Skip to main content

Qualitative Possibility Theory in Information Processing

  • Chapter
Forging New Frontiers: Fuzzy Pioneers II

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 218))

Abstract

This chapter provides a general overview of advances made in qualitative possibility theory and its application to information processing in the last decade. These methodological results reflect a series of works done in few research groups, including the one of the authors. More precisely, the ability of possibility theory to handle positive and negative information (knowledge as well as preferences) in a bipolar way is emphasized including an original revision process, together with its use for representing information in different formats, for formalizing various types of reasoning pervaded with uncertainty, for providing a qualitative framework for decision making, and for learning from imperfect data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

Some General References on Possibility Theory

  • Dubois D., Prade H. Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press, New York, 1988.

    Google Scholar 

  • Dubois D., Prade H. Fuzzy sets in approximate reasoning: A personal view. In: Implementations and Applications for Fuzzy Logic, (M. J. Patyra, D.M. Mlynek, eds.), J. Wiley and B. G. Teubner, New York and Stuttgart, 3–35, 1996.

    Google Scholar 

  • Dubois D., Prade H. Possibility theory: qualitative and quantitative aspects. In: Quantified Representation of Uncertainty and Imprecision, (D. M. Gabbay, Ph. Smets, eds.), Vol. 1 of the Handbook of Defeasible Reasoning and Uncertainty Management Systems, Kluwer Acad. Publ., 169–226, 1998.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Specific References (in the Last Decade)

  • Alsinet T., Logic Programming with Fuzzy Unification and Imprecise Constants : Possibilistic Semantics and Automated Deduction. Ph. D. Thesis, Technical University of Catalunya, Barcelona, 2001.

    Google Scholar 

  • Alsinet T., Godo L. A complete calculus for possibilistic logic programming with fuzzy propositional variables. Proc. of the 16th Conference on Uncertainty in Artificial Intelligence (UAI’00), San Francisco, California, 1–10, 2000.

    Google Scholar 

  • Alsinet T., Godo L., Sandri S. On the semantics and automated deduction for PLFC, a logic of possibilistic uncertainty and fuzziness. Proc. of the 15th Conference on Uncertainty in Artificial Intelligence, (UAI’99), Stockholm, Sweden, 3–20, 1999.

    Google Scholar 

  • Alsinet T., Godo L., Sandri S. Two formalisms of extended possibilistic logic programming with context-dependent fuzzy unification: a comparative description. Elec. Notes in Theor. Computer Sci. 66(5), 2002.

    Google Scholar 

  • Ben Amor N., Benferhat S., Dubois D., Mellouli K., Prade H. A theoretical framework for possibilistic independence in a weakly ordered setting, Inter. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 10, 117–155, 2002.

    MATH  MathSciNet  Google Scholar 

  • Benferhat S., Dubois D., Garcia L., Prade H. On the transformation between possibilistic logic bases and possibilistic causal networks. Inter. J. of Approximate Reasoning, 29, 135–173, 2002.

    Google Scholar 

  • Benferhat S., Lagrue S., and Papini O. Reasoning with partially ordered information in a possibilistic logic framework. Fuzzy Sets and Systems, 144, 25–41, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  • Benferhat S., Prade H. Encoding formulas with partially constrained weights in a possibilistic-like many-sorted propositional logic. Proc. of the 9th Int. Joint Conf. on Artificial Intelligence (IJCAI’05), Edinburgh, Scotland, July 31-Aug. 5, 2005, 1281–1286, 2005.

    Google Scholar 

  • Benferhat S., Prade H. Compiling possibilistic knowledge bases. Proc. of the 17th Europ. Conf. on Artificial Intelligence, Riva del Garda, Italy, Aug. 28th- Sept. 1st, 2006

    Google Scholar 

  • Boldrin L., Sossai C. Local possibilistic logic. J. Applied Non-Classical Logics, 7, 309–333, 1997.

    Google Scholar 

  • Dubois D., Konieczny S., Prade H. Quasi-possibilistic logic and its measures of information and conflict. Fundamenta Informaticae, 57, 101–125, 2003.

    MATH  MathSciNet  Google Scholar 

  • Dubois D., Lehmke S., and Prade H. A comparative study of logics of graded uncertainty and logics of graded truth. In Proc. of the 18th Linz Seminar on Fuzzy Set Theory Enriched Lattice Structures for Many-Valued and Fuzzy Logics (S. Gottwald and E. P. Klement, eds.), pp. 10–15, Linz, Austria, Feb. 25 - Mar. 1, 1997.

    Google Scholar 

  • Dubois D., Prade H. Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems, Elsevier, 144, 3–23, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D., Prade H. and Sandri S. A. Possibilistic logic with fuzzy constants and fuzzily restricted quantifiers. In: Logic Programming and Soft Computing (T. P. Martin, F. Arcelli-Fontana, eds.), Research Studies Press Ltd, Baldock, England, 69–90, 1998.

    Google Scholar 

  • Dupin de Saint-Cyr F., Prade H. Possibilistic handling of uncertain default rules with applications to persistence modeling and fuzzy default reasoning. Proc. 10th Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR 2006), Lake District, UK, June 2-5, 2006, 440–451.

    Google Scholar 

  • Nicolas P., Garcia L., Stéphan I. A possibilistic inconsistency handling in answer set programming. Proc. Europ. Conf. on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU’05) - LNAI 3571, Barcelone, July 6 -8, 2005. (L. Godo, ed.), Springer-Verlag, 402–414.

    Google Scholar 

  • Nicolas P., Garcia L., Stéphan I. Possibilistic stable models. Proc. of the 19th Inter. Joint Conf. on Artificial Intelligence (IJCAI ’05), Edinburgh, Scotland, July 30- Aug. 5, 2005, 248–253.

    Google Scholar 

  • Lehmke S. Logics which Allow Degrees of Truth and Degrees of Validity. PhD dissertation, Universitât Dortmund, Germany, 2001.

    Google Scholar 

Possibilistic Representations of Knowledge and Preferences

  • Benferhat S., Dubois D., Kaci S., Prade H. Bridging logical, comparative and graphical possibilistic representation frameworks. Proc. 6th.European Conf. (ESCQARU 2001), Toulouse, France, Sept. 19–21, 2001. Springer-Verlag, LNAI 2143, 422–431.

    Google Scholar 

  • Benferhat S., Dubois D., Kaci S., Prade H. Bipolar possibilistic representations. Proc. 18th. Conf. on Uncertainty in Artificial Intelligence (UAI 2002), Edmonton, Aug. 1–4, 2002, Morgan Kaufmann Publ., 45–52.

    Google Scholar 

  • Benferhat S., Dubois D., Prade H. Possibilistic and standard probabilistic semantics of conditional knowledge bases. J. of Logic and Computation, 9, 873–895, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  • Benferhat S., Dubois D., Prade H. Towards a possibilistic logic handling of preferences. Applied Intelligence, 14, 303–317, 2001.

    Article  MATH  Google Scholar 

  • Dubois D., Kaci S., Prade H. Expressing preferences from generic rules and examples - A possibilistic approach without aggregation function. Proc. Europ. Conf. on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU’05) - LNAI 3571, Barcelone, July 6 -8, 2005. (L. Godo, ed.), Springer-Verlag, 293–304.

    Google Scholar 

  • Dubois D., Kaci S., Prade H. Approximation of conditional preferences networks ‘‘CP-nets’’ in possibilistic logic. Proc. 2006 IEEE International Conference on Fuzzy Systems, Vancouver

    Google Scholar 

  • Dubois D., Prade H. _A bipolar possibilistic representation of knowledge and preferences and its applications. In : Fuzzy Logic and Applications, 6th Inter. Workshop, (WILF 2005), (I. Bloch, A. Petrosino, A. Tettamanzi, eds.) Crema, Italy, Sept. 15–17, 2005, LNCS 3849, Springer, 1–10, 2006.

    Google Scholar 

Possibilistic Description Logic

  • Dubois D., Mengin J., Prade H. Possibilistic uncertainty and fuzzy features in description logic. A preliminary discussion. In: Fuzzy Logic and the Semantic Web, (E. Sanchez, ed.), Elsevier, 2005.

    Google Scholar 

Possibilistic Information Fusion

  • Benferhat S. Merging possibilistic networks. Proc. of the 17th Europ. Conf. on Artificial Intelligence, Riva del Garda, Italy, Aug. 28th- Sept. 1st, 2006

    Google Scholar 

  • Benferhat S., Dubois D., Kaci S., Prade H. Possibilistic merging and distance-based fusion of propositional information. Annals of Mathematics and Artificial Intelligence, 34, 217–252, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  • Benferhat S., Dubois D., Kaci S., Prade H. Bipolar representation and fusion of preferences in the possibilistic logic framework. Proc. 8th Int. Conf. on Principles of Knowledge Representation and Reasoning, Toulouse, France, April 22–25, 2002. Morgan Kaufmann Publ., 421–432.

    Google Scholar 

  • Benferhat S., Dubois D., Kaci S., Prade H. Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions. Inter. J. on Information Fusion, 7, 135-150, 2006.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D., Prade H., Smets P. Not impossible vs. guaranteed possible in fusion and revision. Proc. 6th.European Conf. (ESCQARU 2001), Toulouse, France, Sept. 19–21, 2001. Springer-Verlag, LNAI 2143, 522–531.

    Google Scholar 

  • Kaci S., van der Torre L. Algorithms for a nonmonotonic logic of preferences. Proc. 8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU’05), 281–292, 2005.

    Google Scholar 

Possibilistic Temporal Reasoning

  • Dubois D., Hadj Ali A., Prade H. Fuzziness and uncertainty in temporal reasoning. J. of Universal Computer Science, 9, 1168–1194, 2003.

    MathSciNet  Google Scholar 

  • Hadj Ali A., Dubois D., Prade H. A possibility theory-based approach to the handling of uncertain relations between temporal points. Proc. of the 11th Inter. Symp. on Temporal Representation and Reasoning (TIME’04), Tatihou Island, France, July1-3, 2004, IEEE, 36-43. Revised version in Int. J. of Intelligent Systems, to appear

    Google Scholar 

Possibilistic Approximate Reasoning

  • Dubois D., Prade H. What are fuzzy rules and how to use them. Fuzzy Sets and Systems, 84, 169–185, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D., Prade H. Bipolarity in possibilistic logic and fuzzy rules. Proc. 29th Conf. on Current Trends in Theory and Practice of Informatics (SOFSEM 2002), Milovy, Czech Republic, Nov. 22 -29, 2002. LNCS 2540, Springer, 168–173.

    Google Scholar 

  • Dubois D., Prade H., Ughetto L. A new perspective on reasoning with fuzzy rules. Inter. J. of Intelligent Systems, 18 , 541–567, 2003.

    Article  MATH  Google Scholar 

  • Ughetto L., Dubois D., Prade H. Implicative and conjunctive fuzzy rules- A tool for reasoning from knowledge and examples. Proc. National Conference in Articial Intelligence (AAAI-99), Orlando, Florida, July 18-22, 1999, AAAI Press/The MIT Press, 214–219.

    Google Scholar 

Possibilistic Case-based Reasoning

  • Dubois D., Hüllermeier E., Prade H. Fuzzy set-based methods in instance-based reasoning. IEEE Trans. on Fuzzy Systems, 10, 322–332, 2002.

    Article  Google Scholar 

  • Dubois D., Hüllermeier E., Prade H. Fuzzy methods for case-based recommendation and decision support. J. of Intelligent Information Systems, to appear

    Google Scholar 

  • Hüllermeier E., Dubois D., Prade H. Model adaptation in possibilistic instance-based reasoning. IEEE Trans. on Fuzzy Systems, 10, 333–339, 2002.

