academic Publ., Dordrecht, 55–63.
Dubois D. and Prade H. (1991a). Epistemic entrenchment and possibilistic logic, Artificial Intelligence, 50, 223–239.
Dubois D. and Prade H. (1991b). 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.
Dubois D. and Prade H. (1992a). Fuzzy rules in knowledge-based systems — Modelling gradedness, uncertainty and preference, An Introduction to Fuzzy Logic Applications in Intelligent Systems (Yager R.R., and Zadeh L.A., Eds.), Kluwer Academic Publ., Dordrecht, The Netherlands, 45–68.
Dubois D. and Prade H. (1992b). When upper probabilities are possibility measures, Fuzzy Sets and Systems, 49, 65–74
Dubois D. and Prade H. (1992c). Possibilistic abduction, IPMU’92-Advanced Methods in Artificial Intelligence (Bouchon-Meunier B. et al., eds), Lecture Notes in Computer Science, Vol. 682, Springer Verlag, Berlin, 3–12.
Dubois D. and Prade H. (1992d). Belief change and possibility theory, Belief Revision (Gärdenfors P., ed.), Cambridge University Press, 1992, 142–182.
Dubois D. and Prade H. (1993). Fuzzy sets and probability: Misunderstandings, bridges and gaps, Proc. of the 2nd IEEE Inter. Conf on Fuzzy Systems (FUZZ-IEEE’93), San Francisco, CA, March 28-April 1st, 1059–1068.
Dubois D. and Prade H. (1994). Possibility theory and data fusion in poorly informed environments, Control Engineering Practice, 2(5), 811–823.
Dubois D. and Prade H. (1995). Possibility theory as a basis for qualitative decision theory, Proc. of the 14th Inter Joint Conf on Artificial Intelligence (IJCAI’95), Montréal, Canada, 1924–1930.
Dubois D. and Prade H. (1996). Focusing vs. revision in possibility theory. In Proc. of the 5th IEEE Inter. Conf on Fuzzy Systems (FUZZ-IEEE’96), New Orleans, LO, Sept. 8–11, 1700–1705.
Dubois D. and Prade H. (1997a). Bayesian conditioning in possibility theory, Fuzzy Sets and Systems, 92, 223–240.
Dubois D. and Prade H. (1997b). 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.
Dubois D. and Prade H. (1998). Possibility theory: Qualitative and quantitative aspects, Handbook of Defeasible Reasoning and Uncertainty Management Systems — Vol. I (Gabbay D.M. and Smets P., eds.), Kluwer Academic Publ., Dordrecht, 169–226.
Dubois D. and Prade H. (1998c). Belief change rules in ordinal and numerical uncertainty theories, Handbook of Defeasible Reasoning and Uncertainty Management Systems — Vol. 3: Belief Change (Dubois D. and Prade H., eds.), Kluwer Academic Publ., Dordrecht, 311–392.
Dubois D. and Prade H. (1999). An overview of ordinal and numerical approaches to causal diagnostic problem solving, Handbook of Defeasible Reasoning and Uncertainty Management Systems — Vol. 4: Abduction and Diagnosis (Gebhardt J. and Kruse R., eds.), Kluwer Academic PubL, Dordrecht, to appear.
Dubois D., Prade H. and Sabbadin R. (1998). Qualitative decision theory with Sugeno integrals, Proc. of the 14th Conf on Uncertainty in Artificial Intelligence (Cooper G.F. and Moral S., eds.), Morgan Kaufmann, San Mateo, CA, 121–128.
Dubois D., Prade H. and Sandri S.A. (1993). On possibility/probability transformations, Fuzzy Logic: State of the Art (Lowen R., Ed.), Kluwer Academic Publ.
Dubois D., Prade H. and Smets P. (1996). Representing partial ignorance, IEEE Trans, on Systems, Man and Cybernetics, 26, 361–377.
Dubois D., Prade H. and Yager R.R. (Eds.) (1993). Readings in Fuzzy Sets and Intelligent Systems, Morgan Kaufmann, San Mateo, CA.
Dubois D., Prade H. and Yager R.R. (1999). Merging fuzzy information, Fuzzy Sets in Approximate Reasoning and Information Systems (Bezdek J.C., Dubois D. and Prade H., eds.), The Handbooks of Fuzzy Sets Series, Kluwer Academic PubL, Boston, 335–401.
Dubois D. and Yager R.R. (1992). Fuzzy set connectives as combinations of belief structures, Information Sciences, 66, 245–275.
Duda R., Gaschnig J. and Hart P. (1981). Model design in the Prospector consultant system for mineral exploration, Expert Systems in the Micro-Electronics Age (Michie D., ed.), Edinburgh University Press, 153–167.
Edwards W. F. (1972). Likelihood, Cambridge University Press, Cambridge, U.K.
Fagin R. and Halpern J.Y. (1989). A new approach to updating beliefs, Research Report RJ 7222, IBM, Research Division, San Jose, CA.
Fariñas del Cerro L. and Herzig A. (1991). A modal analysis of possibility theory, Fundamentals of Artificial Intelligence Research (FAIRf91) (Jorrand Ph. and Kelemen J., Eds.), Lecture Notes in Computer Sciences, Vol. 535, Springer Verlag, Berlin, 11–18.
Fariñas del Cerro L., Herzig A. and Lang J. (1994). From ordering-based nonmonotonic reasoning to conditional logics, Artificial Intelligence, 66, 375–393.
Fine T. L. (1973). Theories of Probability, Academic Press, New York.
Fishburn P.C. (1986). The axioms of subjective probability, Statistical Science, 1, 335–358.
Fodor J. and Yager R.R. (1999). Fuzzy set-theoretic operators and quantifiers, Fundamentals of Fuzzy Sets (Dubois D, and Prade H., eds.), Kluwer Acad. Publ., 1999. This volume.
Fonck P. (1997). A comparative study of possibilistic conditional independence and lack of interaction, Int. J. Approximate Reasoning, 16, 149–172.
Fortemps P. (1997). Fuzzy sets for Modelling and Handling Imprecision and Flexibility, Ph. D. Thesis, Faculté Polytechnique de Mons, Belgium
Fortet R. and Kambouzia M. (1976). Ensembles aléatoires et ensembles flous, Publications Econométriques, IX, 1–23.
French S. (1984), Fuzzy decision analysis: some criticisms, TIMS Studies in the Management Sciences, 20, 29–44
Garbolino P. (1989). On the plausibility of inverse possibility, Discussion paper 8, Ann. Univ. Ferrara, III (Philosophy).
Gaines B.R. (1978). Fuzzy and probability uncertainty logics, Information and Control 38, 154–169.
Gärdenfors P. (1988). Knowledge in Flux — Modeling the Dynamics of Epistemic States, The MIT Press, Cambridge, MA.
Gebhardt J., Gil M.A. and Kruse R. (1998). Fuzzy set-theoretic methods in statistics, Fuzzy Sets in Decision Analysis, Operations Research and Statistics (Slowinski R., ed.), The Handbooks of Fuzzy Sets Series, Kluwer Academic Publ., Boston, 311–347.
Gebhardt J. and Kruse R. (1993). The context model-an intergating view of vagueness and uncertainty. Int J. Approximate Reasoning, 9, 283–314.
Gebhardt J. and Kruse R. (1994a). A new approach to semantic aspects of possibilistic reasoning, Symbolic and Quantitative Approaches to Reasoning and Uncertainty (Clarke M. et al, Eds.), Lecture Notes in Computer Sciences Vol. 747, Springer Verlag, 151–160.
Gebhardt J. and Kruse R. (1994b). On an information compression view of possibility theory, Proc 3rd IEEE Int. Conference on Fuzzy Systems. Orlando, F1, 1285–1288.
Gebhardt JL and Kruse R. (1996). Automated construction of possibilistic networks from data, Applied Mathematics and Computer Science, 6, 529–564.
Geer J.F., and Klir GJ. (1992). A mathematical analysis of information-preserving transformations between probabilistic and possibilistic formulations of uncertainty, Int. J. of General Systems, 20, 143–176.
Gil M.A. (1988). On the loss of information due to fuzziness in experimental observations, Ann. Inst. Statist. Math., 4, 627–639.
Giles R. (1982). Foundations for a theory of possibility, Fuzzy Information and Decision Processes (Gupta M.M. and Sanchez E., eds.), North-Holland, 183–195.
Godai R.C. and Goodman TJ. (1980). Fuzzy sets and Borel, IEEE Trans, on Systems, Man and Cybernetics, 10, 637.
Goodman I.R. (1982), Fuzzy sets as equivalence classes of random sets, Fuzzy Sets and Possibility Theory (Yager R.R., Ed.), Pergamon Press, Oxford, 327–342.
Goodman I.R., Nguyen H.T. and Rogers G.S. (1991). On the scoring approach to admissibility of uncertainty measures in expert systems, J. Math. Anal. and Appl., 159, 550–594.
Grabisch M.L., Murofushi T., and Sugeno M. (1992). Fuzzy measure of fuzzy events defined by fuzzy integrals, Fuzzy Sets and Systems, 50, 293–313.
Grabisch M., Nguyen H.T. and Walker E.A. (1995). Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference, Kluwer Academic Publ., Dordrecht.
Grove A. (1988). Two modellings for theory change, J. Philos. Logic, 17, 157–170.
Gupta C.P. (1993). A note on the transformation of possibilistic information into probabilistic information for investment decisions, Fuzzy Sets and Systems, 56, 175, 182.
Gwét H. (1997). Normalized conditional possibility distributions and informational connection between fuzzy variables, Int. J. Uncertainty, Fuzziness and Knowledge-based Systems, 5, 177–198.
Hacking I. (1975). All kinds of possibility, Philosophical Review, 84, 321–347.
Hajek P. (1994). A qualitative fuzzy possibilistic logic, Int. J. of Approximate Reasoning, 12, 1–19.
Hajek P., Harmancova D., Esteva F., Garcia P. and Godo L. (1994). On modal logics for qualitative possibility in a fuzzy setting, Proc. of the 11th Conf. on Uncertainty in Artificial Intelligence (Lopez de Mantaras R. and Poole D., eds.), Morgan Kaufmann, San Francisco, CA, 278–285.
Halpern J. (1996). Defining relative likelihood in partially-ordered preferential structures, Proc. of the 12th Conf on Uncertainty in Artificial Intelligence (Horvitz E, and Jensen J., eds.), Morgan Kaufmann,, San Francisco, 299–306.
Hardy G.H., Littlewood J.E. and Polya G. (1934). Inequalities, Cambridge University Press. 2nd edition, 1952.
Harmanec D. and Klir GJ. (1997). On information-preserving transformations, Int. J. of General Systems, 26(3), 265–290.
Hersh H.M. and Caramazza A. (1976). A fuzzy set approach to modifiers and vagueness in natural language, J. of Exp. Psycho., General, 105, 254–276.
Herstein I.N. and Milnor J., (19..). An axiomatic approach to measurable utility, Econometrics 21, 291–297.
Hestir K., Nguyen H.T. and Rogers G.S. (1991). A random set formalism for evidential reasoning, Conditional Logic in Expert Systems (Goodman I.R. et al., Eds.), North-Holland, Amsterdam, 309–344.
Higashi and Klir G. (1982). Measures of uncertainty and information based on possibility distributions, Int J. General Systems, 8, 43–58.
Higashi and Klir G. (1983). On the notion of distance representing information closeness, Int. J. General Systems, 9, 103–115.
Hisdal E. (1978). Conditional possibilities independence and noninteraction, Fuzzy Sets and Systems, 1, 283–297.
Hisdal E. (1991). Naturalized logic and chain sets, Information Sciences,57-58, 31–77.
Höhle U. (1976). MaBe auf unscharfen Mengen, Zeitschrift für Wahrscheinlichkeitstheorie and verwandte Gebiete, 36, 179–188.
Horvitz E.J., Heckerman D.E. and Langîotz C.P. (1986). A framework for comparing alternative formalisms for plausible reasoning, Proc. of the 5th National Conf. on Artificial Intelligence (AAAI’86), Philadelphia, PA, 210–214.
Huber PJ. (1981). Robust Statistics, John Wiley & Sons, New York.
Hunter D. (1991). Graphoids and natural conditional functions, Int. J. Approximate Reasoning, 5, 489–504.
Inuiguchi M. and Kume Y. (1994). Necessity measures defined by level set inclusions: Nine kinds of necessity measures and their properties, Int. J. of General Systems, 22, 245–275.
Inuiguichi M., Ichihashi H. and Tanaka H. (1989). Possibilistic linear programming with measurable multiattribute value functions, ORSA J. on Computing, 1, 146–158.
Jaffray J.Y. (1992). Bayesian updating and belief functions, IEEE Trans, on Systems, Man ybernetics, 22, 1144–1152.
Jain P. and Agogino A.M. (1990). Stochastic sensitivity analysis using fuzzy influence diagrams, Uncertainty in Artificial Intelligence 4 (Shachter R.D., Levitt T.S., Kanal L.N. and Lemmer J.F., Eds.), North-Holland, Amsterdam, 79–92.
Joslyn C. (1997). Measurement of possibilistic histograms from interval data, Int. J. of General Systems, 26(1-2), 9–33.
Kampé de Fériet J. (1982). Interpretation of membership functions of fuzzy sets in terms of plausibility and belief, Fuzzy Information and Decision Processes (Gupta M.M. and Sanchez E., Eds.), North-Holland, Amsterdam, 93–98.
Kaufmann A. (1978). Le calcul des admissibilités. Private communication.
Klir G.J. (1990), A principle of uncertainty and information invariance, Int. J. of General Systems, 17, 249–275.
Klir G.J. and Yuan B. (1995). Fuzzy Sets and Fuzzy Logic — Theory and Applications, Prentice Hall, Upper Saddle River, NJ.
Klir GJ. and Folger T. (1988). Fuzzy Sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, NJ.
Klir GJ. and Harmanek D. (1994). On modal logic interpretations of possibility theory, Int. J. of Uncertainty, Fuzziness, and Knowledge-Based Syst., 2, 237–245.
Klir GJ. and Parviz B. (1992). Probability-possibility transformations: A comparison, Int. J. of General Systems, 21, 291–310.
Klir G. J. (1999). Measures of uncertainty and information, Fundamentals of Fuzzy Sets (Dubois D. and Prade H., eds.), Kluvver Acad. Pub]., 1999. This volume.
Kosko B. (1990). Fuzziness vs. probability, Int. J. of General Systems, 17, 211–240.
Kovalerchuk B.Y. and Shapiro D.I. (1988). On the relation of the probability theory and the fuzzy setz theory foundations, Computers and Artificial Intelligence, 7, 385–396.
Kramosil I (1996). Nonstandard approach to possibility theory, Int. J. of Uncertainty, Fuzziness, and Knowledge-Based Syst., 4, 275–301.
Kruse R. and Meyer K.D. (1987). Statistics with Vague Data, D. Reidel, Dordrecht.
Kruse R., Gebhardt J., Klawonn F. (1994). Foundations of Fuzzy Systems, Wiley, New York.
Lapointe S. (1999). Traitement Subjectif de l’Incertitude par la Théorie des Possibilités: Application a la Prévision et au Suivi des Crues, Ph. D. Thesis, IMRS-Eau, Québec University
Lapointe S. Bobée B. (1999). Revision of possibility distributions: A Bayesian inference pattern, to appear in Fuzzy Sets and Systems
Lasserre V., Mauris G. and Foulloy L., (1998). A simple modélisation 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 Médicales et Scientifiques, 10–17.
Laviolette M. and Seaman Jr. J. W. (1994). The efficacy of fuzzy representations of uncertainty. IEEE Trans, on Fuzzy Systems, 2, 4–
Laviolette M., Seaman Jr. J. W., Barrett J.D. and Woodall W.H. (1995). Fuzziness vs. probability, Technometrics, 37, 249–259.
Lewis D. (1973). Counterfactuals, Basil Blackwell, Oxford. 2nd edition, Billing and Sons Ltd., Worcester, UK, 1986.
Lewis D. L. (1979). Counterfactuals and comparative possibility, If s (Harper W. L., Stalnaker R. and Pearce G., eds.), D. Reidel, Dordrecht, 57–86.
Li Q.D. (1997). The random set and the cutting of random fuzzy sets, Fuzzy Sets and Systems, 86, 223–234.
Liang P. and Song F. (1996). What does a probabilistic interpretation of fuzzy sets mean?, IEEE trans, on Fuzzy Systems, 4, 200–205.
Lindley D.V. (1982). Scoring rules and the inevitability of probability, Int. Statist Rev., 50, 1–26.
Loginov V.l. (1966). Probability treatment of Zadeh membership functions and their use in pattern recognition, Eng. Cyber., 68–69.
Mabuchi, S. (1992). An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators-Part I: Case of type 1 fuzzy sets. Fuzzy Sets and Systems, 49, 271–283.
Mabuchi, S. (1997). An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators-Part II. Extensions to three-valued and interval-valued fuzzy sets. Fuzzy Sets and Systems, 92, 31–50.
Maeda, Y. Nguyen, H.T., and Hichihashi H. (1993). Maximum entropy algorithms for uncertainty measures, Int. J. of Uncertainty, Fuzziness, and Knowledge-Based Syst., 1, 69–93.
Manton K.G., Woodbury M.A. and Tolley H.D. Statistical Applications Using Fuzzy Sets., Wiley, New York.
Marichai J.-L. (1998). On Sugeno integral as an aggregation function, Tech. Rep. 9710, GEMME, Fac. d’Ecomomie, Université de Liege, Belgium, Proceedings of EUFIT′98 — Vol. I, Aachen, Germany, 540–544.
Maslov V. (1987). Méthodes Opératorielles, Editions MIR, Moscow.
