FCT (project)

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The FCT project is an open project with the aim to formalize and advance formal fuzzy mathematics within a unified axiomatic framework, based on the methodology of Petr Hájek. Henkin-style higher-order fuzzy logic LPi, also known as Fuzzy Class Theory (or FCT), is proposed for the foundational theory.

Contents

People

People involved in the project are listed on this site under the category Category:FCT researchers. The category is intended to include all people who wrote at least one publication that employs or investigates FCT.

Publications

Full papers related to FCT are on this website categorized under Category:FCT publications. Besides being included in the category, they are listed below for easier reference. Extended abstracts related to FCT do not have individual entries and are only listed here.

Full papers

  • Běhounek L., Cintula P.: Fuzzy class theory. Fuzzy Sets and Systems 154(1): 34-55 (2005).

Extended abstracts

  • Běhounek L., Cintula P., Bodenhofer U., Saminger-Platz S., Sarkoci P.: On a graded notion of t-norm and dominance. In Proceedings of the 40th IEEE International Symposium on Multiple-Valued Logics (ISMVL 2010), pp. 73–76, Barcelona 2010. Preprint.
  • Běhounek L., Bodenhofer U., Cintula P., Saminger-Platz S.: Graded dominance. In E.P. Klement, S.E. Rodabaugh, L.N. Stout (eds.): Foundations of Lattice-Valued Mathematics with Applications to Algebra and Topology. Abstracts of the 29th Linz Seminar on Fuzzy Set Theory, pp. 11-14, Linz 2008. Preprint.
  • Běhounek L., Kroupa T.: Continuous relations over topological spaces in Fuzzy Class Theory. In E.P. Klement, S.E. Rodabaugh, L.N. Stout (eds.): Foundations of Lattice-Valued Mathematics with Applications to Algebra and Topology. Abstracts of the 29th Linz Seminar on Fuzzy Set Theory, pp. 15-18, Linz 2008. Preprint.
  • Běhounek L., Bodenhofer U., Cintula P.: Valverde-style representation results in a graded framework. In M. Štěpnička, V. Novák, U. Bodenhofer (eds.): New Dimensions in Fuzzy Logic and Related Technologies: Proceedings of the 5th Eusflat Conference, vol. I, pp. 153-160, University of Ostrava 2007. Preprint, conference volume online.
  • Běhounek L., Kroupa T.: Interior-based topology in Fuzzy Class Theory. In In M. Štěpnička, V. Novák, U. Bodenhofer (eds.): New Dimensions in Fuzzy Logic and Related Technologies: Proceedings of the 5th Eusflat Conference, vol. I, pp. 145-151, University of Ostrava 2007. Awarded the Distinguished Student Paper Award. Preprint, conference volume online.
  • Cintula P., Horčík R.: Fuzzy Class Theory: Some advanced topics. In M. Štěpnička, V. Novák, U. Bodenhofer (eds.): New Dimensions in Fuzzy Logic and Related Technologies: Proceedings of the 5th Eusflat Conference, vol. I, pp. 137-143, University of Ostrava 2007. Preprint, conference volume online.
  • Běhounek L., Kroupa T.: Topology in Fuzzy Class Theory: Basic notions. In P. Melin, O. Castillo, L.T. Aguilar, J. Kacprzyk, W. Pedrycz (eds.): Foundations of Fuzzy Logic and Soft Computing, pp. 513-522. Lecture Notes in Artificial Intelligence 4529 (IFSA 2007), Springer 2007. Preprint.
  • Běhounek L., Cintula P.: Features of mathematical theories in formal fuzzy logic. In P. Melin, O. Castillo, L.T. Aguilar, J. Kacprzyk, W. Pedrycz (eds.): Foundations of Fuzzy Logic and Soft Computing, pp. 523-532. Lecture Notes in Artificial Intelligence 4529 (IFSA 2007), Springer 2007. Preprint.
  • Běhounek L.: Dubois and Prade's fuzzy elements: A challenge for formal fuzzy logic. In S. Gottwald, P. Hájek, M. Ojeda-Aciego (eds.): LSC'06 Intl Conference on The Logic of Soft Computing & Workshop of the ERCIM Working Group on Soft Computing, pp. 90-95. Málaga 2006. Preprint.
  • Běhounek L., Daňková M.: Automated proofs for composition-based fuzzy relational notions. In S. Gottwald, P. Hajek, M. Ojeda-Aciego (eds.): LSC'06 Intl Conference on The Logic of Soft Computing & Workshop of the ERCIM Working Group on Soft Computing, pp. 96-102. Málaga 2006. Preprint.
  • Běhounek L.: Extensionality in graded properties of fuzzy relations. In Proceedings of the Eleventh International Conference IPMU 2006, pp. 1604-1611, Edition EDK, Paris 2006. Preprint.
  • Běhounek L.: Fuzzy MacNeille and Dedekind completions of crisp dense linear orderings. In F. Hakl (ed.): Doktorandský den '05, pp. 1-6. ICS AS CR & Matfyzpress, Prague 2005. Preprint.
  • Běhounek L.: Two notions of fuzzy lattice completion. In V. Novák, M. Štěpnička: International Conference The Logic of Soft Computing IV & 4th Workshop of the ERCIM Working Group on Soft Computing, pp. 22-24. Research report No. 77, Institute for Research and Application of Fuzzy Modeling, University of Ostrava, Ostrava 2005.
  • Běhounek L.: Towards a formal theory of fuzzy Dedekind reals. In E. Montseny, P. Sobrevilla (eds): Proceedings of the Joint 4th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) and the 11th Rencontres Francophones sur la Logique Floue et ses Applications (LFA), Barcelona, Spain, September 7-9, 2005,, pp. 949-954. Barcelona 2005. Preprint, conference volume online.
  • Cintula P.: Basics of a formal theory of fuzzy partitions. In E. Montseny, P. Sobrevilla (eds): Proceedings of the Joint 4th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) and the 11th Rencontres Francophones sur la Logique Floue et ses Applications (LFA), Barcelona, Spain, September 7-9, 2005, pp. 884-888. Barcelona 2005. Preprint, conference volume online.
  • Kroupa T.: Towards formal theory of measure on clans of fuzzy sets. In E. Montseny, P. Sobrevilla (eds): Proceedings of the Joint 4th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) and the 11th Rencontres Francophones sur la Logique Floue et ses Applications (LFA), Barcelona, Spain, September 7-9, 2005, pp. 351-356. Barcelona 2005. Preprint, conference volume online.
  • Běhounek L., Cintula P.: General logical formalism for fuzzy mathematics: methodology and apparatus. In Y. Liu, G. Chen, M. Ying (eds.): Fuzzy Logic, Soft Computing and Computational Intelligence: Eleventh International Fuzzy Systems Association World Congress, vol. 2, pp. 1233-1238. Tsinghua University Press & Springer, Beijing 2005. Awarded the Best Paper Award at the 11th IFSA World Congress, Beijing 2005. Preprint.
  • Běhounek L., Cintula P.: Fuzzy Class Theory as foundations for fuzzy mathematics. In Y. Liu, G. Chen, M. Ying (eds.): Fuzzy Logic, Soft Computing and Computational Intelligence: Eleventh International Fuzzy Systems Association World Congress, vol. 2, pp. 1227-1238. Tsinghua University Press & Springer, Beijing 2005. Preprint.
  • Bodenhofer U., Běhounek L., Cintula P.: Relations in higher-order fuzzy logic III. In S. Gottwald, P. Hájek, U. Hoehle, E.P. Klement (eds.): Fuzzy Logics and Related Structures: Abstracts of the 26th Linz Seminar on Fuzzy Set Theory, pp. 20-22, Johannes Kepler University, Linz 2005. The volume online.
  • Běhounek L., Cintula P.: Relations in higher-order fuzzy logic I, II. In S. Gottwald, P. Hájek, U. Hoehle, E.P. Klement (eds.): Fuzzy Logics and Related Structures: Abstracts of the 26th Linz Seminar on Fuzzy Set Theory, pp. 10-15, Johannes Kepler University, Linz 2005. The volume online.