    Article  Google Scholar 

Flexible Querying and Possibilistic Data

  • De Calmès M., Prade H., Sedes F. Flexible querying of semi-structured data: a fuzzy set-based approach. Inter. J. of Intelligent Systems, to appear, 2006.

    Google Scholar 

  • G., De Caluwe R., Prade H. Null values revisited in prospect of data integration. In: Semantics of a Networked World (First International IFIP conference, ICSNW 2004), Springer Verlag, LNCS 3226, Paris, (M. Bouzeghoub, C. Goble, V. Kashyap, S. Spaccapietra, eds.), 79–90.

    Google Scholar 

  • Dubois D., Prade H. Bipolarity in flexible querying. Proc. 5th Int. Conf. Flexible Query Answering Systems (FQAS’02), Copenhagen, Denmark, Oct. 27–29, 2002, LNAI, 2522, Springer-Verlag, 174–182.

    Google Scholar 

  • Loiseau Y., Prade H., Boughanem M. Qualitative pattern matching with linguistic terms. AI Communication, 17 (1), 25–34, 2004.

    MATH  MathSciNet  Google Scholar 

Possibilistic Decision and Related Topics

  • Amgoud L., Prade H. Towards argumentation-based decision making: A possibilistic logic approach. Proc. IEEE Int. Conf. on Fuzzy Systems, Budapest, July 25–29, 2004, 1531–1536.

    Google Scholar 

  • Amgoud L., Prade H. Explaining qualitative decision under uncertainty by argumentation. Proc. 21st National Conference on Artificial Intelligence (AAAI-06), Boston, July 16–20, 2006

    Google Scholar 

  • Benferhat S., Dubois D., Fargier H., Prade H. Sabbadin R. Decision, nonmonotonic reasoning and possibilistic logic. In: Logic-Based Artificial Intelligence, (J. Minker, ed.), Kluwer Academic Publishers, 333–358, 2000.

    Google Scholar 

  • Da Costa Pereira C., Garcia F., Lang J., Martin-Clouaire R., Planning with graded nondeterministic actions: a possibilistic approach, Inter. J. of Intelligent Systems 12, 935–962, 1997.

    Article  Google Scholar 

  • de Mouzon O., Guérandel X., Dubois D., Prade H., Boverie S. Online possibilistic diagnosis based on expert knowledge for engine dyno test benches. Proc. of 18th IFIP World Computer Congress - Artificial Intelligence Applications and Innovations (AIAI ’04), Toulouse, France, Aug. 22–27, 2004, Kluwer, 435–448.

    Google Scholar 

  • Dubois D., Fargier H., Fortemps P. Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge. European J. of Operational Reasearch, 147, 231–252, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D., Fargier H., Perny P. Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approach. Artificial Intelligence, 148, 219–260, 2003.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Dubois D., Fargier H., Perny P., Prade H. Qualitative decision theory: From Savage’s axioms to nonmonotic reasoning. J. of the ACM, 49, 455–495, 2002.

    Article  MathSciNet  Google Scholar 

  • Dubois D., Fargier H., Perny P., Prade H.A characterization of generalized concordance rules in multicriteria decision making. Inter. J. of Intelligent Systems, 18, 751–774, 2003.

    Article  MATH  Google Scholar 

  • Dubois D., Godo L., Prade H., Zapico A. On the possibilistic decision model: from decision under uncertainty to case-based decision. Inter. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 7, 631–670, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D., Godo L., Prade H., Zapico A. Advances in qualitative decision theory: Refined rankings. Proc. of Int. Joint Conf. 7th Ibero-American Conference on AI and 15th Brazilian Symposium on AI (IBERAMIA-SBIA’00), Atibaia, Brazil, Springer Verlag, LNAI nˆ 1952, 427–436, 2000.