Maslov V. and Samborski S.N. (\992)Idempotent Analysis. Advances in Soviet Mathematics 13, Amer. Math. Soc., Providence
Mathéron G. (1975). Random Sets and Integral Geometry, John Wiley & Sons, New York.
Maung I. (1995). Two characterizations of a minimum information principle for possibilistic reasoning, Int. X Approximate Reasoning, 12, 133–156.
Mesiar R. (1992). Characterisation of possibility measures of fuzzy events using Markov kernels, Fuzzy Sets and Systems, 46, 301–303.
Mesiar R., (1994). On the integral representation of fuzzy possibility measures, Int. J. of General Systems, 21, 109–121.
Mesiar R. (1997). Possibility measures, integration, and fuzzy possibility measures, Fuzzy Sets and Systems, 92, 191–196.
Molchanov I.S. (1993). Limit Theorems for Unions of Random Closed Sets, Lecture Notes in Mathematics, Vol. 1561, Springer Verlag, Berlin.
Moulin H. (1988). Axioms of Cooperative De cision Making, Cambridge University Press, Cambridge, MA.
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.
Murofushi T. and Sugeno M. (1989). In interpretation of fuzzy measure and the Choquet integral as an integral with respect to a fuzzy measure, Fuzzy Sets and Systems, 29, 201–227.
Murofushi T. and Sugeno M. (1993). Continuous from above possibility measures and f-additive fuzzy measures on separable metic spaces: Characterization and regularity, Fuzzy Sets and Systems, 54, 351–354.
Nahmias S. (1978)/Fuzzy variables, Fuzzy Sets and Systems, 1, 97–110.
Narin’yani A.S. (1980). Sub-definite set — New data-type for knowledge representation, Memo n° 4-232, Computing Center, Novosibirsk, URSS.
Natvig B. (1983). Possibility versus probability, Fuzzy Sets and Systems, 10, 31–36.
Nau R.F. (1992). Decision analysis with indeterminate or incoherent probabilities, Annals of Operations Research — Vol: Choice Under Uncertainty (Fishburn P.C. and LaValle I.H., Eds.), to appear.
Negoita C.V. and Ralescu D. (1987), Simulation, Knowledge-Based Computing, and Fuzzy Statistics, Van Nostrand Reinhold Comp., New York.
Nguyen H.T. (1978a). On random sets and belief functions, J. Math. Anal. and Appl., 65, 531–542
Nguyen H.T. (1978b). On conditional possibility distributions, Fuzzy Sets and Systems, 1, 299–309.
Nguyen H.T. (1984). On modeling of linguistic information using random sets, Information Science, 34, 265–274.
Nguyen H.T. and Walker E.A. (1994), On decision making using belief functions, Advances in the Dempster-Shafer Theory of Evidence (Yager R.R. et al., Eds.), John Wiley & Sons, New York, 311–330.
Norberg T. (1986), Random capacities and their distributions, Proha. Th. Rel. Fields, 73, 281–297.
Okuda T., Tanaka H, and Asai K. (1978). A formulation of fuzzy decision problems with fuzzy information, using probability measures of fuzzy events, Information and Control 38, 135–147.
Orlov A.I. (1978). Fuzzy and random sets, Prikladnoï Mnogomiernii Statisticheskii Analyz (Nauka, Moscow), 262-280 (in Russian).
Pan Y. and Yuan B. (1997), Bayesian inference of fuzzy probabilities, Int. J. of General Systems, 26 (1-2), 73–90.
Paris J.B. (1997). A semantics for fuzzy logic, Soft Computing, 1, 143–147.
Pawlak Z. (1991). Rough sets — Theoretical Aspects of Reasoning about Data, Kiuwer Academic Publ., Dordrecht
Pearl J. (1988). Probabilistic Reasoning Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, San Mateo, CA
Pearl J., (1990). Integrating probability and logic, Readings in Uncertain Reasoning (Shafer G. and Pearl J., Eds.), Morgan Kaufmann, San Mateo, CA, 677–679.
Pirlot M. (1995). A characterization of’ min’ as a procedure for exploiting valued preference relations and related results, J. of Multi-Criteria Decision Analysis, 4, 37–56.
Prade H. (1979). Nomenclature of fuzzy measures, Proc. 1st Int. Seminar on Theory of Fuzzy Sets, Linz, Austria, Sept, 24-29, 9–25.
Prade H. (1982). Modal semantics and fuzzy set theory. In: Fuzzy Set and Possibility Theory. Recent Developments. (R.R. Yager, ed.), Pergamon Press, New York, 232–246.
