SpringerLink
Log in

Fuzzy Geometric Programming: Past, Present, and Future

  • Conference paper
  • First Online:
Fuzzy Information and Engineering-2019

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1094))

Abstract

Cao first proposed the topic of fuzzy geometry programming since 1987, with its greatly developed in this field for 32 years. According to his previous researches, in the paper, he introduces its development process, aiming to promote this new branch, attracting scholars home and abroad to join in ranks of the research, and hel** to solve three conjectures of fuzzy geometric programming.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Cao, B.-Y.: Solution and theory of question for a kind of fuzzy positive geometric program. In: Proceedings of the 2nd IFSA Conference, Tokyo, Japan, vol. 1, pp. 205–208 (1987)

    Google Scholar 

  2. Cao, B.-Y.: Fuzzy geometric programming (I). Int. J. Fuzzy Sets Syst. 53(2), 135–154 (1993)

    Google Scholar 

  3. Cao, B.-Y.: Classification of fuzzy posynomial geometric programming and corresponding class properties. J. Fuzzy Syst. Math. 9(4), 60–64 (1995)

    Google Scholar 

  4. Cao, B.-Y.: Fuzzy geometric programming (II). J. Fuzzy Math. 4(1), 119–129 (1996)

    Google Scholar 

  5. Cao, B.-Y.: Primal algorithm of fuzzy posynomial geometric programming. In: Annual Conference of the North American Fuzzy Information Processing Society—NAFIPS, vol. 1, pp. 31–34 (2001)

    Google Scholar 

  6. Cao, B.-Y.: Antinomy in posynomial geometric programming. Adv. Syst. Sci. Appl. U.S.A. 4(1), 7–12 (2004)

    Google Scholar 

  7. Cao, B.-Y.: Lagrange problem in fuzzy reversed posynomial geometric programming. In: 2006, Fuzzy Systems and Knowledge Discovery—Second International Conference, FSKD 2005, Proceedings. Lecture Notes in Computer Science, LNAI, vol. 3614, pp. 546–550 (2005)

    Google Scholar 

  8. Yang, J.H., Cao, B.-Y.: The origin and its application of geometric programming. In: Proceedings of the Eighth National Conference of Operations Research Society of China, pp. 358–363. Global-Link Publishing Company, Hong Kong (2006). ISBN: 962-8286-09-9

    Google Scholar 

  9. Cao, B.-Y.: New proof to first dual theorem on fuzzy posynomial geometric programming. J. Fuzzy Math. 14(1), 1–14 (2006)

    Google Scholar 

  10. Cao, B.-Y.: Dual method to geometric programming with fuzzy variables. In: Advances in Intelligent and Soft Computing, vol. 62, pp. 1293–1301. Springer, Berlin (2009)

    Google Scholar 

  11. Cao, B.-Y.: The more-for-less paradox in fuzzy posynomial geometric programming. Inf. Sci. 211, 81–92 (2012)

    Google Scholar 

  12. Zahmatkesh, F., Cao, B.-Y.: On the fuzzy fractional posynomial geometric programming problems. In: Advances in Intelligent Systems and Computing, vol. 367, pp. 97–108 (2016)

    Google Scholar 

  13. Cao, B.-Y.: Posynomial geometry programming with L-R fuzzy coefficients. Int. J. Fuzzy Sets Syst. 67(3), 267–276 (1994)

    Google Scholar 

  14. Cao, B.-Y.: Research for a geometric programming model with T-fuzzy variations. J. Fuzzy Math. 5(3), 625–632 (1997)

    Google Scholar 

  15. Cao, B.-Y.: Multi-objective geometric programming with T-fuzzy variables. In: 22nd International Conference of NAFIPS Proceedings, pp. 456–461 (2003)

    Google Scholar 

  16. Cao, B.-Y.: Geometric programming with trapezoidal fuzzy variables. In: Annual Conference of the North American Fuzzy Information Processing Society-NAFIPS, vol. 2, pp. 826–831 (2004)

    Google Scholar 

  17. Cao, B.-Y.: Extension posynomial geometric programming. J. Guangdong Univ. Technol. 18(1), 61–64 (2001)

    Google Scholar 

  18. Cao, B.-Y.: Types of non-distinct multiobjective geometric programming. Hunan Ann. Math. 15(1), 99–106 (1995)

    Google Scholar 

  19. Verma, R.K.: Fuzzy geometric programming with several objective functions. Fuzzy Sets Syst. 35(1), 115–120 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  20. Biswal, M.P.: Fuzzy programming technique to solve multi-objective geometric programming problems. Fuzzy Sets Syst. 51(1), 67–71 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  21. Mandal, N.K., Roy, T.K., Maiti, M.: Multi-objective fuzzy inventory model with three constraints: a geometric programming approach. Fuzzy Sets Syst. 150(1), 87–106 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Cao, B.-Y.: Fuzzy geometric programming optimum seeking of scheme for waste-water disposal in power plant. In: Proceedings of the Fuzz-IEEE /IFES95 Conference, Yokohama, Japan, vol. 5, pp. 793–798 (1995)

    Google Scholar 

  23. Cao, B.-Y.: Fuzzy geometric programming optimum seeking in power supply radius of transformer substation. In: Proceedings of the Fuzz-IEEE99 Conference, Seoul, Korea, vol. 3, pp. 1749–1753 (1999)

    Google Scholar 

  24. Cao, B.-Y.: Reverse geometric programming with fuzzy coefficient and its application in chemical industry production cost analysis. In: IEEE International Conference on Fuzzy Systems, vol. 2, pp. 1311–1316 (2003)

    Google Scholar 

  25. Liu, S.-T.: Fuzzy geometric programming approach to a fuzzy machining economics model. Int. J. Prod. Res. 42(16), 3253–3269 (2004)

    Article  MATH  Google Scholar 

  26. Islam, S., Kumar, R.T.: A new fuzzy multi-objective programming: entropy based geometric programming and its application of transportation problems. Eur. J. Oper. Res. 173(2), 387–404 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. Cao, B.-Y.: Power supply radius optimized with fuzzy geometric program in substation. Fuzzy Optim. Decis. Making 5(2), 123–139 (2006)

    Google Scholar 

  28. Cao, B.-Y.: Fuzzy Geometric Programming. Kluwer Academic Publishers, Dordrecht (2001)

    Google Scholar 

  29. Cao, B.-Y.: Optimal Models and Methods with Fuzzy Quantity. Springer, Berlin (2010)

    Google Scholar 

  30. Cao, B.-Y.: Extensional positive geometric programming. J. Guangdong Univ. Technol. 18(1), 61–64 (2001)

    Google Scholar 

  31. Cao, B.-Y.: Multi-objective geometric programming with T-fuzzy variables. In: Annual Conference of the North American Fuzzy Information Processing Society—NAFIPS, vol. 2003, pp. 456–461, Jan 2003

    Google Scholar 

  32. Dang, L.: Study on the gery posynomial geometric programming. Chin. Q. J. Math. 20(1), 34–41 (2005)

    Google Scholar 

  33. Cao, B.-Y.: Rough posynomial geometric programming. Fuzzy Inf. Eng. 1(1), 37–57 (2009)

    Google Scholar 

  34. Kheiri, Z., Zahmatkesh, F., Cao, B.-Y.: A new ranking approach to fuzzy posynomial geometric programming with trapezoidal fuzzy number. In: Advances in Intelligent and Soft Computing. AISC, vol. 147, pp. 517–523 (2012)

    Google Scholar 

  35. Zahmatkesh, F., Cao, B.-Y.: On the solution of fractional geometric programming problem with fuzzy coefficient. In: 4th Iranian Joint Congress on Fuzzy and Intelligent Systems, CFIS 2015 (2015)

    Google Scholar 

  36. Burnwal, A.P., Mukherjee, S.N., Singh, D.: Fuzzy geometric programming with nonequivalent objectives. Ranchi Univ. Math. J. 27, 53–58 (1996)

    MathSciNet  MATH  Google Scholar 

  37. Yang, J.H., Cao, B.-Y.: Geometric programming with fuzzy relation equation constraints. In: Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 557–560 (2005)

    Google Scholar 

  38. Yang, J.-H., Cao, B.-Y.: Posynomial fuzzy relation geometric programming. In: 2007, IFSA 2007, Proceedings. Lecture Notes in Computer Science. LNAI, vol. 4529, pp. 563–572 (2007)

    Google Scholar 

  39. Yang, J., Cao, B.-Y.: Monomial geometric programming with fuzzy relation equation constraints. Fuzzy Optim. Decis. Making 6(4), 337–349 (2007)

    Google Scholar 

  40. Zhou, X., Cao, B.-Y.: Optimizing the geometric programming problem with single-term exponents subject to max-product fuzzy relational equation. In: Proceedings—5th International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2008, vol. 1, pp. 621–625 (2008)

    Google Scholar 

  41. Yang, X.-P., Zhou, X.-G., Cao, B.-Y.: Single-variable term semi-latticized fuzzy relation geometric programming with max-product operator. Inf. Sci. 325, 271–287 (2015)

    Google Scholar 

  42. Zhou, X.-G., Yang, X.-P., Cao, B.-Y.: Posynomial geometric programming problem subject to max-min fuzzy relation equations. Inf. Sci. 328, 15–25 (2016)

    Google Scholar 

  43. Yang, X.-P., Zhou, X.-G., Cao, B.-Y.: Min-max programming problem subject to addition-min fuzzy relation inequalities. IEEE Trans. Fuzzy Syst. 24(1), 111–119 (2016)

    Google Scholar 

  44. Zhou, X.-G., Cao, B.-Y., Yang, X.-P.: The set of optimal solutions of geometric programming problem with max-product fuzzy relational equations constraints. Int. J. Fuzzy Syst. 18(3), 436–447 (2016)

    Google Scholar 

  45. Zeinab, K., Cao, B.-Y.: Posynomial geometric programming with intuitionistic fuzzy coefficients. In: Advances in Intelligent Systems and Computing, vol. 367, pp. 15–30 (2016)

    Google Scholar 

  46. Qin, Z., Cao, B.-Y., Fang, S.-C.: Geometric programming with discrete variables subject to max-product fuzzy relation constraints. Discrete Dyn. Nat. Soc. 1610349 (2018)

    Google Scholar 

  47. Yang, X.-P., Lin, H.-T., Zhou, X.-G., Cao, B.-Y.: Addition-min fuzzy relation inequalities with application in BitTorrent-like Peer-to-Peer file sharing system. Fuzzy Sets Syst. 343, 126–140 (2018)

    Google Scholar 

  48. Yang, X.-P., Yuan, D.-H., Cao, B.-Y.: Lexicographic optimal solution of the multi-objective programming problem subject to max-product fuzzy relation inequalities. Fuzzy Sets Syst. 341, 92–112 (2018)

    Google Scholar 

  49. Cao, B.-Y.: Three guess of fuzzy geometric programming. In: Advances in Intelligent and Soft Computing, vol. 147, pp. 591–594. Springer, Berlin (2012)

    Google Scholar 

Download references

Acknowledgements

The work was supported by the Natural Science Foundation of Guangdong Province (No. 2016A030313552), the Innovation and Building Strong School Project of Colleges of Guangdong Province (2015KQNCX094) and Guangzhou Vocational College of Science and Technology (2016TD03).

Author information

Authors and Affiliations

  1. Guangzhou Vocational and Technical University of Science and Technology, Guangzhou, Guangdong, 510550, China

    Bing-yuan Cao & Pei-Hua Wang

  2. Foshan University, Foshan, Guangdong, 528000, China

    Bing-yuan Cao

Authors
  1. Bing-yuan Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pei-Hua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pei-Hua Wang .

Editor information

Editors and Affiliations

  1. Foshan University, Foshan, Guangdong, China

    Bing-yuan Cao

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cao, By., Wang, PH. (2020). Fuzzy Geometric Programming: Past, Present, and Future. In: Cao, By. (eds) Fuzzy Information and Engineering-2019. Advances in Intelligent Systems and Computing, vol 1094. Springer, Singapore. https://doi.org/10.1007/978-981-15-2459-2_11

Download citation

Publish with us

Policies and ethics

Search

Navigation