Skip to main content
SpringerLink
Log in

Operations Research

  • Chapter
Fuzzy Mathematics in Economics and Engineering

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 91))

  • 581 Accesses

Abstract

The applications of fuzzy sets and fuzzy logic to operations research has become a vast area of research. The journal of Operations Research [46] lists 51 major classifications for papers submitted for publication. Some of these major classifications, like “Programming”, has numerous secondary classifications. Obviously, we can cover only a few applications in this chapter. In the next section we discuss fuzzy linear programming followed by PERT, inventory control, queuing theory and finally network analysis. We refer the reader to the books ([17],[19],[51],[55],[62]) and paper [26] for other applications, and to the proceedings of IFSA/NAFIPS [27] for recent presentations in the area. It is interesting to note the recent growth in the applications to scheduling as seen by [42], [52] and the conference [18].

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
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. J.J. Buckley: Fuzzy Hierarchical Analysis, Fuzzy Sets and Systems, 17 (1985), pp. 233–247.

    Article  Google Scholar 

  2. J.J. Buckley: Fuzzy PERT, in: G.W. Evans, W. Karwowski and M.R. Wilhelm (eds.), Applications of Fuzzy Set Methodologies in Industrial Engineering, Elsevier Science, Amsterdam, 1989, pp. 103–114.

    Google Scholar 

  3. J.J. Buckley: Elementary Queueing Theory Based on Possibility Theory, Fuzzy Sets and Systems, 37 (1990), pp. 43–52.

    Article  Google Scholar 

  4. J.J. Buckley: Note on: Convergence of Powers of a Fuzzy Matrix, Fuzzy Sets and Systems, 121 (2001), pp. 363–364.

    Article  Google Scholar 

  5. J.J. Buckley and T. Feuring: Evolutionary Algorithm Solution to Fuzzy Problems: Fuzzy Linear Programming, Fuzzy Sets and Systems, 109 (2000), pp. 35–53

    Article  Google Scholar 

  6. J.J. Buckley, T. Feuring and Y. Hayashi: Solving Fuzzy Problems: Operations Research, J. Advanced Computational Intelligence, 3 (1999), pp. 171–176.

    Google Scholar 

  7. J.J. Buckley, T. Feuring and Y. Hayashi: Solving Fuzzy Problems in Operations Research: Fuzzy Inventory Control, Proc. FUZZ-IEEE 2000, May 7–10, 2000, San Antonio, Texas, pp. 352–357.

    Google Scholar 

  8. J.J. Buckley, T. Feuring and Y. Hayashi: Solving Fuzzy Problems in Operations Research: Inventory Control, Proc. IFSA/NAFIPS 2001, July 25–28, 2001, Vancouver, Canada, pp. 2704–2707.

    Google Scholar 

  9. J.J. Buckley, T. Feuring and H. Hayashi: Fuzzy Queueing Theory Revisited, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems. To appear.

    Google Scholar 

  10. J.J. Buckley, T. Feuring and Y. Hayashi: Multiobjective Fully Fuzzified Linear Programming, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems. To appear.

    Google Scholar 

  11. J.J. Buckley, T. Feuring and Y. Hayashi: Fuzzy Markov Chains, Proc. IFSA/NAFIPS 2001, July 2528, 2001, Vancouver, Canada, pp. 2708–2711.

    Google Scholar 

  12. S. Chanas and P. Zielinski: Criticality in the Network with Imprecise Activity Times. Proc. IPUM 2000, July 3–7, 2000, Madrid, Spain, pp. 1233–1238.

    Google Scholar 

  13. S. Chanas and P. Zielinski: Critical Path Analysis in the Network with Fuzzy Activity Times, Fuzzy Sets and Systems, 122 (2001), pp. 195–204.

    Article  Google Scholar 

  14. S.-C. Chang: Fuzzy Production Inventory for Fuzzy Product Quantity with Triangular Fuzzy Numbers, Fuzzy Sets and Systems, 107 (1999), pp. 37–57.

    Article  Google Scholar 

  15. S.J. Chen and C.-L. Hwang: Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, Heidelberg, 1992.

    Book  Google Scholar 

  16. E.W. Davis, J.J. Moder and C.R. Phillps: Project Management with CPM, PERT and Precedence Diagramming, Third Edition, Van Nostrand Reinhold, N.Y., N.Y., 1983.

    Google Scholar 

  17. M. Delgado, J. Kacprzyk, J.-L. Verdegay and M.A. Vila (eds.): Fuzzy Optimization, Physica-Verlag, Heidelberg, 1994.

    Google Scholar 

  18. EUROFUSE Workshop on Scheduling and Planning, European Working Group on Fuzzy Sets, March 31—April 1, 2000, Mons, Belgium.

    Google Scholar 

  19. G. Evens, W. Karwowski and M.R. Wilhelm (eds.): Applications of Fuzzy Set Methodologies in Industrial Engineering, Elsevier, Amsterdam, 1989.

    Google Scholar 

  20. H. Fargier, V. Galvagnon and D. Dubois: Fuzzy PERT in Series-Parallel Graphs, Proc. FUZZ-IEEE 2000, San Antonio, Texas, May 7–10, 2000, pp. 717722.

    Google Scholar 

  21. Fuzzy Sets and Systems, Elsevier Science, Amsterdam: Special Issue on Fuzzy Mathematical Programming, Vol. 111 (2000).

    Google Scholar 

  22. M. Gen, Y. Tsujiomura and D. Zheng: An Application of Fuzzy Set Theory to Inventory Control Problems, Computers in Industrial Engineering, 33 (1997), pp. 553–556.

    Article  Google Scholar 

  23. A.M. Geoffrion: Proper Efficiency and Theory of Vector Maximization, J. Math. Analysis and Appl., 22 (1968), pp. 618–630.

    Article  Google Scholar 

  24. A.L. Guiffrida and R. Nagi: Fuzzy Set Theory Applications in Production Management Research: A Literature Survey, J. Intelligent Manufacturing, 9 (1998), pp. 39–56.

    Article  Google Scholar 

  25. S.-M. Guu, H.-H. Chen and C.-T. Pang: Convergence of Products of Fuzzy Matrices, Fuzzy Sets and Systems, 121 (2001), pp. 203–207.

    Article  Google Scholar 

  26. F. Herrera and J.L. Verdegay: Fuzzy Sets and Operations Research: Prespectives, Fuzzy Sets and Systems, 90 (1997), pp. 207–218.

    Article  Google Scholar 

  27. IFSA/NAFIPS 2001, Special Sessions on “Applications of Fuzzy Sets/Logic to Operations Research ”, July 25–28, 2001, Vancouver, Canada.

    Google Scholar 

  28. T. Imai, Y. Okahara and M. Miyakoshi: The Period of Powers of a Fuzzy Matrix, Fuzzy Sets and Systems, 109 (2000), pp. 405–408.

    Article  Google Scholar 

  29. T. Itoh and H. Ishii: A Model of Fuzzy Shortest Path by Possibility Measure, Japanese J. of Fuzzy Theory and Systems, 8 (1996), pp. 977–990.

    Google Scholar 

  30. J.B. Jo, G. Yamazaki, Y. Tsujimura and M. Gen: Performance of a Fuzzy Queueing Network, Proc. IFSA Conf., Seoul, Korea, 1993, pp. 580–583.

    Google Scholar 

  31. J. Kacprzyk: Multistage Decision-Making under Fuzziness, Verlag TUV Reinland, Köln, Germany, 1983.

    Google Scholar 

  32. H. Katagiri and H. Ishii: Some Inventory Problems with Fuzzy Shortage Cost, Fuzzy Sets and Systems, 111 (2000), pp. 87–97.

    Article  Google Scholar 

  33. G.J. Klir and B. Yuan: Fuzzy Sets and Fuzzy Logic, Prentice Hall, Upper Saddle River, N.J., 1995.

    Google Scholar 

  34. Y.-J. Lai and C.-L. Hwang: Fuzzy Mathematical Programming, Springer-Verlag, Heidelberg, 1992.

    Book  Google Scholar 

  35. H.-M. Lee and J.-S. Yao: Economic Order Quantity in Fuzzy Sense for Inventory without Backorder Model, Fuzzy Sets and Systems, 105 (1999), pp. 1331.

    Article  Google Scholar 

  36. R.J. Li and E.S. Lee: Analysis of Fuzzy Queues, Proc. NAFIPS 1998, San Francisco, June 8–10, 1988, pp. 158–162.

    Google Scholar 

  37. R.J. Li and E.S. Lee: Analysis of Fuzzy Queues, Computers and Mathematics with Applications, 17 (1989), pp. 1143–1147.

    Article  Google Scholar 

  38. D.-C. Lin and J.-S. Tao: Fuzzy Economic Production for Production Inventory, Fuzzy Sets and Systems, 111 (2000), pp. 465–495.

    Article  Google Scholar 

  39. B. Liu: Uncertain Programming, Wiley, N.Y., N.Y., 1999.

    Google Scholar 

  40. B.L. Liu and A.O. Esogbue: Decision Criteria and Optimal Inventory Processes, Kluwer Academic Publishers, Norwell, Mass., 1999.

    Book  Google Scholar 

  41. D.S. Malik and J.N. Mordeson: Fuzzy Discrete Structures, Physica - Verlag, Heidelberg, Germany, 2000.

    Google Scholar 

  42. M.A.S. Monfared and S.J. Steiner: Fuzzy Adaptive Scheduling and Control Systems, Fuzzy Sets and Systems, 115 (2000), pp. 231–246.

    Article  Google Scholar 

  43. S.H. Nasution: Techniques and Applications of Fuzzy Theory to Critical Path Methods, in: C.Leondes (ed.), Fuzzy Theory Systems: Techniques and Applications, Vol. 4, Academic Press, San Diego, Cal., 1999, pp. 1561–1597.

    Chapter  Google Scholar 

  44. D.S. Negi and E.S. Lee: Analysis and Simulation of Fuzzy Queues, Fuzzy Sets and Systems, 46 (1992), pp. 321–330.

    Article  Google Scholar 

  45. S. Okada and T. Soper: A Shortest Path Problem on a Network with Fuzzy Arc Lengths, Fuzzy Sets and Systems, 109 (2000), pp. 129–140.

    Article  Google Scholar 

  46. Operations Research (the journal), Institute for Operations Research and Management Sciences, Linthicum, Maryland, USA.

    Google Scholar 

  47. H.M. Prade: An Outline of Fuzzy or Possibilistic Models for Queueing Systems, in: P.P. Wang and S.K. Chang (eds.), Fuzzy Sets, Plenum Press, N.Y., N.Y., 1980, pp. 147–153.

    Chapter  Google Scholar 

  48. M. Sakawa: Fuzzy Sets and Interactive Multiobjective Optimization, Plenum, N.Y., 1993.

    Google Scholar 

  49. M. Sakawa: Lage Scale Interactive Fuzzy Multiobjective Programming, Springer-Verlag, Heidelberg, 2000.

    Book  Google Scholar 

  50. H.-S. Shih and E.S. Lee: Fuzzy Multi—Level Minimum Cost Flow Problems, Fuzzy Sets and Systems, 107 (1999), pp. 159–176.

    Article  Google Scholar 

  51. R. Slowinski (ed.): Fuzzy Sets in Decision Analysis, Operations Research and Statistics, Kluwer, Boston, 1998.

    Google Scholar 

  52. R. Slowinski and M. Hapke (eds.): Scheduling Under Fuzziness, Springer-Verlag, Heidelberg, 2000.

    Google Scholar 

  53. G. Sommer: Fuzzy Inventory Scheduling in Applied Systems, in; G.E.Lasker (ed.), Applied Systems and Cybernetics, Vol. VI, Pergamon Press, N.Y., 1981, pp. 3052–3062.

    Google Scholar 

  54. H.A. Taha: Operations Research, Fifth Edition, MacMillan, N.Y., N.Y., 1992.

    Google Scholar 

  55. H. Tanaka and P. Guo: Possibilistic Data Analysis for Operations Research, Springer-Verlag, Heidelberg, 1999.

    Google Scholar 

  56. M.G. Thomason: Convergence of Powers of a Fuzzy Matrix, J. Math. Analysis and Appl., 57 (1977), pp. 476–480.

    Article  Google Scholar 

  57. J.-S. Yao and H.-M. Lee: Fuzzy Inventory with or without Backorder Quantity with Trapezoidal Fuzzy Numbers, Fuzzy Sets and Systems, 105 (1999), pp. 311–337.

    Article  Google Scholar 

  58. J.-S. Yao and F.T. Lin: Fuzzy Critical Path Method Based on Signed Distance Ranking of Fuzzy Numbers, IEEE Trans. Systems, Man and Cybernetics, Series A, 30 (2000), pp. 76–82.

    Google Scholar 

  59. J.-S. Yao and F.T. Lin: Corrections to “Fuzzy Critical Path Method Based on Signed Distance Ranking of Fuzzy Numbers”, IEEE Trans. Systems, Man and Cybernetics, Series A, 30 (2000), pp. 230.

    Google Scholar 

  60. J.-S. Yao and J.-S. Su: Fuzzy Inventory with Backorder for Fuzzy Total Demand Based on Interval—Valued Fuzzy Set, European J. Operational Research, 124 (2000), pp. 390–408.

    Article  Google Scholar 

  61. J.-S. Yao, S.-C. Shang and J.-S. Su: Fuzzy Inventory without Backorder for Fuzzy Order Quantity and Fuzzy Total Demand Quantity, Computers and Operations Research, 27 (2000), pp. 935–962.

    Article  Google Scholar 

  62. H.-J. Zimmermann(ed.): Practical Applications of Fuzzy Technology, Kluwer, Boston, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, University of Alabama at Birmingham, 35294, Birmingham, AL, USA

    Professor James J. Buckley

  2. Department of Mathematics, Shahid Bahonar University, Kerman, Iran

    Professor Esfandiar Eslami

  3. Electrical Engineering and Computer Science, University of Siegen, Hölderlinstraße 3, 57068, Siegen, Germany

    Dr. Thomas Feuring

Authors
  1. Professor James J. Buckley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Professor Esfandiar Eslami
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dr. Thomas Feuring
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Buckley, J.J., Eslami, E., Feuring, T. (2002). Operations Research. In: Fuzzy Mathematics in Economics and Engineering. Studies in Fuzziness and Soft Computing, vol 91. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1795-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1795-9_6

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2505-3

  • Online ISBN: 978-3-7908-1795-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation