| Title of paper:
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Square and triangle: Reflections on two prominent mathematical structures for the representation of imprecision
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| Author(s):
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| Chris Cornelis
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| Department of Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling Research Unit, Krijgslaan 281 (S9), B-9000 Gent, Belgium
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| chris.cornelis@UGent.be
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| Glad Deschrijver
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| Department of Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling Research Unit, Krijgslaan 281 (S9), B-9000 Gent, Belgium
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| glad.deschrijver@UGent.be
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| Etienne E. Kerre
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| Department of Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling Research Unit, Krijgslaan 281 (S9), B-9000 Gent, Belgium
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| etienne.kerre@UGent.be
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| Presented at:
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Seventh International Conference on IFSs, Sofia, 23-24 August 2003
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| Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 9 (2003) Number 3, pages 11-21
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| Download:
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 PDF (6930 Kb, File info)
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| Abstract:
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In this paper, we study, from a predominantly syntactical viewpoint, some of the characteristics of and differences between the evaluation structures of intuitionistic fuzzy set theory ("triangle") and fuzzy four-valued or Belnap logic ("square").
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| References:
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- K. T. Atanassov, Intuitionistic Fuzzy Sets, Physica- Verlag, Heidelberg, New York, 1999.
- K. T. Atanassov, Remark on a property of the intuitionistic fuzzy interpretation triangle, Notes on Intuitionistic Fuzzy Sets 8, 2002, 34-36.
- N. Belnap, A Useful Four-Valued Logic, Modern Uses of Multiple-Valued Logics (D. Reidel, ed.), 1977, 8-37.
- C. Cornelis, G. Deschrijver, The Compositional Rule of Inference in an Intuitionistic Fuzzy Logic Framework, Proceedings of ESSLLI 2001 Student Session, (Kristina Striegnitz, ed.), Kluwer Academic Publishers, 2001, 83-94.
- C. Cornelis, G. Deschrijver, E. E. Kerre, Classification of Intuitionistic Fuzzy Implicators: an Algebraic Approach, Proceedings of 6th Joint Conference on Information Sciences (H. J. Caulfield, S. Chen, H. Chen, R. Duro, V. Honavar, E. E. Kerre, M. Lu, M. G. Romay, T. K. Shih, D. Ventura, P. P. Wang, Y. Yang, eds.), 2002, 105-108.
- C. Cornelis, E. E. Kerre, On the Structure and Interpretation of an Intuitionistic Fuzzy Expert System, Proceedings of EUROFUSE 2002 (B. De Baets, J. Fodor, G. Pasi, eds.), 2002, 173-178.
- B. De Baets, R. Mesiar, Triangular norms on product lattices, Fuzzy Sets and Systems 104, 1999, 61-75.
- G. Deschrijver, C. Cornelis, E. E. Kerre, Intuitionistic Fuzzy Connectives Revisited, Proceedings of 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2002, 1839-1844.
- G. Deschrijver, C. Cornelis, E. E. Kerre, On the Representation of Intuitionistic Fuzzy t-norms and t-conorms, IEEE Transactions on Fuzzy Systems, in press.
- G. Deschrijver, E. E. Kerre, On the Relationship Between Some Extensions of Fuzzy Set Theory. Fuzzy Sets and Systems, 133, 2003, 227-235.
- S. Jenei, B. De Baets, On the direct decomposability of t-norms on product lattices, Fuzzy Sets and Systems, in press.
- P. Smets, P. Magrez, Implication in Fuzzy Logic, International Journal of Approximate Reasoning, 1, 1987, 327-347.
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