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Original Articles

Fuzzy modal-like approximation operators based on double residuated lattices

Pages 485-506 | Published online: 13 Apr 2012

References

  • BOIXADER , D. , JACAS , J. and RECASENS , J. 2000 . A new map closely related to the structure of a T-indistinguishability operator . Proceedings of the 8th International Conference on Information Processing and Management of Uncertainty in Knowledge–Based Systems IPMU'2000 . 2000 , Madrid , Spain. pp. 841 – 848 .
  • CHELLAS , B. F. 1980 . Modal Logic: An Introduction , Cambridge : Cambridge University Press .
  • DILWORTH , R. P. 1939 . Non-commutative residuated lattices . Transactions of the American Mathematical Society , 46 : 426 – 444 .
  • DILWORTH , R. P. and WARD , N. 1939 . Residuated lattices . Transactions of the American Mathematical Society , 45 : 335 – 354 .
  • DUBOIS , D. and PRADE , H. 1990 . Rough Fuzzy Sets and Fuzzy Rough Sets . Int. J. of General Systems , 17 ( 2–3 ) : 191 – 209 .
  • DUBOIS , D. and PRADE , H. 1992 . “ Putting fuzzy sets and rough sets together ” . In Intelligent Decision Support , Edited by: SŁOWIŃSKI , R. 203 – 232 . Kluwer Academic .
  • DUNTSCH , I. and GEDIGA , G. 2002 . “ Approximation operators in qualitative data analysis ” . In Theory and Application of Relational Structures as Knowledge Instruments, vol. 2929 of Lecture Notes in Computer Science , Edited by: DE SWART , H. C. M. , ORŁOWSKA , E. , SCHMIDT , G. and ROUBENS , M. 214 – 230 . Springer-Verlag .
  • DUNTSCH , I. and GEDIGA , G. 2002 . Modal-like operators in qualitative data analysis . Proceedings of the 2nd IEEE International Conference on Data Mining ICDM'2002 . 2002 , Maebashi City , Japan. pp. 155 – 162 .
  • ESTEVA , F. and GODO , L. 2001 . Monoidal t-norm based logic: towards a logic for leftcontinuous t-norms . Fuzzy Sets and Systems , 124 : 271 – 288 .
  • GOUGEN , J. A. 1967 . L-fuzzy sets . Journal of Mathematical Analysis and Applications , 18 : 145 – 174 .
  • HAJEK , P. 1998 . Metamathematics of Fuzzy Logics , Dordrecht : Kluwer .
  • HART , J. B. , RAFTER , L. and TSINAKSIS , C. 2001 . The structure of commutative residuated lattices . Internat. J. Algebra Comput. , 12 ( 4 ) : 509 – 524 .
  • HUMBERSTONE , I. 1983 . Inaccessible words . Notre Dame Journal of Formal Logic , 24 : 346 – 352 .
  • JIPSEN , P. and TSINAKIS , C. 2003 . “ A Survey of Residuated Lattices ” . In Ordered Algebraic Structures , Edited by: MARTINEZ , J. 19 – 56 . Dordrecht : Kluwer Academic Publishers .
  • KLIR , G. J. and YUAN , B. 1995 . Fuzzy Sets and Fuzzy Logic: Theory and Applications , Englewood Cliffs , NJ : Prentice-Hall .
  • NANDA , S. and MAJUMDAR , S. 1992 . Fuzzy rough sets . Fuzzy Sets and Systems , 45 : 157 – 160 .
  • ORŁOWSKA , E. , ed. 1998 . Incomplete Information: Rough Set Analysis , Springer-Verlag .
  • ORŁOWSKA , E. and RADZIKOWSKA , A. M. 2001 . Information relations and operators based on double residuated lattices . Proceedings of the 6th InternationalWorkshop on Relational Methods in Computer Science RelMiCS'01 . 2001 , Oisterwijk , The Netherlands. pp. 185 – 199 .
  • ORŁOWSKA , E. and RADZIKOWSKA , A. M. 2002 . “ Double residuated lattices and their applications ” . In RelationalMethods in Computer Science, vol. 2561 of Lecture Notes in Computer Science , Edited by: DE SWART , H. C. M. 171 – 189 . Heidelberg : Springer-Verlag .
  • PAL , S. K. and SKOWRON , A. 1999 . Rough Fuzzy Hybridization: A New Trend in Decision Making , Springer-Verlag .
  • PAWLAK , Z. 1982 . Rough sets . Int. Journal of Computer and Information Science , 11 ( 5 ) : 341 – 356 .
  • PAWLAK , Z. 1992 . Rough Sets–Theoretical Aspects of Reasoning about Data , Kluwer Academic Publishers .
  • RADZIKOWSKA , A. M. and KERRE , E. E. 2002 . A comparative study of fuzzy rough sets . Fuzzy Sets and Systems , 126 : 137 – 155 .
  • RADZIKOWSKA , A. M. and KERRE , E. E. 2002 . “ A fuzzy generalisation of information relations ” . In Beyond Two: Theory and Applications of Multiple-Valued Logics , Edited by: ORŁOWSKA , E. and FITTING , M. 264 – 290 . Springer-Verlag .
  • RADZIKOWSKA , A. M. and KERRE , E. E. 2004 . “ An Algebraic Approach to Fuzzy Modalities ” . In Issues in Soft Computing- Decisions and Operation Research , Edited by: HRYNIEWICZ , O. , KACPRZYK , J. and KUCHTA , D. 71 – 86 . Warsaw , , Poland : EXIT .
  • RADZIKOWSKA , A. M. and KERRE , E. E. 2004 . An algebraic characterisation of fuzzy rough sets . Proceedings of IEEE International Conference on Fuzzy Systems FUZZ– IEEE'2004 . 2004 , Budapest , Hungary. vol. 1 , pp. 115 – 120 .
  • RADZIKOWSKA , A. M. and KERRE , E. E. 2004 . “ Fuzzy Rough Sets based on Residuated Lattices ” . In Transactions on Rough Sets II: Rough Sets and Fuzzy Sets, vol. 3135 of Lecture Notes in Computer Science , Edited by: PETERS , J. F. , SKOWRON , A. , DUBOIS , D. , GRZYMAŁA-BUSSE , J. W. , INUIGUCHI , M. and POLKOWSKI , L. 278 – 296 . Springer-Verlag .
  • RADZIKOWSKA , A. M. and KERRE , E. E. 2004 . “ On L-valued fuzzy rough sets ” . In Artificial Intelligence and Soft Computing ICAISC-2004, vol. 3070 of Lecture Notes in Artificial Intelligence , Edited by: RUTKOWSKI , L. , SIEKMANN , J. , TADEUSIEWICZ , R. and ZADEH , L. A. 526 – 531 . Springer-Verlag .
  • RADZIKOWSKA , A. M. 2005 . “ A Fuzzy Approach to Some Set Approximation Operations ” . In Artificial Neural Networks: Formal Models and Their Applications–ICAAN 2005, vol. 3697 of Lecture Notes in Computer Science , Edited by: DUCH , W. , KACPRZYK , J. , OJA , E. and ZADROŻNY , S. 673 – 678 . Springer-Verlag .
  • RADZIKOWSKA , A. M. 2006 . Fuzzy Approximation Operations Based on Residuated Lattices . Proceedings of the 11th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU'2006 . 2006 , Paris , France. Vol. 1 , pp. 444 – 451 .
  • RASIOWA , H. and SIKORSKI , R. 1970 . The Mathematics of Metamathematics , 3rd edition , Warsaw , , Poland : Polish Scientific Publishers PWN .
  • RAUSZER , C. 1974 . Semi-Boolean algebras and their applications to intuitionistic logic with dual operations . Fundamenta Mathematicae , 83
  • SCHWEIZER , B. and SKLAR , A. 1983 . Probabilistic Metric Spaces North Holland Amsterdam
  • SKOWRON , A. and POLKOWSKI , L. 1998 . Rough Sets and Knowledge Discovery , Vol. 1–2 , Springer-Verlag .
  • SŁOWIŃ SKI , R. , ed. 1992 . Decision Support by Experience–Applications of the Rough Set Theory , Kluwer Academic Publishers .
  • SŁOWIŃSKI , R. and VANDERPOOTEN , D. 2000 . A generalised definition of rough approximations based on similarity . IEEE Transactions on Knowledge and Data Engineering , 12 : 331 – 336 .
  • THIELE , H. 1993 . On the definition of modal operators in fuzzy logic . Proceedings of International Symposium on Multiple-Valued Logics ISMVL'93 . 1993 , Sacramento , California , USA. pp. 62 – 67 .
  • TURUNEN , E. 1999 . Mathematics Behind Fuzzy Logics , Physica-Verlag .
  • ZADEH , L. A. 1965 . Fuzzy sets . Information and Control , 8 : 338 – 358 .
  • ZIARKO , W. P. , ed. 1994 . Rough Sets, Fuzzy Sets, and Knowledge Discovery , London : Springer-Verlag .

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