Tools

  • The Bib file we use in our project (current version).
  • LaTeX macros we use for fuzzy mathematics (current version).

Presentations

Slides

  • Kroupa T.: Measures on MV-algebras. Seminar for Ph.D. Students at Dept. Math. Inf., University of Salerno, 8 June 2005.

Planned presentations

TBA

Past presentations

(Seminars and small workshops not listed.)

Conference Date Place Talk By
ISMVL 2010 2010 May 26–28 Barcelona, Spain On a graded notion of t-norm and dominance L. Běhounek, U. Bodenhofer, P. Cintula, S. Saminger-Platz, P. Sarkoci
Tenth International Conference on Fuzzy Set Theory and Applications (FSTA) 2010 Feb 1-5 Liptovský Ján, Slovakia Graded properties of t-norms L. Běhounek, U. Bodenhofer, P. Cintula, S. Saminger-Platz, P. Sarkoci
Graded properties of dominance L. Běhounek, U. Bodenhofer, P. Cintula, S. Saminger-Platz, P. Sarkoci
2009 EUSFLAT Conference 2009 Jul 20-24 Lisbon, Portugal Number-free mathematics based on t-norm fuzzy logic L. Běhounek
30th Linz Seminar in Fuzzy Set Theory 2009 Jan 3-7 Linz, Austria Fuzzy Class Theory: a state of the art (invited) P. Cintula
29th Linz Seminar on Fuzzy Set Theory 2008 Feb 12-16 Linz, Austria Continuous relations over topological spaces in Fuzzy Class Theory L. Běhounek, T. Kroupa
Graded dominance L. Běhounek, U. Bodenhofer, P. Cintula, S. Saminger-Platz
Interval analysis done in Fuzzy Class Theory R. Horčík
5th Conference of EUSFLAT (special session Axiomatic Fuzzy Mathematics) 2007 Sep 11-14 Ostrava, Czech Republic Fuzzy Class Theory: Some advanced topics P. Cintula, R. Horčík
Interior-based topology in Fuzzy Class Theory (Distinguished Student Paper Award) L. Běhounek, T. Kroupa
Valverde-style representation results in a graded framework L. Běhounek, U. Bodenhofer, P. Cintula
12th IFSA World Congress 2007 Jun 18-21 Cancún, Mexico Features of mathematical theories in formal fuzzy logic L. Běhounek, P. Cintula
Topology in Fuzzy Class Theory: Basic notions L. Běhounek, T. Kroupa
How to solve a system of linear equations with fuzzy numbers R. Horčík
The Logic of Soft Computing V and the 5th workshop of the ERCIM working group of Soft Computing 2006 Sep 13-15 Málaga, Spain Dubois and Prade's fuzzy elements: A challenge for formal fuzzy logic L. Běhounek
Automated proofs for composition-based fuzzy relational notions M. Daňková, L. Běhounek
11th International Conference IPMU 2006 Jul 2-7 Paris, France Extensionality in Graded Properties of Fuzzy Relations L. Běhounek
8th International Conference on Fuzzy Set Theory and Applications (FSTA) (special session Logical Foundations of Fuzzy Mathematics) 2006 Jan 31 - Feb 3 Liptovský Ján, Slovakia The apparatus of Fuzzy Class Theory (plenary) L. Běhounek, P. Cintula
Relation compositions in Fuzzy Class Theory L. Běhounek, M. Daňková
Formal theory of generalized fuzzy partitions P. Cintula
Note on constrained fuzzy arithmetic R. Horčík
Filters and ultrafilters in Fuzzy Class Theory: Basic concepts T. Kroupa, L. Běhounek
The Logic of Soft Computing IV 2005 Oct 5-7 Ostrava, Czech Republic Two notions of fuzzy lattice completion L. Běhounek
EUSFLAT-LFA 2005 Joint Conference 2005 Sep 7-9 Barcelona, Spain Towards formal theory of measure on clans of fuzzy sets T. Kroupa
Basics of a formal theory of fuzzy partitions P. Cintula
Towards a formal theory of fuzzy Dedekind reals L. Běhounek
11th IFSA World Congress 2005 Jul 28-31 Beijing, China Fuzzy Class Theory as foundations for fuzzy mathematics L. Běhounek, P. Cintula
General logical formalism for fuzzy mathematics: Methodology and apparatus (Best Paper Award)
26th Linz Seminar on Fuzzy Set Theory 2005 Feb 1-5 Linz, Austria Relations in higher-order fuzzy logic I, II, III L. Běhounek, U. Bodenhofer, P. Cintula
The Challenge of Semantics 2004 Jul 12-17 Vienna, Austria From fuzzy logic to fuzzy mathematics: A methodological manifesto L. Běhounek, P. Cintula
Fuzzy Intensional Semantics and Its Applications L. Běhounek
3rd ERCIM Workshop on Soft Computing 2004 Jul 13-15 Vienna, Austria Universal fuzzy type theory L. Běhounek, P. Cintula
Residuated Lattices and Many-Valued Logic 2004 Jun 2-5 Patras, Greece Intensional semantics of fuzzy logics L. Běhounek
The 7th International Conference on Fuzzy Sets Theory and Its Applications (FSTA) 2004 Jan 26-30 Liptovský Ján, Slovakia Class theory over LPi logic L. Běhounek, P. Cintula
8th Flemish-Polish Workshop on Adaptive and Erotetic Logics and Their Application to the Philosophy of Science (VlaPoLo) 2003 Nov 20-22 Zielona Góra, Poland Fuzzification of Groenendijk-Stokhof erotetic logic L. Běhounek

Awards

  • In 2005-2007, the project was supported by the junior research grant No. B100300502 Formal Theories of Mathematical Structures with Vagueness of the Grant Agency of the Academy of Sciences of the Czech Republic (team members: Petr Cintula, Tomáš Kroupa, Rostislav Horčík, Libor Běhounek).
  • The paper General logical formalism for fuzzy mathematics: methodology and apparatus (by Libor Běhounek and Petr Cintula), which describes the project, has been awarded the Best Paper Award at the 11th IFSA World Congress, Beijing 2005.
  • The paper Interior-based topology in Fuzzy Class Theory (by Libor Běhounek and Tomáš Kroupa) has been awarded the Distinguished Student Paper Award at the 5th Conference of EUSFLAT, Ostrava 2007.
  • In 2010-2012, part of the project is supported by Libor Běhounek's postdoctoral grant No. P103/10/P234 Logic-based Fuzzy Mathematics of the Czech Science Foundation.
  • In 2010, Libor Běhounek's dissertation Logical Foundations of Fuzzy Mathematics was awarded the annual Antonin Svoboda Prize for the best Czech PhD thesis in computer science by the Czech Society for Cybernetics and Informatics.