Prade H. and Yager R.R. (1994). Estimations of expectedness and potential surprize in possibility theory, Int. J. Uncertainty, Fuzziness and Knowledge-based Systems, 2, 417–428.
Puri M. L. and Ralescu D. (1982). A possibility measure is not a fuzzy measure, Fuzzy Sets and Systems, 7, 311–313.
Ralescu D. and Adams G. (1980). The fuzzy integral, J. Math, Anal. and Appl. 75, 562–570.
Ramer A. (1989). Conditional possibility measures, Cybernetics and Systems, 20, 233–247.
Ramer A. (1990a). Structure of possibilistic information metrics and distances: Properties, Int. J. of General Systems, 17, 21–32.
Ramer A. (1990b). Possibilistic information metrics and distances: Characterizations of structure, Int. J. of General Systems, 18, 1–10.
Ramer A. (1990c). Uncertainty in the Dempster-Shafer theory: A critical re-examination, Int J. of General Systems, 18, 155–166.
Raufaste E. and Da Silva Neves R. (1998). Empirical evaluation of possibility theory in human radiological diagnosis, Prot\ of the 13th Europ. Conf on Artificial Intelligence (ECAl’98) (Prade H., ed.), John Wiley & Sons, 124–128.
Robbins H.E. (1944). On the measure of a random set. Ann. Math. Statist, 15, 70–74.
Ruspini E.H. (1991). Approximate reasoning: Past, present, future, Information Sciences, 57-58, 297–317.
Sales T. (1982). Fuzzy sets as set classes, Stochastica, 6, 249–264.
Sanchez E. (1978). On possibility-qualification in natural languages, Information Sciences, 15, 45–76.
Sanguessa R., Cabos J. and Cortes U. (1998). Possibiiistic conditional independence: A similarity-based measure and its application to causal network learning, InL J. Approximate Reasoning, 18, 145–167.
Sanguessa R., Cortes U. and Gisolfi A. (1998), Possibiiistic conditional independence: a similarity-based measure and its application to causal network learning, Int. J. Approximate Reasoning, 18, 251–270.
Schmeidler D. (1986). Integral representation without additivity, Proc. Amer. Math. Soc, 97(2), 255–261.
Shackle G. L. S. (1961). Decision, Order and Time in Human Affairs, (2nd edition), Cambridge University Press, UK.
Shafer G. (1976a). A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ.
Shafer G. (1976b). A theory of statistical evidence, Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Sciences — Vol. II, (Harper and Hooker, eds.), D. Reidel, Dordrecht, 365–436.
Shafer G. (1987). Belief functions and possibility measures, Analysis of Fuzzy Information — Vol. I: Mathematics and Logic (Bezdek J.C., Ed.), CRC Press, Boca Raton, FL, 51–84.
Shapley S. (1971). Cores of convex games, Int. J. of Game Theory, 1, 12–26.
Shenoy P. (1991). On Spohn’s rule for revision of beliefs, Int. J. Approximate Reasoning, 5, 149–181.
Shenoy P. (1992). Using possibility theory in expert systems. Fuzzy Sets and Systems, 52, 129–142.
Shilkret N. (1971). Maxitive measure and integration, Indag. Math., 33, 109–116.
Shoham Y. (1988). Reasoning About Change — Time and Causation from the Standpoint of Artificial Intelligence, The MIT Press, Cambridge, MA.
Slowinski R. (Eds.) (1998). Fuzzy Sets in Decision Analysis, Operations Research and Statistics, The Handbooks of Fuzzy Sets Series (Dubois D. and Prade H., eds.), Kluwer Academic Publ., Boston.
Smets P. (1982). Possibiiistic inference from statistical data, Proc. of the 2nd World Conf on Mathematics at the Sendee of Man, Las Palmas (Canary Island), Spain, 611–613.
Smets P. (1990). Constructing the pignistic probability function in a context of uncertainty, Uncertainty in Artificial Intelligence 5 (Henrion M. et al, Eds.), North-Holland, Amsterdam, 29–39.
Smets P. and Kennes R. (1994). The transferable belief model, Artificial Intelligence, 66, 191–234.
Smith CA.B. (1961). Consistency in statistical inference and decision, J. Royal Statist. Soc., B-23, 1–37.
Spohn W. (1988). Ordinal conditional functions: A dynamic theory of epistemic states, Causation in Decision, Belief Change and Statistics (Harper W. and Skyrms B., Eds.), 105–134.
Spohn W. (1990). A general non-probabilistic theory of inductive reasoning, Uncertainty in Artificial Intelligence 4 (Shachter R.D., Levitt T.S., Kanal L.N. and Lemmer J.F., Eds.), North-Holland, Amsterdam, 149–158.
Spott M. (1999). A theory of possibility distributions, Fuzzy Sets and Systems, 102, 135–155.
Stallings W, (1977). Fuzzy set theory versus Bayesian statistics, IEEE Trans, on Systems, Man and Cybernetics, 216–219.
Studeny M. (1995). Conditional independence and natural conditional functions, Int. J. Approximate Reasoning, 12, 43–68.
Suarez Garcia F. and Gil Alvarez P. (1986). Two families of fuzzy integrals, Fuzzy Sets and Systems, 18, 67-81
Sudkamp T. (1992a). On probability-possibility transformations, Fuzzy Sets and Systems, 51, 73–81.
Sudkamp T. (1992b). The semantics of plausibility and possibility, Int. J. of General Systems, 21, 273–289.
Sudkamp T. (1993). Geometric measures of possibilistic uncertainty, Int. J. of General Systems, 22, 7–23.
Sugeno M. (1974). Theory of fuzzy integrals and its applications, Ph. D. Thesis, Tokyo Institute of Technology, Japan.
Sugeno M. (1977). Fuzzy measures and fuzzy integrals — A survey, Fuzzy Automata and Decision Processes (Gupta M.M., Saridis G.N. and Gaines B.R., eds.), North-Holland, Amsterdam, 89–102.
Tanaka H., and Guo P.J. (1999). Possibilistic Data Analysis for Operations Research, Physic a-Verlag, Heidelberg.
Tanaka H. and Ishibuchi H. (1993). Evidence theory of exponential possibility distributions. Int. J. Approximate Reasoning, 8, 123–140.
Tanaka H., Ishibuchi H., Hayashi I. (1993). Identification method of possibility distributions and its application to discriminant analysis, Fuzzy Sets and Systems, 58, 41–50.
Thomas S.F. (1979). A theory of semantics and possible inference with application to decision analysis, PhD Thesis, University of Toronto, Canada.
Thomas S.F. (1981). Possibilistic uncertainty and statistical inference, ORSA/TIMS Meeting, Houston, Texas.
Thomas S.F. (1995). Fuzziness and Probability, ACG Press, Wichita, Kansas.
Tribus M. (1978). Comments on fuzzy sets, fuzzy algebras, and fuzzy statistics, Proc. IEEE, 67, 1168–1169.
Tsiporkova E. and De Baets B. (1998). A general framework for upper and lower possibilities and necessities, Int. J. Uncertainty, Fuzziness and Knowledge-based Systems, 6, 1–33.
Viertl R. (1996). Statistical Methods for Non-Precise Data, CRC Press, Boca Raton, FL.
Viertl R. and Hule H. (1991). On Bayes’ theorems for fuzzy data, Statistical Papers, 32, 115–122.
Vincke P. (1982). Aggregation of preferences: A review, Europ. J. Operational res., 9, 17–22.
Walley P. (1991). Statistical Reasoning with Imprecise Probabilities, Chapman and Hall
Walley P. (1996). Measures of uncertainty in expert systems, Artificial Intelligence, 83, 1–58.
Walley P., (1997). Statisticaél inferences based on a second-order possibility distribution, Int J. of General Systems, 26, 337–383.
Walley P. and de Cooman G.(1999) A behavioural model for linguistic uncertainty, Computing With Words (Wang P.P., ed.), Wiley, to appear.
Wallsten T.S., Budescu D.V., Rapoport A., Zwick R. and Forsyth B, (1986). Measuring the vague meanings of probability terms, J. of Experimental Psychology: General, 115, 348–365.
Wang P.Z. (1983). From the fuzzy statistics to the falling random subsets, Advances in Fuzzy Sets, Possibility Theory and Applications (Wang P.P., Eds.), Plenum Press, New York, 81–96.
Wang P.Z. (1982). Fuzzy contactability and fuzzy variables, Fuzzy Sets and Systems, 8, 81–92.
Wang P.Z. and Sanchez E. (1982). Treating a fuzzy subset as a projectable random set, Fuzzy Information and Decision Processes (Gupta M.M. and Sanchez E., Eds.), North-Holland, Amsterdam, 213–220.
Wang Z. and Klir G. (1992). Fuzzy measure theory, Plenum Press, New-York.
Wasserman L.A. (1987). Some applications of belief functions to statistical inference, Thesis, Univ. of Toronto, Canada.
Watson S.R., Weiss JJ. and Donnell M. (1979). Fuzzy decision analysis, IEEE Trans. on Systems, Man and Cybernetics, 9, 1–9.
Whalen T. (1984). Decision making under uncertainty with various assumptions about available information, IEEE Trans, on Systems, Man and Cybernetics, 14, 888–900.
Wolkenhauer O. (1988). Possibility Theory with Applications to Data Analysis, Research Studies Press, Hertfordshire, UK.
Wonneberger S. (1994). Generalization of an in verüble mapping between probability and possibility, Fuzzy Sets and Systems, 64, 229–240.
Yager R.R. (1979). Possibilistic decision making, IEEE Trans, on Systems, Man and Cybernetics, 9, 388–392.
Yager R.R. (1980). A foundation for a theory of possibility, J. Cybernetics, 10, 177–204.
Yager R.R. (1981). A new methodology for ordinal multiobjective decisions based on fuzzy set, Decision Sciences, 12, 589–600.
Yager R.R. (1983). An introduction to applications of possibility theory, Human Systems Management, 3, 246–269.
Yager R.R. (1984). General multiple objective decision making and linguistically quantified statements, Int J. of Man-Machine Studies, 21, 389–400.
Yager R.R. (1985a). Q-projections of possibility distributions, IEEE trans. on Systems Man & Cybern., 15, 775–777.
Yager R.R. (1985b). On the relationships of methods of aggregation evidence in expert systems, Cybernetics and Systems, 16, 1–21.
Yager R.R. (1990). Ordinal measures of specificity, Int. J. Gener. Syst., 17, 57–72.
Yager R.R. (1992). On the specificity of a possibility distribution, Fuzzy Sets and Systems, 50, 279–292.
Yager R.R. (1993a). On the completion of qualitative possibility measures, IEEE Trans. on Fuzzy Systems, 1, 184–195.
Yager R.R. (1993b). On the completion of priority orderings in non-monotonic reasoning systems. Int. J. of Uncertainty, Fuzziness, and Knowledge-Based Syst., 1, 139–165.
Yan B. (1993). Semiconormed possibility integrals for application-oriented modelling, Fuzzy Sets and Systems, 57, 239–248.
Yan B. (1994). Seminormed possibility integrals for application-oriented modelling, Fuzzy Sets and Systems, 61, 189–198.
Young V.R. and Wang S.S., Upating non-additive measures with fuzzy information. Fuzzy Sets and Systems, 94, 355–366.
Zadeh LA. (1965). Fuzzy sets, Information and Control, 8, 338–353.
Zadeh L.A. (1968). Probability measures of fuzzy events, J. Math, Anal. Appl., 23, 421–427.
Zadeh L. A. (1975a). The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, Part I: 8, 199–249; Part II: 8, 301–357; Part III: 9, 43–80.
Zadeh L. A. (1975b). Calculus of fuzzy restrictions, Fuzzy Sets and Their Applications to Cognitive and Decision Processes (Zadeh L. A., Fu K. S., Shimura M. and Tanuka K., eds.), Academic Press, New York, 1–39.
Zadeh L.A. (1978). Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3-28. Reprinted in Fuzzy Sets and Applications; Selected Papers (Zadeh L.A., Yager R.R., Ovchinnikov S., Tong R.M. and Nguyen HT., Eds.), Wiley, New York, 1987, 193–218.
Zadeh L.A. (1979a).A theory of approximate reasoning, Machine Intelligence, Vol. 9 (Hayes J. E., Michie D. and Mikulich L. L., eds.), John Wiley & Sons, New York, 149–194.
Zadeh L.A. (1979b). Fuzzy sets and information granularity. In: Advances in Fuzzy Set Theory and Applications, (MM. Gupta, R.K. Ragade, R.R., eds.), North-Holland, Amsterdam, 3–18.
Zadeh L.A. (1985). Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions, IEEE Trans, on Systems, Man and Cybernetics, 15, 754–763.
Zadeh L.A. (1995). Discussion: Probability theory and fuzzy logic are complementary rather than competitive, Technometrics, 37, 271–276.
Zimmermann HJ. (1987). Fuzzy Sets, Decision Making, and Expert Systems, Kluwer Academic Publ., Boston.
Zwirn D. and Zwirn H. (1995). Confirmation non-probabiliste, Méthodes Logiques pour les Sciences Cognitives (Dubucs J. and Lepage F., eds.). Hermès, Paris., 77–98.
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Dubois, D., Nguyen, H.T., Prade, H. (2000). Possibility Theory, Probability and Fuzzy Sets Misunderstandings, Bridges and Gaps. In: Dubois, D., Prade, H. (eds) Fundamentals of Fuzzy Sets. The Handbooks of Fuzzy Sets Series, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4429-6_8
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