    Google Scholar 

  • Dubois D., Le Berre D., Prade H., Sabbadin R. Using possibilistic logic for modeling qualitative decision: ATMS-based algorithms. Fundamenta Informaticae, 37, 1–30, 1999.

    MATH  MathSciNet  Google Scholar 

  • Dubois D., Prade H. Sabbadin R. Decision-theoretic foundations of qualitative possibility theory. European J. of Operational Research, 128, 459–478, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  • Fargier H., Lamothe J. Handling soft constraints in hoist scheduling problems: the fuzzy approach. Engineering Applications of Artificial Intelligence, 14, 387–399, 2001.

    Article  Google Scholar 

  • Fargier H., Lang J., Sabbadin R. Towards qualitative approaches to multi-stage decision making. Inter. J. of Approximate Reasoning, 19, 441–471, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  • Fargier H., Lang J., Schiex T. Mixed constraint satisfaction: A framework for decision problems under incomplete knowledge. Proc. of the 13th National Conf. on Artificial Intelligence (AAAI’96), Portland, Oregon, AAAI Press and The MIT Press, USA, 175–180, Aug. 1996.

    Google Scholar 

  • Fargier H., Sabbadin R. Qualitative decision under uncertainty: back to expected utility. Artificial Intelligence, 164, 245–280, 2005.

    Article  MathSciNet  Google Scholar 

  • Garcia L., Sabbadin R. Possibilistic influence diagrams. Proc. 17th Europ. Conf. on Artificial Intelligence (ECAI’06),_ Riva del Garda, Italy, Aug. 28 - Sept. 1, 2006.

    Google Scholar 

  • Godo L., Zapico A. On the possibilistic-based decision model: Characterization of preference relations under partial inconsistency. Appl. Intell. 14 319–333 (2001)

    Article  MATH  Google Scholar 

  • Moura Pires J., Prade H. Flexibility as relaxation - the fuzzy set view. In: Soft Constraints: Theory and Practice (workshop associated to CP’00 - 6th Int. Conf. on Principles and Practice of Constraint Programming, Singapore, September 22, 2000.

    Google Scholar 

  • Sabbadin R. Empirical comparison of probabilistic and possibilistic Markov decision processes algorithms. ECAI 2000: 586–590.

    Google Scholar 

  • Sabbadin R. A possibilistic model for qualitative sequential decision problems under uncertainty in partially observable environments. UAI 1999: 567–574.

    Google Scholar 

  • Zapico A. Weakening commensurability hypothesis in possibilistic qualitative decision theory. Proc. IJCAI 2001: 717–722

    Google Scholar 

Possibilistic Learning

  • Prade H., Serrurier M. Version space learning for possibilistic hypotheses, Proc. 17th Europ. Conf. on Artificial Intelligence (ECAI’06),_ Riva del Garda, Italy, Aug. 28 - Sept. 1, 2006, 801–802.

    Google Scholar 

  • Sabbadin R. Towards possibilistic reinforcement learning algorithms. FUZZ-IEEE 2001: 404–407.

    Google Scholar 

  • Serrurier M., Prade H. Possibilistic inductive logic programming. Proc. Europ. Conf. on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU’05), LNAI 3571, Barcelone, July 6–8, 2005. (L. Godo, ed.), Springer-Verlag, 675–686.

    Google Scholar 

  • Serrurier M., Prade H. Coping with exceptions in multiclass ILP problems using possibilistic logic. Proc. of the 19th Inter. Joint Conf. on Artificial Intelligence (IJCAI ’05), Edinburgh, Scotland, July 30-Aug. 5, 2005, 1761–1762.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Dubois, D., Prade, H. (2008). Qualitative Possibility Theory in Information Processing. In: Forging New Frontiers: Fuzzy Pioneers II. Studies in Fuzziness and Soft Computing, vol 218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73185-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73185-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73184-9

  • Online ISBN: 978-3-540-73185-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics