Papers

Published papers


  1. A. Buikis and S. Solovyov, Influence of input data on the solution of the multiphase liquid flow model, Math. Model. Anal. 6 (2001), no. 1, 39-47.
  2. S. Solovjovs, Some remarks on the category SET(L), Acta Univ. Latv. 688 (2005), 83-97.
  3. S. Solovjovs, On fuzzification of algebraic and topological structures, Proceedings of the 5th EUSFLAT Conference (M. Stepnicka, V. Novak, and U. Bodenhofer, eds.), vol. II, University of Ostrava, 2007, pp. 395-401.
  4. S. Solovyov, On some properties of the forgetful functor U: SET(L)-->SET, Proc. Latv. Acad. Sci., Sect. B, Nat. Exact Appl. Sci. 57 (2003), 117-120.
  5. S. Solovyov, Some remarks on the category SET(L), part II, Mat. Vesn. 55 (2003), 65-82.
  6. S. Solovyov, Some remarks on the category SET(L), part III, Glas. Mat. 39 (2004), 1-20.
  7. S. Solovyov, Categories of lattice-valued sets as categories of arrows, Fuzzy Sets Syst. 157 (2006), no. 6, 843-854.
  8. S. Solovyov, On the category Set(JCPos), Fuzzy Sets Syst. 157 (2006), no. 3, 459-465.
  9. S. Solovyov, Completion of partially ordered sets, Discuss. Math., Gen. Algebra Appl. 27 (2007), 59-67.
  10. S. Solovyov, On a generalization of Goguen's category Set(L), Fuzzy Sets Syst. 158 (2007), no. 4, 367-385.
  11. S. Solovyov, Categorical frameworks for variable-basis sobriety and spatiality, Math. Stud. (Tartu) 4 (2008), 89-103.
  12. S. Solovyov, On coproducts of quantale algebras, Math. Stud. (Tartu) 3 (2008), 115-126.
  13. S. Solovyov, On the category Q-Mod, Algebra Univers. 58 (2008), no. 1, 35-58.
  14. S. Solovyov, A representation theorem for quantale algebras, Contr. Gen. Alg. 18 (2008), 189-198.
  15. S. Solovyov, Sobriety and spatiality in varieties of algebras, Fuzzy Sets Syst. 159 (2008), no. 19, 2567-2585.
  16. S. Solovyov, On ordered categories as a framework for fuzzification of algebraic and topological structures, Fuzzy Sets Syst. 160 (2009), no. 20, 2910-2925.
  17. S. Solovyov, Categorically-algebraic dualities, Acta Univ. M. Belii, Ser. Math. 17 (2010), 57-100.
  18. S. Solovyov, Categorically-algebraic frameworks for Priestley duality, Contr. Gen. Alg. 19 (2010), 187-208.
  19. S. Solovyov, From quantale algebroids to topological spaces: fixed- and variable-basis approaches, Fuzzy Sets Syst. 161 (2010), no. 9, 1270-1287.
  20. S. Solovyov, Hypergraph functor and attachment, Fuzzy Sets Syst. 161 (2010), no. 22, 2945-2961.
  21. S. Solovyov, On fuzzification of the notion of quantaloid, Kybernetika 46 (2010), no. 6, 1025-1048.
  22. S. Solovyov, On monadic quantale algebras: basic properties and representation theorems, Discuss. Math., Gen. Algebra Appl. 30 (2010), no. 1, 91-118.
  23. S. Solovyov, Variable-basis topological systems versus variable-basis topological spaces, Soft Comput. 14 (2010), no. 10, 1059-1068.
  24. S. Solovyov, Fuzzy algebras as a framework for fuzzy topology, Fuzzy Sets Syst. 173 (2011), no. 1, 81-99.
  25. S. Solovyov, Generalized fuzzy topology versus non-commutative topology, Fuzzy Sets Syst. 173 (2011), no. 1, 100-115.
  26. S. Solovyov, Localification of variable-basis topological systems, Quaest. Math. 34 (2011), no. 1, 11-33.
  27. S. Solovyov, A note on nuclei of quantale algebras, Bull. Sect. Logic 40 (2011), no. 1/2, 91-112.
  28. S. Solovyov, On a generalization of the concept of state property system, Soft Comput. 15 (2011), no. 12, 2467-2478.
  29. S. Solovyov, On algebraic and coalgebraic categories of variety-based topological systems, Iran. J. Fuzzy Syst. 8 (2011), no. 5, 13-30.
  30. S. Solovyov, On limits and colimits of variety-based topological systems, Fuzzy Sets Syst. 178 (2011), no. 1, 54-73.
  31. S. Solovyov, Powerset operator foundations for catalg fuzzy set theories, Iran. J. Fuzzy Syst. 8 (2011), no. 2, 1-46.
  32. S. Solovyov, Extended-order algebras as a generalization of posets, Demonstratio Math. 44 (2011), no. 3, 589-614.
  33. A. Frascella, C. Guido, and S. Solovyov, Dual attachment pairs in categorically-algebraic topology, Appl. Gen. Topol. 12 (2011), no. 2, 101-134.
  34. S. Solovyov, Categorical foundations of variety-based topology and topological systems, Fuzzy Sets Syst. 192 (2012), 176-200.
  35. S. Solovyov, On cartesian closed categories of modified weak extended-order algebras, Contr. Gen. Alg. 20 (2012), 85-100.
  36. S. Solovyov, Composite variety-based topological theories, Fuzzy Sets Syst. 195 (2012), 1-32.
  37. S. Solovyov, Sobriety and spatiality in categories of lattice-valued algebras, Fuzzy Sets Syst. 204 (2012), 1-26.
  38. S. Solovyov, Topological systems and Artin glueing, Math. Slovaca 62 (2012), no. 4, 647-688.
  39. S. Solovyov, Lattice-valued topological systems as a framework for lattice-valued Formal Concept Analysis, Journal of Mathematics 2013 (2013), Article ID 506275, 33 pages, http://dx.doi.org/10.1155/2013/506275
  40. A. Frascella, C. Guido, and S. Solovyov, Algebraically-topological systems and attachments, Iran. J. Fuzzy Syst. 10 (2013), no. 3, 65-102.
  41. S. Solovyov, Categorically-algebraic topology versus universal topology, Fuzzy Sets Syst. 227 (2013), 25-45.
  42. S. Solovyov, Lattice-valued soft algebras, Soft Comput. 17 (2013), no. 10, 1751-1766.
  43. S. Solovyov, On fuzzification of topological categories, Fuzzy Sets Syst. 238 (2014), 1-25.
  44. J. Paseka, S. Solovyov, and M. Stehlik, On the category of lattice-valued bornological vector spaces, J. Math. Anal. Appl. 419 (2014), no. 1, 138-155.
  45. C. Guido and S. Solovyov, Topological systems versus attachment relations, Quaest. Math. 37 (2014), no. 4, 455-484.
  46. S. Solovyov, Variable-basis categorically-algebraic dualities, Fuzzy Inf. Eng. 6 (2014), no. 4, 393-425.
  47. J. T. Denniston, A. Melton, S. E. Rodabaugh, and S. Solovyov, Lattice-valued preordered sets as lattice-valued topological systems, Fuzzy Sets Syst. 259 (2015), 89-110.
  48. J. Paseka, S. Solovyov, and M. Stehlik, Lattice-valued bornological systems, Fuzzy Sets Syst. 259 (2015), 68-88.
  49. S. Solovyov, On a lax-algebraic characterization of closed maps, Appl. Categ. Struct. 23 (2015), no. 3, 263-277.
  50. S. Solovyov, Categorically-algebraic topology and its applications, Iran. J. Fuzzy Syst. 12 (2015), no. 3, 57-94.
  51. S. Solovyov, Many for the price of one duality principle for affine sets, Appl. Categ. Struct. 23 (2015), no. 5, 643-663.
  52. S. Solovyov, Characterization of a category for monoidal topology, Algebra Univers. 74 (2015), no. 3, 389-410.
  53. S. Solovyov, Functorial semantics of topological theories, Iran. J. Fuzzy Syst. 12 (2015), no. 5, 1-43.
  54. S. Solovyov, Localification procedure for affine systems, Cah. Topol. Geom. Differ. Categ. 56 (2015), no. 2, 109-131.
  55. J. Paseka and S. Solovyov, Categorical foundations of variety-based bornology, Fuzzy Sets Syst. 291 (2016), 132-143.
  56. J. T. Denniston, A. Melton, S. E. Rodabaugh, and S. Solovyov, Topological systems as a framework for institutions, Fuzzy Sets Syst. 298 (2016), 91-108.
  57. J. Paseka, S. Solovyov, and M. Stehlik, On a topological universe of L-bornological spaces, Soft Comput. 20 (2016), no. 7, 2503-2512.
  58. S. Solovyov, On lax-algebraic (co)nuclei, Math. Appl. 5 (2016), 55-82.
  59. S. Solovyov, Quantale algebras as a generalization of lattice-valued frames, Hacet. J. Math. Stat. 45 (2016), no. 3, 781-809.

Published books


  1. S. Solovjovs, On a Categorical Generalization of the Concept of Fuzzy Set: Basic Definitions, Properties, Examples, VDM Verlag Dr. Muller, Germany, 2008 (updated version of the PhD Thesis published as a book).

Accepted papers


  1. J. T. Denniston, A. Melton, S. E. Rodabaugh, and S. Solovyov, Sierpinski object for affine systems, to appear in Fuzzy Sets Syst.

Submitted papers


  1. J. T. Denniston, A. Melton, S. E. Rodabaugh, and S. Solovyov, Relational topological spaces and topological systems, submitted.
  2. J. T. Denniston, A. Melton, S. E. Rodabaugh, and S. Solovyov, Classifying categories for many-valued mathematics and topological systems, submitted.