How to Divide a Territory? A New Simple Differential Formalism for Optimization of Set Functions

International Journal of Intelligent Systems

Volumn 14, Issue 2-3, 1999, Pages 223-251

  Nguyen, Hung T ^a   Kreinovich, Vladik ^b  

^a NEW MEXICO STATE UNIVERSITY   (United States)

^b University of Texas at El Paso   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; FUNCTIONS; OPTIMIZATION; PROBLEM SOLVING;

SET FUNCTIONS; TERRITORIAL DIVISION PROBLEMS;

SET THEORY;

EID: 0033101186     PISSN: 08848173     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1098-111x(199903)14:3<223::aid-int1>3.0.co;2-7     Document Type: Article

References (70)

1. Garey, M.; Johnson, D. Computers and Intractability: A Guide to the Theory of NP-Completeness; Freeman, San Francisco, CA, 1979.
2. Papadimitriou, C. H. Computational Complexity; Addison-Wesley, San Diego, CA, 1994.
3. Kreinovich, V.; Lakeyev, A; Rohn, J.; Kahl, P. Computational Complexity and Feasibility of Data Processing and Interval Computations; Kluwer Academic: Dordrecht, 1997.
4. Pardalos, P. M. Complexity in Numerical Optimization; World Scientific, Singapore, 1993.
5. Vavasis, S. A. Nonlinear Optimization: Complexity Issues; Oxford Univ. Press: New York, 1991.
6. Feynman, R. P.; Leighton, R. B.; Sands, M. L. The Feynman Lectures On Physics; Addison-Wesley: Redwood City, CA, 1989.
7. Landau, L. D.; Lifschitz, E. M. The Classical Theory of Fields; Butterworth-Heinemanm: Oxford, U.K., 1987.
8. Sinyansky, V. I.; Stotsky, A. A.; Kreinovich, V. Y. In Radioastronomical Hardware Antennas and Methods. Proc. of the XIV USSR National Radioastronomical Conference, October 28-30, 1982; Armenian Academy of Sciences, Erevan; pp 246-247, in Russian.
9. Luce, D. R.; Raiffa, H. Games and Decisions, Introduction and Critical Survey; Wiley, New York, 1957.
10. Myerson, R. B. Game Theory Analysis of Conflict; Harvard Univ. Press: Cambridge, MA, 1991.
11. Goutsias, J.; Mahler, R. P. S.; Nguyen, H. T., Eds., Random Sets: Theory and Applications; Springer-Verlag: New York, 1997.
12. Aubin, J.-P. Mutational and Morphological Analysis, Birkhauser: Basel, 1998.
13. Delfour, M. C.; Zolesio, J.-P. Ann Mat Pura Appl (4), 1988, 151, 19-212.
14. Delfour, M. C.; Zolesio, J.-P. SIAM J Contr Optim 1988, 26(4), 834-862.
15. Delfour, M. C.; Zolesio, J.-P. In Analyse Non Linéaire; Attouch, H.; Aubin, J.-P.; Clarke, F.; Ekeland, I., Eds.; Gauthiei-Villars: Paris; C.R.M. Université de Montréal, 1989; pp 211-228.
16. Delfour, M. C.; Zolesio, J.-P. SIAM J Contr Optim 1991, 24(5), 835-883.
17. Delfour, M. C.; Zolesio, J.-P. Proc. IFIP Workshop on Boundary Control and Boundary Variation, Sophia Antipolis, June 1992.
18. Delfour, M. C.; Zolesio, J.-P. J Funct Anal 1994, 123, 129-201.
19. Delfour, M. C.; Zolesio, J.-P. J Differ Equ 1995, 119, 426-449.
20. Delfour, M. C.; Zolesio, J.-P. J Differ Equ 1996, 128, 125-167.
21. Delfour, M. C.; Zolesio, J.-P. J Funct Anal, to appear.
22. Delfour, M. C.; Zolesio, J.-P. Intrinsic Differential Geometry and Theory of Thin Shells; Scuola Normale di Pisa, to appear.
23. Doyen, L. Optimisation, Évolution et Contrôle de Formes, Thèse de l'Université de Paris-Dauphine, Paris, France 1993.
24. Doyen, L. Set-Valued Analysis 1993, 1, 289-303.
25. Doyen, L. SIAM J Contr Optim 1994, 32(6), 1621-1642.
26. Doyen, L. J Math Imaging Vis, to appear.
27. Doyen, L. J Math Anal Appl, to appear.
28. Doyen, L. Proc of IFIP Workshop Boundary Control, Centre de Mathématiques Appliquées, Ecole des Mines, Sophia-Antipolis, to appear.
29. Mattioli, J. In SPIE: Application of Artificial Neural Network; San Diego, CA, Society of Optical Engineers, July 11-16, 1993.
30. Mattioli, J. Thèse de l'Université de Paris-Dauphine, 1993.
31. Mattioli, J. Proc of the Conference on Mathematical Morphology and its Applications to Signal Processing, Barcelona, Spain, May 12-14, 1993.
32. Mattioli, J. Rev Tech Thomson-CSF 1993, 25(1), 281-303.
33. Mattioli, J. CR Acad Sci Paris 1993, 316, 879-884.
34. Mattioli, J. Set-Valued Analysis, to appear.
35. Sokolowski, J.; Zolesio, J.-P. Introduction to Shape Optimization; Springer-Verlag: Berlin/New York, 1992.
36. Kosheleva, O. M.; Kreinovich, V. "On the Optimal Territory Division"; Technical Report, Leningrad Technological Center "Informatika"; Leningrad, 1989, in Russian.
37. Kreinovich, V. Proc of the 3rd USSR National Conference on Game Theory; Odessa, 1974; pp 117-118, in Russian.
38. Klir, G.; Yuan, B. Fuzzy Sets and Fuzzy Logic: Theory and Applications; Prentice-Hall: Englewood Cliffs, NJ, 1995.
39. Nguyen, H. T.; Walker, E. A. A First Course in Fuzzy Logic; CRC Press, Boca Raton, FL, 1997.
40. Gerald, C. F.; Wheatley, P. O. Applied Numerical Analysis; Addison-Wesley, Reading, MA, 1992.
41. Natanson, I. P. Theory of Functions of a Real Variable; Ungar: New York, 1961.
42. Hahn, H.; Rosenthal, A. Set Functions; Univ. of New Mexico Press: Albuquerque, NM, 1948.
43. Hayes, C. A.; Pauc, C. Y. Derivation and Martingales; Springer-Verlag: New York, 1970.
44. Shilov, G. E.; Gurevich, B. L. Integral, Measure, and Derivative: A Unified Approach; Dover: New York, 1977.
45. Száz, A. Tatra Mountains Math Publ 1993, 2, 167-174.
46. Lebesgue, H. Leçons sur l'Integration et la Recherche des Fonctions Primitives; Gauthier-Villars: Paris, 1904; 2nd ed., 1928.
47. Petrescu-Prodan, C. Stud Cere Mat 1992, 4(3), 253-259.
48. Tanaka, K.; Maruyama, Y. J Inform Optim Sci 1984, 5, 293-306.
49. Kendall, M. G.; Stuart, A. The Advanced Theory of Statistics; Griffin: London, 1961.
50. Lehmann, E. L. Testing Statistical Hypotheses; Wiley: New York, 1959.
51. Hartigan, J. A. J Amer Statist Assoc 1987, 82(397), 267-270.
52. Müller, D. W.; Sawitzki, G. Using Excess Mass Estimates to Investigate the Modality of a Distribution; University of Heidelberg, Preprint No. 398, SFB 123.
53. Nolan, D. J Multivariate Anal 1991, 39, 348-371.
54. Polonik, W. Ann Statist 1995, 23(3), 855-881.
55. Zakharevich, M. I. In Problems of Cybernetics; VINITI: Moscow, 1987; Vol. 131, pp 63-76, in Russian; English translation in Problems of Reducing the Exhaustive Search; Kreinovich, V.; Mints, G., Eds., Am Math Soc, Providence, RI, 1997; pp 53-64.
56. Zakharevich, M. I. In Problems of Cybernetics; VINITI: Moscow, 1987; Vol. 131, pp 63-76, in Russian; English translation in Problems of Reducing the Exhaustive Search; Kreinovich, V.; Mints, G., Eds., Am Math Soc, Providence, RI, 1997; pp 53-64.
57. Kreinovich, V. In Problems of Cybernetics, VINITI: Moscow, 1987, Vol. 131, pp 30-62, in Russian; English translation in Problems of Reducing the Exhaustive Search; Kreinovich, V.; Mints, G., Eds.; Am Math Soc: Providence, RI, 1997; pp 23-52.
58. Kreinovich, V. In Problems of Cybernetics, VINITI: Moscow, 1987, Vol. 131, pp 30-62, in Russian; English translation in Problems of Reducing the Exhaustive Search; Kreinovich, V.; Mints, G., Eds.; Am Math Soc: Providence, RI, 1997; pp 23-52.
59. Kreinovich, V. In Problems of Reducing the Exhaustive Search; Kreinovich, V.; Mints, G., Eds.; Am Math Soc: Providence, RI, 1997; pp 175-189.
60. Kreinovich, V.; Mints, G., Eds. Problems of Reducing the Exhaustive Search; Am Math Soc: Providence, RI, 1997.
61. Maslov, S. Y. Abstracts of the 9th All-Union Symposium on Cybernetics, 1981; pp 52-56, in Russian.
62. Maslov, S. Y. Semiotika i Informatika; VINITI: Moscow 1983; Vol. 20, pp 3-31, in Russian.
63. Maslov, S. Y. Theory of Deductive Systems and its Applications; MIT Press: Cambridge, MA, 1987.
64. Kreinovich, V.; Fuentes, L. O. In Proc of the World Congress on Expert Systems, Orlando, Florida, 1991; Liebowitz, J. Ed.; Pergamon Press: New York, Vol. 3; pp 1510-1517.
65. Sirisaengtaksin, O.; Fuentes, L. O.; Kreinovich, V. Proc of the First International Conference on Neural, Parallel, and Scientific Computations, Atlanta, GA, May 28-31, 1995; Vol. 1, pp 427-430.
66. Finkelstein, A.; Kosheleva, O.; Kreinovich, V. ACM SIGNUM Newslett 1996, 31(4), 3-25.
67. Finkelstein, A.; Kosheleva, O.; Kreinovich, V. Int J Theor Phys 1997, 36(4), 1009-1020.
68. Finkelstein, A.; Kosheleva, O.; Kreinovich, V. Geombinatorics, 1997, VI(4), 125-139.
69. Osegueda, R.; Ferregut, C.; George, M. J.; Gutierrez, J. M.; Kreinovich, V. Proc of the International Conference on Intelligent Systems and Semiotics (ISAS'97), National Institute of Standards and Technology Pub., Gaithersburg, MD, 1997; pp 378-382.
70. Osegueda, R.; Ferregut, C.; George, M. J.; Gutierrez, J. M.; Kreinovich, V. In Proc of the International Workshop on Intelligent NDE Sciences for Aging and Futuristic Aircraft, El Paso, TX; Ferregut, C.; Osegueda, R.; Nuñez, A., Eds.; Sept 30-Oct 2, 1997; pp 59-71.