Sergei Ovchinnikov

List of Publications

Books

1. Limits, Moscow University Publications (1966) 60 pages (in Russian).
2. Arithmetic, Algebra, Geometry, and Trigonometry, Institute of Business and Economics Publications, Moscow (1977) 148 pages (with Carlos Vega, in Russian).
3. Media Theory, Springer (2008) (with David Eppstein and Jean-Claude Falmagne).
4. Graphs and Cubes, Springer (2011).

Editor

1. Theory of Measurement, by J.Pfanzagl, (Russian translation), Mir, Moscow, 1976.
2. Fuzzy Sets and Applications: Selected Papers by L.A. Zadeh, John Willey & Sons, 1987 (684 pages).

Papers

1. Positive-definite functions on Chevaley groups, Functional Analysis and Applications 5 (1971) 79-80.
2. Positive definite functions on Chevaley groups, Matematika Izv. VUZ'ov 8 (111) (1971) 77-87 (in Russian).
3. Optimal control with a quadratic payoff function, in: Works of CSRIIA 36 Moscow (1973) (in Russian).
4. Numerical data in geometric problems, Kvant 11 (1973) (in Russian).
5. Measurements in ordinal scales, Automation and Remote Control 35 (1974) 1797-1892 (with V.B. Kuz'min).
6. Geometry of preference spaces I, Automation and Remote Control 36 (1975) 2059-2063 (with V.B. Kuz'min).
7. A geometric approach to the treatment of data in ordinal scales, in: Topics in Quality Control (1975) Moscow, 188-204 (with V.B.Kuz'min, in Russian).
8. Geometry of preference spaces II, Automation and Remote Control 37 (1976) 110-113 (with V.B. Kuz'min).
9. Apriori models of preferences, in: Collected Papers of the Institute of Control Science 9 (1976), Moscow, 51-54 (in Russian).
10. Plane switching circuits, Kvant 1 (1976) 12-18 (in Russian).
11. On spaces of binary relations, in: Statistical Methods in Analysis of Expert Judgments, Nauka, Moscow (1977) 58-68 (in Russian).
12. Binary relation spaces, in: Research in Statistical Simulation, CIME, Moscow (1977) 131-135 (with V.B.Kuz'min, in Russian).
13. An incidence of points to lines and planes, Kvant 3 (1978), 48-53 (in Russian).
14. Construction of group decisions in a space of fuzzy binary relations, Voprosy Kibernetiki 58 (1979) 91-109 (in Russian, with Kuz'min ).
15. Absolute value inequalities, Kvant 2 (1979) 48-51 (in Russian).
16. Problems in 3D geometry, Kvant 6 (1979) (in Russian).
17. Maxima and minima of functions, Kvant 10 (1979) (in Russian).
18. Design of group decisions, in: Collected Papers of the Institute for System Studies, Issue 4, Moscow (1979) 28-37 (with V.B.Kuz'min, in Russian).
19. Group choice in spaces of binary relations, in: Topics in Cybernetics, Moscow (1979) (with V.B.Kuz'min, in Russian).
20. Group decisions I, Fuzzy Sets and Systems 4 (1980) 53-62 (with V.B. Kuz'min).
21. Group decisions II, Fuzzy Sets and Systems 4 (1980) 153- 165 (with V.B. Kuz'min).
22. Convexity in subsets of lattices, Stochastica IV (1980) 129-140.
23. Involutions in fuzzy set theory, Stochastica IV (1980) 227-231.
24. Convexity in subsets of lattices, Matematika Izv. VUZ'ov 2 (1980) 70-72 (in Russian).
25. Structure of fuzzy binary relations, Fuzzy Sets and Systems, 6 (1981) 169-195.
26. Optimization and choice based on ratio-scales, Proc. of IEEE 20th Conference on Decisions and Control, San Diego, December 1981, 1104-1109.
27. Representations of synonyms and antonyms in fuzzy set theory, Stochastica V (1981) 95-107.
28. On fuzzy classifications, in: Recent Development in Fuzzy Set and Possibility Theory, R.R.Yager (ed.), Pergamon Press, N.Y. (1982) 119-132 (with T. Riera).
29. Choice theory for cardinal scales, in: Fuzzy Information and Decision Processes, M.M.Gupta, E.Sanchez (eds.), North-Holland (1982) 323-336.
30. On fuzzy relational systems, Proc. of the 2nd World Conference on Mathematics at the Service of Man, Las Palmas, Spain, June-July 1982, 566-568.
