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References

  1. Alcalde, C., Burusco, A., Díaz-Moreno, J.C. and Medina, J. (2017). Fuzzy concept lattices and fuzzy relation equations in the retrieval processing of images and signals, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems25(Supplement-1): 99–120.10.1142/s0218488517400050
  2. Benítez-Caballero, M.J., Medina, J., Ramírez-Poussa, E. and Ślęzak, D. (2020). A computational procedure for variable selection preserving different initial conditions, International Journal of Computer Mathematics97(1–2): 387–404.10.1080/00207160.2019.1613530
  3. Birkhoff, G. (1967). Lattice Theory, 3rd Edn, American Mathematical Society, Providence, RI.
  4. Bloch, I. (2000). On links between mathematical morphology and rough sets, Pattern Recognition33(9): 1487–1496.10.1016/S0031-3203(99)00129-6
  5. Bustince, H., Madrid, N. and Ojeda-Aciego, M. (2015). The notion of weak-contradiction: Definition and measures, IEEE Transactions on Fuzzy Systems23(4): 1057–1069.10.1109/TFUZZ.2014.2337934
  6. Cornejo, M.E., Díaz-Moreno, J.C. and Medina, J. (2017a). Multi-adjoint relation equations: A decision support system for fuzzy logic, International Journal of Intelligent Systems32(8): 778–800.10.1002/int.21889
  7. Cornejo, M.E., Lobo, D. and Medina, J. (2018a). Syntax and semantics of multi-adjoint normal logic programming, Fuzzy Sets and Systems345: 41–62, DOI: 10.1016/j.fss.2017.12.009.10.1016/j.fss.2017.12.009
  8. Cornejo, M.E., Medina, J. and Ramírez-Poussa, E. (2017b). Attribute and size reduction mechanisms in multi-adjoint concept lattices, Journal of Computational and Applied Mathematics318: 388–402.10.1016/j.cam.2016.07.012
  9. Cornejo, M.E., Medina, J. and Ramírez-Poussa, E. (2018b). Characterizing reducts in multi-adjoint concept lattices, Information Sciences422: 364–376.10.1016/j.ins.2017.08.099
  10. Cornelis, C., Medina, J. and Verbiest, N. (2014). Multi-adjoint fuzzy rough sets: Definition, properties and attribute selection, International Journal of Approximate Reasoning55(1): 412–426.10.1016/j.ijar.2013.09.007
  11. Couso, I. and Dubois, D. (2011). Rough sets, coverings and incomplete information, Fundamenta Informaticae108(3–4): 223–247.10.3233/FI-2011-421
  12. Davey, B. and Priestley, H. (2002). Introduction to Lattices and Order, 2nd Edn, Cambridge University Press, Cambridge.10.1017/CBO9780511809088
  13. Denecke, K., Erné, M. and Wismath, S.L. (Eds) (2004). Galois Connections and Applications, Kluwer Academic Publishers, Dordrecht.10.1007/978-1-4020-1898-5
  14. Di Nola, A., Sanchez, E., Pedrycz, W. and Sessa, S. (1989). Fuzzy Relation Equations and Their Applications to Knowledge Engineering, Kluwer Academic Publishers, Norwell, MA.10.1007/978-94-017-1650-5
  15. Díaz-Moreno, J.C. and Medina, J. (2013). Multi-adjoint relation equations: Definition, properties and solutions using concept lattices, Information Sciences253: 100–109.10.1016/j.ins.2013.07.024
  16. Díaz-Moreno, J.C., Medina, J. and Turunen, E. (2017). Minimal solutions of general fuzzy relation equations on linear carriers. An algebraic characterization, Fuzzy Sets and Systems311: 112–123.
  17. Ganter, B. and Wille, R. (1999). Formal Concept Analysis: Mathematical Foundation, Springer Verlag, Berlin.10.1007/978-3-642-59830-2
  18. Grant, J. and Hunter, A. (2006). Measuring inconsistency in knowledge bases, Journal of Intelligent Information Systems27(2): 159–184.10.1007/s10844-006-2974-4
  19. Hajek, P. (1998). Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht.10.1007/978-94-011-5300-3
  20. Han, S.-E. (2019). Roughness measures of locally finite covering rough sets, International Journal of Approximate Reasoning105: 368–385.10.1016/j.ijar.2018.12.003
  21. Hassanien, A.E., Abraham, A., Peters, J.F., Schaefer, G. and Henry, C. (2009). Rough sets and near sets in medical imaging: A review, IEEE Transactions on Information Technology in Biomedicine13(6): 955–968.10.1109/TITB.2009.201701719304490
  22. Hassanien, A.E., Schaefer, G. and Darwish, A. (2010). Computational intelligence in speech and audio processing: Recent advances, in X.-Z. Gao et al. (Eds), Soft Computing in Industrial Applications, Springer, Berlin/Heidelberg, pp. 303–311.10.1007/978-3-642-11282-9_32
  23. Järvinen, J., Radeleczki, S. and Veres, L. (2009). Rough sets determined by quasiorders, Order26(4): 337–355.10.1007/s11083-009-9130-z
  24. Kortelainen, J. (1994). On relationship between modified sets, topological spaces and rough sets, Fuzzy Sets and Systems61(1): 91–95.10.1016/0165-0114(94)90288-7
  25. Luo, C., Li, T., Chen, H., Fujita, H. and Yi, Z. (2018). Incremental rough set approach for hierarchical multicriteria classification, Information Sciences429: 72–87.10.1016/j.ins.2017.11.004
  26. Madrid, N. (2017). An extension of f-transforms to more general data: Potential applications, Soft Computing21(13): 3551–3565.10.1007/s00500-017-2622-7
  27. Madrid, N. and Ojeda-Aciego, M. (2011a). Measuring inconsistency in fuzzy answer set semantics, IEEE Transactions on Fuzzy Systems19(4): 605–622.10.1109/TFUZZ.2011.2114669
  28. Madrid, N. and Ojeda-Aciego, M. (2011b). On the existence and unicity of stable models in normal residuated logic programs, International Journal of Computer Mathematics89(3): 310–324.10.1080/00207160.2011.580842
  29. Madrid, N. and Ojeda-Aciego, M. (2017). A view of f-indexes of inclusion under different axiomatic definitions of fuzzy inclusion, in S. Moral et al. (Eds), Scalable Uncertainty Management, Springer, Cham, pp. 307–318.10.1007/978-3-319-67582-4_22
  30. Madrid, N., Ojeda-Aciego, M., Medina, J. and Perfilieva, I. (2019). L-fuzzy relational mathematical morphology based on adjoint triples, Information Sciences474: 75–89.10.1016/j.ins.2018.09.028
  31. Medina, J. (2012a). Multi-adjoint property-oriented and object-oriented concept lattices, Information Sciences190: 95–106.10.1016/j.ins.2011.11.016
  32. Medina, J. (2012b). Relating attribute reduction in formal, object-oriented and property-oriented concept lattices, Computers & Mathematics with Applications64(6): 1992–2002.10.1016/j.camwa.2012.03.087
  33. Medina, J. (2017). Minimal solutions of generalized fuzzy relational equations: Clarifications and corrections towards a more flexible setting, International Journal of Approximate Reasoning84: 33–38.10.1016/j.ijar.2017.02.002
  34. Medina, J., Ojeda-Aciego, M. and Ruiz-Calviño, J. (2009). Formal concept analysis via multi-adjoint concept lattices, Fuzzy Sets and Systems160(2): 130–144.10.1016/j.fss.2008.05.004
  35. Medina, J., Ojeda-Aciego, M. and Vojtáš, P. (2004). Similarity-based unification: A multi-adjoint approach, Fuzzy Sets and Systems146(1): 43–62.10.1016/j.fss.2003.11.005
  36. Novák, V., Mockor, J. and Perfilieva, I. (1999). Mathematical Principles of Fuzzy Logic, Kluwer, Boston, MA.10.1007/978-1-4615-5217-8
  37. Pagliani, P. (2014). The relational construction of conceptual patterns—Tools, implementation and theory, in M. Kryszkiewicz et al. (Eds), Rough Sets and Intelligent Systems Paradigms, Springer International Publishing, Cham, pp. 14–27.10.1007/978-3-319-08729-0_2
  38. Pagliani, P. (2016). Covering Rough Sets and Formal Topology—A Uniform Approach Through Intensional and Extensional Constructors, Springer, Berlin/Heidelberg, pp. 109–145.
  39. Pagliani, P. and Chakraborty, M. (2008). A Geometry of Approximation: Rough Set Theory Logic, Algebra and Topology of Conceptual Patterns (Trends in Logic), 1st Edn, Springer Publishing Company, Berlin/Heidelberg.10.1007/978-1-4020-8622-9
  40. Pawlak, Z. (1982). Rough sets, International Journal of Computer and Information Science11: 341–356.10.1007/BF01001956
  41. Pawlak, Z. (1991). Rough Sets—Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht.10.1007/978-94-011-3534-4_7
  42. Perfilieva, I. (2006). Fuzzy transforms: Theory and applications, Fuzzy Sets and Systems157(8): 993–1023.10.1016/j.fss.2005.11.012
  43. Perfilieva, I., Singh, A.P. and Tiwari, S.P. (2017). On the relationship among f-transform, fuzzy rough set and fuzzy topology, Soft Computing21(13): 3513–3523.10.1007/s00500-017-2559-x
  44. Ronse, C. and Heijmans, H.J.A.M. (1991). The algebraic basis of mathematical morphology. II: Openings and closings, CVGIP: Image Understanding54(1): 74–97.
  45. Sanchez, E. (1976). Resolution of composite fuzzy relation equations, Information and Control30(1): 38–48.10.1016/S0019-9958(76)90446-0
  46. Shao, M.-W., Liu, M. and Zhang, W.-X. (2007). Set approximations in fuzzy formal concept analysis, Fuzzy Sets and Systems158(23): 2627–2640.10.1016/j.fss.2007.05.002
  47. Skowron, A., Swiniarski, R. and Synak, P. (2004). Approximation spaces and information granulation, in S. Tsumoto et al. (Eds), Rough Sets and Current Trends in Computing, Springer, Berlin/Heidelberg, pp. 116–126.10.1007/978-3-540-25929-9_13
  48. Slowinski, R. and Vanderpooten, D. (1997). Similarity relation as a basis for rough approximations, in P.P.Wang (Ed.), Advances in Machine Intelligence and Soft Computing, Duke University, Durham, NC, pp. 17–33.
  49. Stell, J.G. (2007). Relations in mathematical morphology with applications to graphs and rough sets, in S. Winter et al. (Eds), Spatial Information Theory, Springer, Berlin, Heidelberg, pp. 438–454.10.1007/978-3-540-74788-8_27
  50. Tan, A., Wu, W.-Z. and Tao, Y. (2018). A unified framework for characterizing rough sets with evidence theory in various approximation spaces, Information Sciences454–455: 144–160.10.1016/j.ins.2018.04.073
  51. Varma, P.R.K., Kumari, V.V. and Kumar, S.S. (2015). A novel rough set attribute reduction based on ant colony optimisation, International Journal of Intelligent Systems Technologies and Applications14(3–4): 330–353.10.1504/IJISTA.2015.074333
  52. Wille, R. (1982). Restructuring lattice theory: An approach based on hierarchies of concepts, in I. Rival (Ed.), Ordered Sets, Reidel, Dordrecht, pp. 445–470.10.1007/978-94-009-7798-3_15
  53. Wille, R. (2005). Formal concept analysis as mathematical theory of concepts and concept hierarchies, in B. Ganter et al. (Eds), Formal Concept Analysis, Lecture Notes in Computer Science, Vol. 3626, Springer, Berlin/Heidelberg, pp. 1–33.10.1007/11528784_1
  54. Zakowski, W. (1983). Approximations in the space (u, π), Demonstratio Mathematica16(3): 761–769.10.1515/dema-1983-0319
  55. Yang, X., Li, T., Fujita, H., Liu, D. and Yao, Y. (2017). A unified model of sequential three-way decisions and multilevel incremental processing, Knowledge-Based Systems134: 172–188.10.1016/j.knosys.2017.07.031
  56. Yao, Y. (1998a). A comparative study of fuzzy sets and rough sets, Information Sciences109(1): 227–242.10.1016/S0020-0255(98)10023-3
  57. Yao, Y. (1998b). Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences111(1): 239–259.10.1016/S0020-0255(98)10006-3
  58. Yao, Y. (2018). Three-way decision and granular computing, International Journal of Approximate Reasoning103: 107–123.10.1016/j.ijar.2018.09.005
  59. Yao, Y. and Chen, Y. (2006). Rough set approximations in formal concept analysis, in J.F. Peters and A. Skowron (Eds), Transactions on Rough Sets V, Springer, Berlin/Heidelberg, pp. 285–305.10.1007/11847465_14
  60. Yao, Y. and Lingras, P. (1998). Interpretations of belief functions in the theory of rough sets, Information Sciences104(1): 81–106.10.1016/S0020-0255(97)00076-5
  61. Yao, Y.Y. (1996). Two views of the theory of rough sets in finite universes, International Journal of Approximate Reasoning15(4): 291–317.10.1016/S0888-613X(96)00071-0
  62. Yao, Y.Y. (2004). A comparative study of formal concept analysis and rough set theory in data analysis, in S. Tsumoto et al. (Eds), Rough Sets and Current Trends in Computing, Springer, Berlin/Heidelberg, pp. 59–68.10.1007/978-3-540-25929-9_6
  63. Yao, Y. and Yao, B. (2012). Covering based rough set approximations, Information Sciences200: 91–107.10.1016/j.ins.2012.02.065
  64. Zhang, Q., Xie, Q. and Wang, G. (2016). A survey on rough set theory and its applications, CAAI Transactions on Intelligence Technology1(4): 323–333.10.1016/j.trit.2016.11.001
  65. Zhu, W. (2007). Generalized rough sets based on relations, Information Sciences177(22): 4997–5011.10.1016/j.ins.2007.05.037
  66. Ziarko,W. (2008). Probabilistic approach to rough sets, International Journal of Approximate Reasoning49(2): 272–284.10.1016/j.ijar.2007.06.014
DOI: https://doi.org/10.34768/amcs-2020-0023 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 299 - 313
Submitted on: Jun 9, 2019
Accepted on: Feb 13, 2020
Published on: Jul 4, 2020
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2020 Nicolás Madrid, Jesús Medina, Eloísa Ramírez-Poussa, published by University of Zielona Góra
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