On possibility theory, formal concept analysis and granulation: Survey

Applied and Computational Mathematics

Volumn 10, Issue 1, 2011, Pages 10-19

  Dubois, Didier ^a   Prade, Henri ^a  

^a UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Formal Concept Analysis; Granulation; Possibility Theory; Similarity Relations

Indexed keywords

EID: 79951646049     PISSN: 16833511     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. Assaghir, Z., Kaytoue, M. and Prade, H. A possibility theory-oriented discussion of conceptual pattern struc-tures, In A. Deshpande and A. Hunter, editors, Proc. 4th Inter. Conf. on Scalable Uncertainty Management (SUM'10), Toulouse, Sept. 27-29, V.6379 of LNAI, 2010, pp.70-83.
2. Bellman, R. E., Kalaba, R. and Zadeh, L.A. Abstraction and pattern classication, J. of Mathematical Analysis and Applications, V.13, 1966, pp.1-7.
3. Bellman, R. E. and Zadeh, L.A. Decision making in a fuzzy environment, Management Science, V.17, 1970, pp.B141-B164.
4. Bělohlávek, R. Fuzzy Galois connections, Math. Logic Quart, V.45, 1999, pp.497-504.
5. Benferhat, S., Dubois, D., Kaci, S. and Prade, H. Bipolar possibility theory in preference modeling: Repre-sentation, fusion and optimal solutions, Information Fusion, V.7, 2006, pp.135-150.
6. Carpineto, C. and Romano, G. GALOIS: An order-theoretic approach to conceptual clustering, Proc. of the Tenth Inter. Conf. on Machine Learning, Amherst, MA, June 27-29, Morgan Kaufmann Publ., 1993, pp.33-40.
7. Djouadi, Y., Dubois, D. and Prade, H. Possibility theory and formal concept analysis: Context decompositionand uncertainty handling. In E. Hüllermeier, R. Kruse, and F. Hoffmann, editors, Computational Intelligencefor Knowledge-Based Systems Design (IPMU 2010), V.6178 of LNCS, Springer, 2010, pp.260-269.
8. Dubois, D., Dupin de Saint Cyr, F. and Prade, H. A possibilty-theoretic view of formal concept analysis, Fundamenta Informaticae, V.75, N.1-4, 2007, pp.195-213.
9. Dubois, D. and Prade, H. Fuzzy sets and systems: theory and applications, Academic Press, New-York, 1980.
10. Dubois, D. and Prade, H. Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press, 1988.
11. Dubois, D. and Prade, H. Possibility theory as a basis for preference propagation in automated reasoning, In Proc. 1st IEEE Inter. Conf. on Fuzzy Systems 1992 (FUZZ-IEEE'92), San Diego, Ca., March 8-12, 1992, pp.821-832.
12. Dubois, D. and Prade, H. What are fuzzy rules and how to use them, Fuzzy Sets and Systems, V.84, 1996, pp.169-185.
13. Dubois, D. and Prade, H. The three semantics of fuzzy sets, Fuzzy Sets and Systems, V.90, 1997, pp.141-150.
14. Dubois, D. and Prade, H. Possibility theory: qualitative and quantitative aspects, In D. Gabbay and P. Smets, editors, Quantified Representation of Uncertainty and Imprecision, volume 1 of Handbook of Defeasible Reasoning and Uncertainty Management Systems, Kluwer Acad. Publ., 1998, pp.169-226.
15. Dubois, D. and Prade, H. Possibility theory, In R. Meyers, editor, Encyclopedia of Complexity and Systems Science, Springer, 2009, pp.6927-6939.
16. Dubois, D. and Prade, H. Possibility theory and formal concept analysis in information systems, In Proc. Inter. Fuzzy Systems Assoc. World Congress and Conf. of the Europ. Soc. for Fuzzy Logic and Technology (IFSA-EUSFLAT'09), Lisbon, July 20-24, 2009, pp.1021-1026.
17. Dubois, D. and Prade, H. Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets, Fuzzy Setsand Systems, 2011, (to appear).
18. Düntsch, I. and Gediga, G. Approximation operators in qualitative data analysis, In: Theory and Applicationof Relational Structures as Knowledge Instruments, 2003, pp.216-233.
19. Düntsch, I. and Orlowska, E. Mixing modal and sufficiency operators, Bulletin of the Section of Logic, Polish Academy of Sciences, V.28, N.2, 1999, pp.99-106.
20. Ganter, B. and Kuznetsov, S.O. Pattern structures and their projections, In ICCS'01: Proceedings of the9th International Conference on Conceptual Structures, Springer-Verlag, 2001, pp.129-142.
21. Ganter, B. and Wille, R. Formal Concept Analysis, Springer-Verlag, 1999.
22. Gaume, B., Navarro, E. and Prade, H. A parallel between extended formal concept analysis and bipartitegraphs analysis, In E. Hüllermeier, R. Kruse, and F. Hoffmann, editors, Computational Intelligence for Knowledge-Based Systems Design, Proc.13th Inter. Conf. on Information Processing and Management of Uncertainty (IPMU 2010), Dortmund, June 28 - July 2, V.6178 of LNCS, Springer, 2010, pp.270-280.
23. Georgescu, G. and Popescu, A. Non-dual fuzzy connections, Arch. Math. Log., V.43, N.8, 2004, pp.1009-1039.
24. Höhle, U. Quotients with respect to similarity relations, Fuzzy Sets and Systems, V.27, 1988, pp.31-44.
25. Höppner, F., Klawonn, F., Kruse, R. and Runkler, T. Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition, Wiley, New York, 1999.
26. Höppner, F., Klawonn, F. and Eklund, P. Learning indistinguishability from data, Soft Comput., V.6, 2002, pp.6-13.
27. Klawonn, F. Fuzzy points, fuzzy relations and fuzzy functions, In V. Novák and I. Perfilieva, editors, Discovering the World with Fuzzy Logic, Physica-Verlag, Heidelberg, 2000, pp.431-453.
28. Pawlak, Z. Rough sets. theoretical aspects of. reasoning about data, Kluwer Acad. Publ., Dordrecht, 1991.
29. Popescu, A. A general approach to fuzzy concepts. Mathematical Logic Quarterly, V.50, 2004, pp.265-280.
30. Recassens, J. Indistinguishabilty operators, modelling fuzzy equalities and fuzzy equivalence relations, Springer, Berlin, 2010.
31. Schaeffer, E. Graph clustering. Computer Science Review, V.1, 2007, pp.27-64.
32. Valverde, L. On the structure of F-indistinguishability operators, Fuzzy Sets and Systems, V.17, 1985, pp.313-328.
33. Yao, Y.Y. and Chen, Y. Rough set approximations in formal concept analysis, Transactions on Rough Sets V, LNCS 4100, 2006, pp.285-305.
34. Yao, Y.Y. A comparative study of formal concept analysis and rough set theory in data analysis. In Rough Sets and Current Trends in Computing, 4th International Conference, RSCTC 2004, Uppsala, Sweden, June1-5 2004, LNCS 3066, Springer, pp.59-68.
35. Zadeh, L.A. Fuzzy sets, Inform Control, V.8, 1965, pp.338-353.
36. Zadeh, L.A. Similarity relations and fuzzy orderings, Information Sciences, V.3, 1971, pp.177-200.
37. Zadeh, L.A. Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1978, pp.3-28.
38. Zadeh, L.A. Toward a theory of fuzzy information granulation and its centrality in human reasoning andfuzzy logic, Fuzzy Sets and Systems, V.90, 1997, pp.111-128.
39. Zadeh, L.A. Toward a generalized theory of uncertainty (GTU) - an outline, Information Sciences, V.172, 2005, pp.1-40.