Skip to main content
SpringerLink
Log in

Bibliography

  • Chapter
Fuzzy Geometric Programming

Part of the book series: Applied Optimization ((APOP,volume 76))

  • 284 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. F. Arikan and Z. Güngör. An application of fuzzy goal programming to a multiobjective project network problem. International J. of Fuzzy Sets and Systems, 2001, 119: 49–58.

    Article  Google Scholar 

  2. P. Aliev, G. Mamedova, and R. Aliev. Fuzzy Sets Theory and Its Application. Talriz University Press, 1993.

    Google Scholar 

  3. K. Asai Writing, R.H. Zhao Translation. An Introduction to the Theory of Fuzzy Systems. Peking: Peking Norm. University Press, 1982.

    Google Scholar 

  4. M. Avriel. Nonlinear programming Analysis and Methods. Englewood Cliffs, New Jersey: Prentice Hall Co. Inc., 1976.

    MATH  Google Scholar 

  5. M. Avriel and A.C. Williams. Complementary geometric programming. SIAM J. Appl. Math., 1970, 19: 125–141.

    Article  MathSciNet  MATH  Google Scholar 

  6. M.P. Biwal. Fuzzy programming technique to solve multi-objective geometric programming problems. International J. of Fuzzy Sets and Systems, 1992, 51: 67–71.

    Article  Google Scholar 

  7. C.S. Beightler and D.T. Phillips. Applied Geometric Programming. New York: John Wiley and Sons, 1976.

    MATH  Google Scholar 

  8. M.S. Bazaraa and C.M. Shetty. Nonlinear Programming—Theory and Algorithms. New York: John Wiley and Sons, 1979.

    MATH  Google Scholar 

  9. W. Cai. The extension set and incompatible problem. J. of Scientific Exploration, 1983, 1: 81–93.

    Google Scholar 

  10. B.Y. Cao. Solution and theory of question for a kind of fuzzy positive geometric program. Proc. of 2nd IFSA Congress, 1987 July 20–July 25, Vol.1, Tokyo, 205–208.

    Google Scholar 

  11. B.Y. Cao. Solution and theorem of question for a kind of fuzzy positive geometric program. J. of Changsha Norm. Univ. of Water Resources and Electric Power (Natural Sci. Ed.), 1987, 2(4): 51–61).

    Google Scholar 

  12. B.Y. Cao. Study of fuzzy positive geometric programming dual form. Proc. 3rd IFSA Congress, 1989, August 6–August 11; Seattle. 775–778.

    Google Scholar 

  13. B.Y. Cao. Study on non-distinct self-regression forecast model. Kexue Tongbao, 1989, 34(17): 1291–1294.

    MathSciNet  Google Scholar 

  14. B.Y. Cao. Study for a kind of regression forecasting model with fuzzy datums. J. of Mathematical Statistics and Applied Probability, 1989, 4(2): 182–189.

    Google Scholar 

  15. B.Y. Cao. Study on non-distinct self-regression forecast model. Chinese Sci. Bull., 1990, 35(13): 1057–1062.

    MathSciNet  MATH  Google Scholar 

  16. B.Y. Cao. Extension convex set. Acta Science Naturalium Univ. Norm Hunanenist, 1990, 13(1): 18–24.

    MATH  Google Scholar 

  17. B.Y. Cao. A method of fuzzy set for studying linear programming “Contrary Theory”. J. Hunan Educational Institute, 1991, 9(2): 17–22.

    Google Scholar 

  18. B.Y. Cao. Further study of posynomial geometric programming with fuzzy coefficients. Mathematics Applicata, 1992, 5(4): 119–120.

    Google Scholar 

  19. B.Y. Cao. Another proof of fuzzy posynomial geometric programming dual theorem, BUSEFAL, 1996, Vol.66: 43–47.

    Google Scholar 

  20. B.Y. Cao, Chief Editor. Proceedings of the Results Congress on Fuzzy Sets and Systems. Changsha: Hunan Science Technology Press, 1992.

    Google Scholar 

  21. B.Y. Cao. Fuzzy geometric programming(I). International J. of Fuzzy Sets and Systems, 1993, 53: 135–153.

    Article  MATH  Google Scholar 

  22. B. Y. Cao. Input-output mathematical model with T-fuzzy data. International J. of Fuzzy Sets and Systems, 1993, 59: 15–23.

    Article  MATH  Google Scholar 

  23. B.Y. Cao. Extended fuzzy geometric programming. J. of Fuzzy Mathematics, 1993, 2: 285–293.

    Google Scholar 

  24. B.Y. Cao. Fuzzy strong dual results for fuzzy posynomial geometric programming. Proc. of 5th IFSA Congress, 1993, July 4–July 9, Seoul. 588–591.

    Google Scholar 

  25. B.Y. Cao. Posynomial geometric programming with L-R fuzzy coefficients. International Fuzzy Sets and Systems, 1994, 64: 267–276.

    Google Scholar 

  26. B.Y. Cao. Lecture in Economic Mathematics—Linear Programming and Fuzzy Mathematics. Tiangjing: Tiangjing Translating Press of Science and Technology, 1994.

    Google Scholar 

  27. B.Y. Cao. The study of geometric programming with (·, c)-fuzzy parameters. J. of Changsha Univ. of Electric Power (Natural Sci. Ed.), 1995, 1: 15–21.

    Google Scholar 

  28. B.Y. Cao. Fuzzy geometric programming optimum seeking of scheme for waste water disposal in power plant. Proc. of FUZZY-IEEE/IFES’95, 1995 August 22–August 25; Yokohama. 793–798.

    Google Scholar 

  29. B.Y. Cao. B.Y. Cao, Types of non-distinct multi-objective geometric programming. Hunan Annals of Mathematics, 1995, 15(1): 99–106.

    MathSciNet  Google Scholar 

  30. B.Y. Cao. Study of fuzzy positive geometric programming dual form. J. of Changsha Univ. of Electric Power (Natural Sci. Ed.), 1995, 10(4): 343–351.

    Google Scholar 

  31. B.Y. Cao. Classification of fuzzy posynomial geometric programming and corresponding class properties. J. of Fuzzy Systems and Mathematics, 1995, 9(4): 60–64.

    MATH  Google Scholar 

  32. B.Y. Cao. New model with T-fuzzy variable in linear programming. International Fuzzy Sets and Systems, 1996; 78: 289–292.

    Article  MATH  Google Scholar 

  33. B.Y. Cao Fuzzy geometric programming (II)—Fuzzy strong dual results for fuzzy posynomial geometric programming. J. of Fuzzy Mathematics, 1996, 4(1): 119–129.

    MATH  Google Scholar 

  34. B.Y. Cao. Research for a geometric programming model with T-fuzzy variable. J. of Fuzzy Mathematics, 1997, 5(3): 625–632.

    MATH  Google Scholar 

  35. B.Y. Cao. Fuzzy geometric programming optimum seeking of scheme for wastewater disposal in power plant. Systems Engineering—Theory & Practice, 1997, 5: 140–144.

    Google Scholar 

  36. B.Y. Cao. Further research of solution to fuzzy posynomial geometric programming. Academic Periodical Abstracts of China, 1998, 4(12): 1435–1437.

    Google Scholar 

  37. B.Y. Cao. “Advance in fuzzy geometric programming”. In: Popular Works by Centuries’ World Celebrities, Z. X. Man ed., U. S. World Celebrity Books LLC, California: World Science Press, 1998; 15–20.

    Google Scholar 

  38. B.Y. Cao. Fuzzy geometric programming optimum seeking in power supply radius of transformer substation. 1999 IEEE Int. Fuzzy Systems Conference Proceedings, 1999 July 25–July 29; Korea. 3: III-1749–1753.

    Google Scholar 

  39. B.Y. Cao. Research of posynomial geometric programming with flat fuzzy coefficients. J. of Shantou University (Natural Sci. Ed.), 2000, 15(1): 13–19.

    Google Scholar 

  40. B.Y. Cao. Primal algorithm of fuzzy posynomial geometric programming. Joint 9th IFSA World Congress and 20th NAFIPS International Conference Proceedings, July 25–July 28; Vancouver. 31–34, 2001.

    Google Scholar 

  41. B.Y. Cao. Model of fuzzy geometric programming in economical power supply radius and optimum seeking method. Engineer Sciences, 2001, 3: 52–55.

    Google Scholar 

  42. B.Y. Cao. Application of geometric programming and fuzzy geometric one with fuzzy coefficients in seeking power supply radius transformer substation. Systems Engineering—Theory & Practice, 2001, 21(7): 92–95.

    Google Scholar 

  43. B.Y. Cao. Extension posynomial geometric programming. J. of Guangdong University of Technology, 2001, 18(1): 61–64.

    Google Scholar 

  44. B.Y. Cao. Direct algorithm of fuzzy posynomial geometric programming. J. of Fuzzy Systems and Mathematics, 2001, 15(4): 81–86.

    Google Scholar 

  45. B.Y. Cao. Fuzzy reversed posynomial geometric programming and its dual form, update.

    Google Scholar 

  46. A. Charnes, S. Duffuaa, and M. Ryan. The more-for-less paradox in linear programming. European Journal of Operational Research, 1987, 31: 194–197.

    Article  MathSciNet  MATH  Google Scholar 

  47. S. Chants. The use of parametric programming in fuzzy linear programming. International J. of Fuzzy Sets and Systems, 1983, 11: 243–251.

    Article  Google Scholar 

  48. A. Charnes and D. Klingman. The more-for-less paradox in the distribution model. Cahiers de Center d’Etudes Recharche Operationelle, 1971, 13(1): 11–22.

    MathSciNet  MATH  Google Scholar 

  49. G.B. Dantzing. Linear Programming and Extensions. New Jersey: Princeton U.P., Princeton,1963.

    Google Scholar 

  50. P. Diamond. “Least squares fitting of several fuzzy data”. Proc. of IFSA Congress, 1987, July 20–July 25, Vol.1, Tokyo, pp. 329–332.

    MathSciNet  Google Scholar 

  51. R.J. Duffin and E.L. Peterson. Duality theory for geometric programming. SIAM J. Appl. Math., 1966, 14: 1307–1349.

    Article  MathSciNet  MATH  Google Scholar 

  52. R.J. Duffin and E.L. Peterson. Reversed geometric programming treated by harmonic means. Indiana Univ. Math. J., 1972; 22: 531–550.

    Article  MathSciNet  MATH  Google Scholar 

  53. R.J. Duffin and E.L. Peterson. Geometric programming with signomials. J. Optimization Theory Appl., 1973; 11: 3–35.

    Article  MathSciNet  MATH  Google Scholar 

  54. D. Dubois and H. Prade. Fuzzy Sets and Systems—Theory and Applications. New York: Academic Press, 1980.

    MATH  Google Scholar 

  55. R.J. Duffin, E.L. Peterson, and C. Zener. Geometric Programming: Theory and Applications. New York: John Wiley and Sons, 1967.

    Google Scholar 

  56. R.J. Duffin. Dual programs and minimum cost. SIAM J.Appl. Math., 1962, 10: 119–123.

    Article  MathSciNet  MATH  Google Scholar 

  57. R.J. Duffin. Cost minimization problems treated by geometric means. Operations Res., 1962, 10: 668–675.

    Article  MathSciNet  MATH  Google Scholar 

  58. R.J. Duffin. Linearizing geometric programs. SIAM. Review, 1970, 12: 211–227.

    Article  MathSciNet  MATH  Google Scholar 

  59. J.G. Ecker. Geometric programming. SIAM Review, 1980, 22(3): 338–362.

    Article  MathSciNet  MATH  Google Scholar 

  60. J.G. Eckerand and M. Kupferschmid. An ellipsoid algorithm for non-linear programming. Mathematical Programming, 1987, 27: 83–106.

    Article  Google Scholar 

  61. G. Finke. Aunified approach to reshipment, overshipmemt and post-optimization problems. Proceedings of the 8th IFIP Conference on Optimization Techniques, 1977, part 2: 201–208.

    Google Scholar 

  62. J.A. Goguen. L—fuzzy sets. J. Math. Anal Appl., 1967; 18: 145–174.

    Article  MathSciNet  MATH  Google Scholar 

  63. M.G. Guan and H.D. Zheng. Linear Programming. Jinan: Shandong Science Technology Press, 1983.

    Google Scholar 

  64. T.R. Jefferson and C.H. Scott. Avenues of geometric programming. New Zealand Operational Res., 1978, 6: 109–136.

    Google Scholar 

  65. J.C. Kuester and J.H. Mize. Optimization Techniques with Fortran. New York: McGraw-Hill, 1973.

    MATH  Google Scholar 

  66. Y. Lin. On “Contrary Theory” in general linear programming. Chinese J. of Operations Research, 1986, 5(1): 79–81.

    Google Scholar 

  67. T. León and V. Liern. A fuzzy method to repair infeasibility in linearly constrained problems. International J. of Fuzzy Sets and Systems, 2001, 122: 237–243.

    Article  MATH  Google Scholar 

  68. C.Z. Luo. The extension principle and fuzzy numbers (I). Fuzzy Mathematics, 1984, 4(3): 109–116.

    MathSciNet  Google Scholar 

  69. C.Z. Luo. The extension principle and fuzzy numbers (II). Fuzzy Mathematics, 1984, 4(4): 105–114.

    MathSciNet  Google Scholar 

  70. Lu Minggen, Wu Wangming. Interval value and derivate of fuzzy-valued function. J. Fuzzy Systems and Mathematics, 1992, 6 (Special Issue): 182–184.

    Google Scholar 

  71. Liu B.D., Zhao R.Q., Stochastic Programming and Fuzzy Programming. Peking: Tsinghua University Press, 1998.

    Google Scholar 

  72. O.L. Mangasarian. Uniqueness of solution in linear programming. Linear Algebra and Its Applications, 1979, 25: 151–162.

    Article  MathSciNet  MATH  Google Scholar 

  73. H.R. Maleki, M. Tata, M. Mashinchi. Linear programming with fuzzy variable. International J. of Fuzzy Sets and Systems, 2000, 109: 21–33.

    Article  MathSciNet  MATH  Google Scholar 

  74. C.V. Negoita and M. Sularia. Fuzzy linear programming and tolerance in planning. Econ. Comp. Econ. Cybernetic Stud. Res., 1976, 1: 613–615.

    MathSciNet  Google Scholar 

  75. M.M. Obrad. Mathematical dynamic model for long-term distribution system planning. IEEE Transaction on Power Systems, 1986, 1: 34–41.

    Google Scholar 

  76. L.D. Pascual and A. Ben-Israel. Vector-valued criteria in geometric programming. Operations Res., 1971, 19: 98–104.

    Article  MathSciNet  MATH  Google Scholar 

  77. E.L. Peterson. Geometric programming. SIAM Review, 1978, 18: 1–51.

    Article  Google Scholar 

  78. M.J. Rijckaert. Survey of programs in geometric programming. C.C.E.R.O., 1974, 16: 369–382.

    MathSciNet  MATH  Google Scholar 

  79. M. Roubens. “Inequality constraints between fuzzy numbers and their use in mathematical programming.” In Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertainty, Slowinski R. and Teghem J., eds, Dordrecht: Kluwer Academic Publishers, 1991, 321–330.

    Google Scholar 

  80. M. Roubens and J.J. Teghem. Comparison of methodologies for fuzzy and stochastic multi-objective programming. International J. of Fuzzy Sets and Systems, 1991, 42: 119–132.

    Article  MathSciNet  MATH  Google Scholar 

  81. G.Y. Shi. Algorithm and convergence about a general geometric programming. J. Dalian Institute Technol., 1981, 20: 19–25.

    Google Scholar 

  82. H. Tanaka and K. Asai. Fuzzy linear programming problem with fuzzy number. International J. of Fuzzy Sets and Systems, 1984, 13: 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  83. H. Tanaka, T. Okuda, and K. Asai. On fuzzy mathematical programming. J. Cybern., 1973, 3(4): 37–46.

    Article  MathSciNet  MATH  Google Scholar 

  84. J.L. Verdegay. A dual approach to solve the fuzzy linear programming problem. International J. of Fuzzy Sets and Systems, 1984, 14: 131–140.

    Article  MathSciNet  MATH  Google Scholar 

  85. R.K. Verma. Fuzzy geometric programming with several objective functions. International Fuzzy Sets and Systems, 1990, 35: 115–120.

    Article  MATH  Google Scholar 

  86. D.J. Wilde and C.S. Beightler. Foundations of Optimization. Englewood Cliffs, New Jersey: Prentice Hall Co. Inc., 1967, 76–109.

    MATH  Google Scholar 

  87. W.X. Xing and J.X. Xie. Modern Optimization for Calculation Method. Peking: Tsinghua Press, 1999.

    Google Scholar 

  88. F. Wu and Y.Y. Yuan. Geometric programming. Math. in Practice and Theory, 1982, 1–2: 46–63, 61–72, 60–80, 68–81.

    MathSciNet  Google Scholar 

  89. Y.Y. Yu, B.Y. Cao, and X.R. Li. “The application of geometric and fuzzy geometric programming in option of economic supply radius of transformer substations.” In: Proceedings of Int. Conference on Inform and Knowledge Engineering, K.Q. Zhou ed., Dalian, China: Dalian Maritime University Publishing House, August 21–August 25, 245–249, 1995. (or in Information Engineering, K.Q.Zhou ed., Harbin, China: Harbin Engineering University Press, 69–74, 1996.)

    Google Scholar 

  90. C.E. Yang, D.Y. Jin. The more-for-less paradox in linear programming and nonlinear programming. Systems Engineering, 1991, 9(2): 62–68.

    Google Scholar 

  91. Y.Y. Yu, X.Z. Wang, Y.W. Yang. Optimizational selection for substation feel economic radius. J. of Changsha Normal University of Water Resources and Electric Power, 1991, 6(1): 118–124.

    Google Scholar 

  92. Q.Y. Yang, Z.L. Zhang, M.Z. Yang. Transformer substation capacity dynamic optimizing in city power network planning. Proc. of Colleges and Univ. Speciality of Power System and Its Automation. The Third a Academic Annual Conference, Xian: Xian Jiao Tong Univ. Press, 1987, 7–11.

    Google Scholar 

  93. L.A. Zadeh. Fuzzy Sets. Inform. and Control., 1965, 8: 338–353.

    Article  MathSciNet  MATH  Google Scholar 

  94. L.A. Zadeh. Fuzzy sets and systems. Proc. of the Symposium on Systems Theory, NY: Polytechnic Press of Polytechnic Institute of Brooklyn, 1965.

    Google Scholar 

  95. C. Zener. A mathematical aid in optimizing engineering design. Proc. Nat. Acad. Sci. U.S.A., 1961; 47: 537–539.

    Article  MathSciNet  MATH  Google Scholar 

  96. H.-J. Zimmermann. Description and optimization of fuzzy systems. Internat. J. General Systems, 1976, 2: 209–215.

    Article  MATH  Google Scholar 

  97. H.-J. Zimmermann. Fuzzy programming and linear programming with several objective functions. International J. of Fuzzy Sets and Systems, 1978, 1: 45–55.

    Article  MATH  Google Scholar 

  98. H.-J. Zimmermann. Fuzzy Sets Theory and Its Application. Boston: Kluwer Academic Publishers, 1991.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department & Institute of Mathematics, Shantou University, Guangdong, P.R. China

    Bing-Yuan Cao

Authors
  1. Bing-Yuan Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Cao, BY. (2002). Bibliography. In: Fuzzy Geometric Programming. Applied Optimization, vol 76. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0009-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-0009-4_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-4884-9

  • Online ISBN: 978-1-4615-0009-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation