Sergei Ovchinnikov

**List of Publications**

**Books**

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

**Editor**

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

**Papers**

- Positive-definite functions on Chevaley
groups,
*Functional Analysis and Applications***5**(1971) 79-80. - Positive definite functions on Chevaley
groups,
*Matematika Izv. VUZ'ov***8**(111) (1971) 77-87 (in Russian). - Optimal control with a quadratic payoff
function, in:
*Works of CSRIIA***36**Moscow (1973) (in Russian). - Numerical data in geometric problems,
*Kvant***11**(1973) (in Russian). - Measurements in ordinal scales,
*Automation and Remote Control***35**(1974) 1797-1892 (with V.B. Kuz'min). - Geometry of preference spaces I,
*Automation and Remote Control***36**(1975) 2059-2063 (with V.B. Kuz'min). - 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). - Geometry of preference spaces II,
*Automation and Remote Control***37**(1976) 110-113 (with V.B. Kuz'min). - Apriori models of preferences, in:
*Collected Papers of the Institute of Control Science***9**(1976), Moscow, 51-54 (in Russian). - Plane switching circuits,
*Kvant***1**(1976) 12-18 (in Russian). - On spaces of binary relations, in:
*Statistical Methods in Analysis of Expert Judgments*, Nauka, Moscow (1977) 58-68 (in Russian). - Binary relation spaces, in:
*Research in Statistical Simulation*, CIME, Moscow (1977) 131-135 (with V.B.Kuz'min, in Russian). - An incidence of points to lines and
planes,
*Kvant***3**(1978), 48-53 (in Russian). - Construction of group decisions in a space
of fuzzy binary relations,
*Voprosy Kibernetiki***58**(1979) 91-109 (in Russian, with Kuz'min ). - Absolute value inequalities,
*Kvant***2**(1979) 48-51 (in Russian). - Problems in 3D geometry,
*Kvant***6**(1979) (in Russian). - Maxima and minima of functions,
*Kvant***10**(1979) (in Russian). - 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). - Group choice in spaces of binary
relations, in:
*Topics in Cybernetics*, Moscow (1979) (with V.B.Kuz'min, in Russian). - Group decisions I,
*Fuzzy Sets and Systems***4**(1980) 53-62 (with V.B. Kuz'min). - Group decisions II,
*Fuzzy Sets and Systems***4**(1980) 153- 165 (with V.B. Kuz'min). - Convexity in subsets of lattices,
*Stochastica***IV**(1980) 129-140. - Involutions in fuzzy set theory,
*Stochastica***IV**(1980) 227-231. - Convexity in subsets of lattices,
*Matematika Izv. VUZ'ov***2**(1980) 70-72 (in Russian). - Structure of fuzzy binary relations,
*Fuzzy Sets and Systems*,**6**(1981) 169-195. - Optimization and choice based on
ratio-scales,
*Proc. of IEEE 20th Conference on Decisions and Control*, San Diego, December 1981, 1104-1109. - Representations of synonyms and antonyms
in fuzzy set theory,
*Stochastica***V**(1981) 95-107. - 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). - Choice theory for cardinal scales, in:
*Fuzzy Information and Decision Processes*, M.M.Gupta, E.Sanchez (eds.), North-Holland (1982) 323-336. - 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. - General negations in fuzzy set theory,
*J. of Math. Analysis and Applications***92**(1983) 234-239. - Convex geometry and group choice,
*Mathematical Social Sciences*,**5**(1983) 1-16. - Fuzzy choice functions,
*Fuzzy Information, Knowledge Representation and Decision Analysis*, IFAC Symposium, Marseilles, France, 1983, 359-365. - On fuzzy binary relations,
*Stochastica***VII**(1983) 229- 242 (with T. Riera). - Representations of fuzzy symmetric
relations,
*Proc. of FISAL-84*, Porto Colon, Spain, 1984 (with L.Valverde). - Representations of transitive fuzzy
relations, in:
*Aspects of Vagueness*, H.Skala, S.Termini, E.Trillas (eds.), D.Reidel Publ. Co. (1984) 105-118. - Fuzzy choice functions, in:
*IFAC Proc. Series***6**, IFAC, Laxenburg (1984) 369-374. - A stochastic model of choice,
*Stochastica***IX**(1985) 135-152. - Preference and choice in a fuzzy
environment,
*Proc. of the 1st IFSA Congress*, Mallorca, Spain, 1985 - Tutorial on fuzzy logic in simulation,
*Proc. of 1985 Winter Simulation Conference*, San Francisco, December 1985 (with M.L. McAllister and P. Adlasnik). - Representation theorems for probabilistic
relations,
*Proc. of International Congress of Mathematicians*, Berkeley, CA, 1986. - On the transitivity property,
*Fuzzy Sets and Systems***20**(1986) 241-243. - 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. - On ranking fuzzy sets,
*Fuzzy Sets and Systems***24**(1987) 113-116 (with M. Migdal). - Using fuzzy binary relations for
identifying noninferior decision alternatives,
*Fuzzy Sets and Systems***25**(1988) 21-32 (with V. Ozernoy). - 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. - 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). - Measurements in a fuzzy environment,
*Proc. of the Conference on Fuzzy Sets in Informatics*, Moscow, USSR, 1988. - Survey of research on fuzzy sets in the
Soviet Union,
*The Journal of Statistical Planning and Inference***20**(1989) 413-428. - Transitive fuzzy orderings of fuzzy
numbers,
*Fuzzy Sets and Systems***30**(1989) 283-296. - Modeling valued preference relations,
*Proc. of the 19th International Symposium on Multiple-Valued Logic*, China, May 1989, 82-87. - On modeling fuzzy transitive relations,
*Proc. of the European Congress on System Studies*, Lausanne, Switzerland, October 3-6, 1989, vol.1, 413-420. - 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). - 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. - 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. - The duality principle in fuzzy set theory,
*Fuzzy Sets and Systems***42**(1991) 133-144. - On strict preference relations,
*Fuzzy Sets and Systems***43**(1991) 319-326 (with M. Roubens). - Social choice and Lukaciewicz logic,
*Fuzzy Sets and Systems***43**(1991) 275-289. - Similarity relations, fuzzy partitions,
and fuzzy orderings,
*Fuzzy Sets and Systems***40**(1991) 107-126. - On fuzzy preference relations,
*International J. of Intelligent Systems***6**(1991) 225-234. - 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. - 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) - 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. - Aggregating transitive fuzzy binary
relations,
*Proceedings of IPMU'92*, Mallorca, Spain, July 6-10 1992, 457-460. - On strict preference, idifference, and
incomarabilty valued binary relations,
*Fuzzy Sets and Systems***47**(1992) 313-318. - 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. - 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. - Fuzzy sets and secure computer systems,
*Proc. of the New Security Paradigms Workshop*, August 3 - 5, 1994, Little Compton, RI. - 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. - Aggregating transitive valued binary
relations,
*Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems***3**(1) 47-56 (1995) - On aggregation of T-transitive fuzzy
binary relations,
*Fuzzy Sets and Systems***72**(1995) 135-145. - Continuous fuzzy groups,
*Fuzzy Sets and Systems***76**(2) 253-258 (1995). - Meaningful means on ordered sets, in:
*Fuzzy Logic and Soft Computing*, vol.4, World. Sci. Publishing, River Edge, NJ (1995) 189-193. - On robust fuzzy systems,
*Proc. Of the 1996 Biennial NAFIPS Conference*, Berkeley, California, June 19-22, 182-183. - Modeling security systems in a fuzzy
environment,
*Proc. of IPMU'96*, Granada, Spain, July 1-5, 1996, 617-622. - Means on ordered sets,
*Mathematical Social Sciences***32**(1996) 39-56. - On the image of a fuzzy subgroup,
*Fuzzy Sets and Systems***81**(1996) 235-236. - Letter to the Editor,
*Fuzzy Sets and Systems***88**(1997) 264. - Problem 1535,
*Mathematics Magazine***70**no. 5, (1997) 381. - On robust means,
*Proc. International Conference on Fuzzy Logic and Applications*, Zichron Yaakov, Israel, May 18-21, 1997, 35-38. - Problem Q881,
*Mathematics Magazine***71**no. 3, (1998) 226. - On robust aggregation procedures, in: B.
Bouchon-Meunier (ed.)
*Aggregation and Fusion of Imperfect Information*(Physic Verlag, 1998) 3-10. - An analytic characterization of some
aggregation operators,
*Internationsl Journal of Intelligent Systems***13**(1998) 59-68. - On the image of L-fuzzy group,
*Fuzzy Sets and Systems***94**(1998) 129-131. - Invariant functions on simple orders,
*ORDER***14**(1998) 365-371. - 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. - Invariance properties of ordinal OWA
operators,
*International Journal of Intelligent Systems***14**(1999) 413-418. - 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. - Introduction to fuzzy relations, in: D.
Dubois and H. Prade (eds)
*Fundamentals of Fuzzy Sets*(Kluwer Academic Publ., 2000), 233-259. - Integral representation of invariant
functionals,
*J. of Math. Analysis and Appl.***244**(2000) 228-232 (with A. Dukhovny). - Advances in media theory,
*Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems***8**(1) (2000) 45-72 (with A. Dukhovny) - Lattical token systems,
*MATHWARE***7(1)**(2000) 29-34. - Topological automorphism groups of chains,
*MATHWARE***8(1)**(2001) 47-60. - Universal metric spaces according to W. Holsztynski, e-print available at http://xxx.lanl.gov/abs/math.GN/0004091.
- On ordered structures of scale type (N,N),
*J. of Math. Psychology***45**(2001) 913-916. - Boolean representation of manifolds and functions,
*J. of Math. Analysis and Appl.***263**(2001) 294-300. - Media theory,
*Discrete Applied Mathematics*(with J.-Cl. Falmagne)**120**(2002) 83-101. - On order invariant aggregation functionals,
*J. of Math. Psychology*(with A. Dukhovny)**46**(2002) 12-18. - Well graded spaces of valued relations,
*Discrete Mathematics***245**(2002) 217-233. - Numerical representations of transitive fuzzy relations,
*Fuzzy Sets and Systems***126**(2002) 225-232. - Families of valued sets as media (with A.Dukhovny), in:
*Technologies for Constracting Intelligent Systems*, Springer-Verlag (2002) 205-212. - The lattice dimension of a tree, e-print available at http://arxiv.org/abs/math.CO/0402246.
- Weak order complexes, e-print available at http://arxiv.org/abs/math.CO/0403191.
- Max-Min representation of piecewise linear
functions,
*Contributions to Algebra and Geometry***43**(2002) 297-302. - Piecewise linear aggregation
functions,
*Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems***10**(2002) 17-24 - Families of valued sets as media, in:
*Technologies for Constructing Intelligent Systems*, Springer-Verlag (2002), 205-212 (with A. Dukhovny) - Numerical representations of relational systems, in:
*Intelligent Systems for Information Processing*, Elsevier (2003), 375-380. - Extensions of set functions,
*MATHWARE*, Vol.X, n.1 (2003) 5 - 16. - Hyperplane arrangements in preference modelling,
*J. of Math. Psychology*, 49 (2005) 481-488. - Homogeneity properties of some $\ell-1$-spaces
,
*Discrete & Computational Geometry*,**35**(2006) 301-310. - Decision making with ternary relations, in: B. Bouchon-Meunier, G. Coletti, and R.R. Yager (eds.)
*Modern Information Processing*(Elsevier, 2006). - Metric geometry of hypercubes,
*MATHWARE*, XIV, no.1 (2007), 23-33. - Primer on media theory,
*MATHWARE*, XIV, no.2 (2007), 129-145. - Fundamentals of media theory,
*Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems*15 (2007), 649-680. - Media theory - representations and examples,
*Discrete Applied Mathematics*, 156 (2008), 1197-1219. - Representations of T-similarity relations,
*Fuzzy Sets and Systems*, 159 (2008), 2211-2220. - Cubical token systems,
*Mathematical Social Sciences*, 56 (2008) 149-165. - Partial cubes: structures and constructions,
*Discrete Mathematics*, 308 (2008) 5597-5621. - 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. - 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. - Discrete piecewise linear functions,
*European Journal of Combinatorics*, 91 (2010) 1283-1294. - Series with inverse function terms,
*The College Mathematics Journal*42(4) (2011) 283-288.

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