31. General negations in fuzzy set theory, J. of Math. Analysis and Applications 92 (1983) 234-239.
32. Convex geometry and group choice, Mathematical Social Sciences, 5 (1983) 1-16.
33. Fuzzy choice functions, Fuzzy Information, Knowledge Representation and Decision Analysis, IFAC Symposium, Marseilles, France, 1983, 359-365.
34. On fuzzy binary relations, Stochastica VII (1983) 229- 242 (with T. Riera).
35. Representations of fuzzy symmetric relations, Proc. of FISAL-84, Porto Colon, Spain, 1984 (with L.Valverde).
36. Representations of transitive fuzzy relations, in: Aspects of Vagueness, H.Skala, S.Termini, E.Trillas (eds.), D.Reidel Publ. Co. (1984) 105-118.
37. Fuzzy choice functions, in: IFAC Proc. Series 6, IFAC, Laxenburg (1984) 369-374.
38. A stochastic model of choice, Stochastica IX (1985) 135-152.
39. Preference and choice in a fuzzy environment, Proc. of the 1st IFSA Congress, Mallorca, Spain, 1985
40. Tutorial on fuzzy logic in simulation, Proc. of 1985 Winter Simulation Conference, San Francisco, December 1985 (with M.L. McAllister and P. Adlasnik).
41. Representation theorems for probabilistic relations, Proc. of International Congress of Mathematicians, Berkeley, CA, 1986.
42. On the transitivity property, Fuzzy Sets and Systems 20 (1986) 241-243.
43. Preference and choice in a fuzzy environment, in: Optimization Models Using Fuzzy Sets and Possibility Theory, J.Kacprzyk, S.Orlovski (eds.), Verlag TUV Rheinland, Cologne, W.Germany (1987) 91-98.
44. On ranking fuzzy sets, Fuzzy Sets and Systems 24 (1987) 113-116 (with M. Migdal).
45. Using fuzzy binary relations for identifying noninferior decision alternatives, Fuzzy Sets and Systems 25 (1988) 21-32 (with V. Ozernoy).
46. On orderings of fuzzy numbers, in: Uncertainty and Intelligent Systems, B. Bouchon, L. Saitta, R. Yager (eds.), Lecture Notes in Computer Science 313 Springer-Verlag (1988) 79-86.
47. Identifying noninferior decision alternatives based on fuzzy binary relations, in: Non-Conventional Preference Relations in Decision Making, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag (1988) 82-95 (with V. Ozernoy).
48. Measurements in a fuzzy environment, Proc. of the Conference on Fuzzy Sets in Informatics, Moscow, USSR, 1988.
49. Survey of research on fuzzy sets in the Soviet Union, The Journal of Statistical Planning and Inference 20 (1989) 413-428.
50. Transitive fuzzy orderings of fuzzy numbers, Fuzzy Sets and Systems 30 (1989) 283-296.
51. Modeling valued preference relations, Proc. of the 19th International Symposium on Multiple-Valued Logic, China, May 1989, 82-87.
52. On modeling fuzzy transitive relations, Proc. of the European Congress on System Studies, Lausanne, Switzerland, October 3-6, 1989, vol.1, 413-420.
53. A fuzzy method for identifying nondominated alternatives in expert systems for multiple criteria decision making, in: Approximate Reasoning Tools for Artificial Intelligence, J.-L. Verdegay and M. Delgado (eds), Verlag TUV Rheinland (1990) 159-175 (with V. Ozernoy).
54. Means and social welfare functions in fuzzy binary relation spaces, in: Multiperson Decision Making Using Fuzzy Sets and Possibility Theory, J. Kacprzyk and M. Fedrizzi (eds.), Kluver Academic Publishers (1990), 143-154.
55. Modeling valued preference relations, in: Multiperson Decision Making Using Fuzzy Sets and Possibility Theory, J. Kacprzyk and M. Fedrizzi (eds.), Kluver Academic Publishers (1990), 64-70.
56. The duality principle in fuzzy set theory, Fuzzy Sets and Systems 42 (1991) 133-144.
57. On strict preference relations, Fuzzy Sets and Systems 43 (1991) 319-326 (with M. Roubens).
58. Social choice and Lukaciewicz logic, Fuzzy Sets and Systems 43 (1991) 275-289.
59. Similarity relations, fuzzy partitions, and fuzzy orderings, Fuzzy Sets and Systems 40 (1991) 107-126.
60. On fuzzy preference relations, International J. of Intelligent Systems 6 (1991) 225-234.
61. On modeling fuzzy preference relations, in: Uncertainty in Knowledge Bases, B. Bouchon-Meunier, R. Yager, and L. Zadeh (eds.), Lecture Notes in Computer Science, 521, Springer-Verlag (1991), 154-164.
62. Logicas y tecnologias fuzzy en los Estados Unidos, in: Aplicaciones de la Logica Borrosa, Consejo Superior de Investigaciones Cientificas, E. Trillas and J. G. Rios (eds.), Madrid (1992) 145-150. (in Spanish)
63. On aggregation of max-product transitive valued binary relations, Proceedings of IEEE International Conference on Fuzzy Systems, March 8-12, 1992, San Diego, California, 1245-1252.
64. Aggregating transitive fuzzy binary relations, Proceedings of IPMU'92, Mallorca, Spain, July 6-10 1992, 457-460.
65. On strict preference, idifference, and incomarabilty valued binary relations, Fuzzy Sets and Systems 47 (1992) 313-318.
66. On some bisymmetric functions on closed intervals, in: Estudios de Logica Borrosa y Aplicaciones, A. Sobrino and S. Barro (eds), Universidade de Santiago de Compostela (1993) 353-364.
67. On some fuzzy binary relations related to implication functions, in: Fuzzy Logic, State of the Art, R. Lowen and M. Roubens (eds.), Kluwer Academic Press (1993) 17-28.
68. Fuzzy sets and secure computer systems, Proc. of the New Security Paradigms Workshop, August 3 - 5, 1994, Little Compton, RI.
69. Fuzzy logic for computer security, Proc. of the Third Int. Workshop on Rough Sets and Soft Computing, November 10-12, 1994, San Jose, California (published by SIMULATION COUNCILS, INC. 1995), with H.H.Hosmer.
70. Aggregating transitive valued binary relations, Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 3 (1) 47-56 (1995)
71. On aggregation of T-transitive fuzzy binary relations, Fuzzy Sets and Systems 72 (1995) 135-145.
72. Continuous fuzzy groups, Fuzzy Sets and Systems 76(2) 253-258 (1995).
73. Meaningful means on ordered sets, in: Fuzzy Logic and Soft Computing, vol.4, World. Sci. Publishing, River Edge, NJ (1995) 189-193.
74. On robust fuzzy systems, Proc. Of the 1996 Biennial NAFIPS Conference, Berkeley, California, June 19-22, 182-183.
75. Modeling security systems in a fuzzy environment, Proc. of IPMU'96, Granada, Spain, July 1-5, 1996, 617-622.
76. Means on ordered sets, Mathematical Social Sciences 32 (1996) 39-56.
77. On the image of a fuzzy subgroup, Fuzzy Sets and Systems 81 (1996) 235-236.
78. Letter to the Editor, Fuzzy Sets and Systems 88 (1997) 264.
79. Problem 1535, Mathematics Magazine 70 no. 5, (1997) 381.
80. On robust means, Proc. International Conference on Fuzzy Logic and Applications, Zichron Yaakov, Israel, May 18-21, 1997, 35-38.
81. Problem Q881, Mathematics Magazine 71 no. 3, (1998) 226.
82. On robust aggregation procedures, in: B. Bouchon-Meunier (ed.) Aggregation and Fusion of Imperfect Information (Physic Verlag, 1998) 3-10.
83. An analytic characterization of some aggregation operators, Internationsl Journal of Intelligent Systems 13 (1998) 59-68.
84. On the image of L-fuzzy group, Fuzzy Sets and Systems 94 (1998) 129-131.
85. Invariant functions on simple orders, ORDER 14 (1998) 365-371.
86. Fuzzy relations, in: E. Ruspini, P. Bonissone, and W. Pedrycz (eds.) Handbook of Fuzzy Computing (Institute of Physics Publishing, Bristol and Philadelphia, 1998), B2.4:1 - B2.4:13.
87. Invariance properties of ordinal OWA operators, International Journal of Intelligent Systems 14 (1999) 413-418.
88. Invariance properties of OWA operators, in: B. Bouchon-Meunier, R. R. Yager and L.A. Zadeh (eds), Information, Uncertainty, Fusion (Kluwer Scientific Publishers, 1999) 319-330.
89. Introduction to fuzzy relations, in: D. Dubois and H. Prade (eds) Fundamentals of Fuzzy Sets (Kluwer Academic Publ., 2000), 233-259.
90. Integral representation of invariant functionals, J. of Math. Analysis and Appl. 244 (2000) 228-232 (with A. Dukhovny).
91. Advances in media theory, Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 8 (1) (2000) 45-72 (with A. Dukhovny)
92. Lattical token systems, MATHWARE 7(1) (2000) 29-34.
93. Topological automorphism groups of chains, MATHWARE 8(1) (2001) 47-60.
94. Universal metric spaces according to W. Holsztynski, e-print available at http://xxx.lanl.gov/abs/math.GN/0004091.
95. On ordered structures of scale type (N,N), J. of Math. Psychology 45 (2001) 913-916.
96. Boolean representation of manifolds and functions, J. of Math. Analysis and Appl. 263 (2001) 294-300.
97. Media theory, Discrete Applied Mathematics (with J.-Cl. Falmagne) 120 (2002) 83-101.
98. On order invariant aggregation functionals, J. of Math. Psychology (with A. Dukhovny) 46 (2002) 12-18.
99. Well graded spaces of valued relations, Discrete Mathematics 245 (2002) 217-233.
100. Numerical representations of transitive fuzzy relations, Fuzzy Sets and Systems 126 (2002) 225-232.
101. Families of valued sets as media (with A.Dukhovny), in: Technologies for Constracting Intelligent Systems, Springer-Verlag (2002) 205-212.
102. The lattice dimension of a tree, e-print available at http://arxiv.org/abs/math.CO/0402246.
103. Weak order complexes, e-print available at http://arxiv.org/abs/math.CO/0403191.
104. Max-Min representation of piecewise linear functions, Contributions to Algebra and Geometry 43 (2002) 297-302.
105. Piecewise linear aggregation functions, Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 10 (2002) 17-24
106. Families of valued sets as media, in: Technologies for Constructing Intelligent Systems, Springer-Verlag (2002), 205-212 (with A. Dukhovny)
107. Numerical representations of relational systems, in: Intelligent Systems for Information Processing, Elsevier (2003), 375-380.
108. Extensions of set functions, MATHWARE, Vol.X, n.1 (2003) 5 - 16.
109. Hyperplane arrangements in preference modelling, J. of Math. Psychology, 49 (2005) 481-488.
110. Homogeneity properties of some $\ell-1$-spaces , Discrete & Computational Geometry, 35 (2006) 301-310.
111. Decision making with ternary relations, in: B. Bouchon-Meunier, G. Coletti, and R.R. Yager (eds.) Modern Information Processing (Elsevier, 2006).
112. Metric geometry of hypercubes, MATHWARE, XIV, no.1 (2007), 23-33.
113. Primer on media theory, MATHWARE, XIV, no.2 (2007), 129-145.
114. Fundamentals of media theory, Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 15 (2007), 649-680.
115. Media theory - representations and examples, Discrete Applied Mathematics, 156 (2008), 1197-1219.
116. Representations of T-similarity relations, Fuzzy Sets and Systems, 159 (2008), 2211-2220.
117. Cubical token systems, Mathematical Social Sciences, 56 (2008) 149-165.
118. Partial cubes: structures and constructions, Discrete Mathematics, 308 (2008) 5597-5621.
119. Geometric representations of weak orders, in: Uncertainty and Intelligent Information Systems, B. Bouchon-Meunier, R.R. Yager, C. Marsala, and M. Rifqi eds, World Scientific Publishing Co Pte Ltd (Singapore) (2008), 447-456.
120. Mediatic Graphs, (with J.-Cl. Falmagne), in: The Mathematics of Preference, Choice and Order, S.J Brams, W.V. Gehrlein, F. Roberts eds, Springer (2009), 325-343.
121. Discrete piecewise linear functions, European Journal of Combinatorics, 91 (2010) 1283-1294.
122. Series with inverse function terms, The College Mathematics Journal 42(4) (2011) 283-288.