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2019 | 48 | 4 |

Tytuł artykułu

Many Faces of Lattice Tolerances

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Abstrakty

EN
Our aim is to overview and discuss some of the most popular approaches to the notion of a tolerance relation in algebraic structures with the special emphasis on lattices.

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Tom

48

Numer

4

Opis fizyczny

Daty

wydano
2019-12-31

Twórcy

  • Institute of Philosophy, Jan Długosz University of Częstochowa, Poland

Bibliografia

  • [1] M. Arbib, Tolerance automata, Kybernetika, Vol. 3 (1967), pp. 223–233.
  • [2] H. Poincaré (Author) and J. W. Bolduc (Translator), Mathematics and Science: Last essays (1913), Kessinger Publishing, 2010.
  • [3] H. J. Bandelt, Tolerance relations of lattices, Bulletin of the Australian Mathematical Society, Vol. 23 (1981), pp. 367–381. https://doi.org/10.1017/S0004972700007255
  • [4] I. Chajda, Algebraic Theory of Tolerance Relations, Univerzita Palackého Olomouc, Olomouc, 1991.
  • [5] I. Chajda, G. Czédli, and R. Halaš, Independent joins of tolerance factorable varieties, Algebra Universalis, Vol. 69 (2013), pp. 83–92. https://doi.org/10.1007/s00012-012-0213-0
  • [6] I. Chajda, G. Czédli, R. Halaš, and P. Lipparini, Tolerances as images of congruences in varieties defined by linear identities, Algebra Universalis, Vol. 69 (2013), pp. 167–169. https://doi.org/10.1007/s00012-013-0219-2
  • [7] I. Chajda and J. Duda, Blocks of binary relations, Annales Universitatis Scientiarium Budapestinensis, Sectio Mathematica, Vol. 13–14 (1979–1980), pp. 3–9.
  • [8] I. Chajda, J. Niederle, and B. Zelinka, On existence conditions for compatible tolerances, Czechoslovak Mathematical Journal, Vol. 2, (1976), pp. 304–311.
  • [9] I. Chajda and B. Zelinka, Lattices of tolerances, Časopis pro pěstování matematiky, Vol. 102 (1977), pp. 10–24.
  • [10] G. Czédli, Factor lattices by tolerances, Acta Scientiarum Mathematicarum (Szeged), Vol. 44 (1982), pp. 35–42.
  • [11] G. Czédli and G. Grätzer, Lattice tolerances and congruences, Algebra Universalis, Vol. 66 (2011), pp. 5–6. https://doi.org/10.1007/s00012-011-0139-y
  • [12] G. Czédli and E. W. Kiss, Varieties whose tolerances are homomorphic images of their congruences, Bulletin of the Australian Mathematical Society, Vol. 87 (2013), pp. 326–338. https://doi.org/10.1017/S0004972712000603
  • [13] A. Day and Ch. Herrmann, Gluings of modular lattices, Order, Vol. 5 (1988), pp. 85–101. https://doi.org/10.1007/BF00143900
  • [14] A. Day and B. Jónsson, Non-arguesian configurations and gluings of modular lattices, Algebra Universalis, Vol. 26 (1989), pp. 208–215. https://doi.org/10.1007/BF01236867
  • [15] R. P. Dilworth, Lattices with unique irreducible decompositions, Annals of Mathematics, Vol. 41, No. 2 (1940), pp. 771–777. https://doi.org/10.2307/1968857
  • [16] E. Fried and G. Grätzer, Notes on tolerance relations of lattices: A conjecture of R.N. McKenzie, Journal of Pure and Applied Algebra, Vol. 68 (1990), pp. 127–134. https://doi.org/10.1016/0022-4049(90)90138-8
  • [17] B. Ganter and R. Wille, Formal concept analysis. Mathematical Foundations, Springer–Verlag, 1999. https://doi.org/10.1007/978-3-642-59830-2
  • [18] G. Grätzer and G. H. Wenzel, Notes on tolerance relations on lattices, Acta Scientiarum Mathematicarum (Szeged), Vol. 54 (1990), pp. 229–240.
  • [19] J. Grygiel, The concept of gluing for lattices, Wydawnictwo WSP, Cz¸estochowa, 2004.
  • [20] J. Grygiel and S. Radeleczki, On the tolerance lattice of tolerance factors, Acta Mathematica Hungarica, Vol. 141, No. 3 (2013), pp. 220–237. https://doi.org/10.1007/s10474-013-0340-x
  • [21] Ch. Herrmann, S-verklebte Summen von Verbänden, Mathematische Zeitschrift, Vol. 130 (1973), pp. 255–274. https://doi.org/10.1007/BF01246623
  • [22] Ch. Herrmann, Alan Day’s work on modular and Arguesian lattices, Algebra Universalis, Vol. 34, No. 3 (1995), pp. 35–60. https://doi.org/10.1007/BF01200489
  • [23] D. Hobby and R. McKenzie, The Structure of Finite Algebras, volume 76 of Contemporary Mathematics, American Mathematical Society, 2000. http://dx.doi.org/10.1090/conm/076
  • [24] J. Järvinen and S. Radeleczki, Rough sets determined by tolerances, International Journal of Approximate Reasoning, Vol. 55, No. 6 (2014), pp. 1419–1438. https://doi.org/10.1016/j.ijar.2013.12.005
  • [25] B. Jónsson, Algebras whose congruence lattices are distributive, Mathematica Scandinavia, Vol. 21, No. 1 (1967), pp. 110–121. https://doi.org/10.7146/math.scand.a-10850
  • [26] J. F. Peters and P. Wasilewski, Tolerance spaces: Origins, theoretical aspects and applications, Information Sciences: Informatics and Computer Science, Intelligent Systems, Applications, Vol. 195 (2012), pp. 211–225. https://doi.org/10.1016/j.ins.2012.01.023
  • [27] J. Pogonowski, Tolerance spaces with applications to linguistics, Wydawnictwo Naukowe UAM, Poznan, 1983.
  • [28] J. A. Szrejder, Równosc, podobienstwo, porzadek, Wydawnictwa Naukowo-Techniczne, Warszawa, 1975.
  • [29] E. Ch. Zeeman, The topology of the brain and visual perception, [in:] M. K. Fort (ed.), Topology of 3-Manifolds and related topics, New Jersey, 1962.

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Bibliografia

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