Skip to main content
SpringerLink
Log in

Interval and Fuzzy Arithmetic in Logistic

  • Chapter
Soft Computing in Economics and Finance

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 6))

  • 1202 Accesses

Abstract

This chapter deals with the so-called distribution problem, which belong to the wide class of the logistic problems.

It is known that distribution and transportation problems have similar mathematical structures and are usually treated as particular cases of the general linear programming problem.

There are many effective algorithms for the solution of transportation and distribution problems proposed in the scientific literature and in the textbooks. So we can say that these problems in the case of real valued parameters are, generally, solved. Nevertheless, in practice, we often meet different kinds of uncertainty when the parameters of these optimization problems are presented by intervals or fuzzy values.

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 129.00
Price excludes VAT (USA)
  • Available as 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 shipping worldwide - see info
Hardcover Book
USD 169.99
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.

References

  1. Ali, M.M., Törn, A.: Population set-based global algorithms: some modifications and numerical studies. Computers and Operations Research 31, 1703–1725 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ammar, E.E., Youness, E.A.: Study on multiobjective transportation problem with fuzzy numbers. Applied Mathematics and Computation 166, 241–253 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bellman, R., Zadeh, L.: Decision-making in fuzzy environment. Management Science 17, 141–164 (1970)

    Article  MathSciNet  Google Scholar 

  4. Bit, A.K., Biswal, M.P., Alam, S.S.: Fuzzy programming approach to multicriteria decision making transportation problem. Fuzzy Sets and Systems 50, 35–41 (1992)

    Article  MathSciNet  Google Scholar 

  5. Bit, A.K., Biswal, M.P., Alam, S.S.: Fuzzy programming approach to multiobjective solid transportation problem. Fuzzy Sets and Systems 57, 183–194 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bit, A.K., Biswal, M.P., Alam, S.S.: An additive fuzzy programming model for multiobjective transportation problem. Fuzzy Sets and Systems 57, 13–19 (1993)

    Google Scholar 

  7. Buckley, J.J., Feuring, T.: Evolutionary algorithm solution to fuzzy problems: Fuzzy linear programming. Fuzzy Sets and Systems 109, 35–53 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Challam, G.A.: Fuzzy goal programming (FGP) approach to a stochastic transportation problem under budgetary constraints. Fuzzy Sets and Systems 66, 293–299 (1994)

    Article  Google Scholar 

  9. Chanas, S.: The use of parametric programming in fuzzy linear programming. Fuzzy Sets and Systems 11, 243–251 (1983)

    Article  MATH  Google Scholar 

  10. Chanas, S., Kolodziejckzy, W., Machaj, A.A.: A fuzzy approach to the transportation problem. Fuzzy Sets and Systems 13, 211–221 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  11. Chanas, S., Kuchta, D.: Fuzzy integer transportation problem. Fuzzy Sets and Systems 98, 291–298 (1998)

    Article  MathSciNet  Google Scholar 

  12. Chanas, S., Kuchta, D.: Multiobjective programming in optimization of interval objective functions - A generalized approach. European Journal of Operational Research 94, 594–598 (1996)

    Article  MATH  Google Scholar 

  13. Chanas, S., Kuchta, D.: A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets and Systems 3, 299–305 (1996)

    Article  MathSciNet  Google Scholar 

  14. Choi, D.Y., Oh, K.W.: Asa and its application to multi-criteria decision making. Fuzzy Sets and Systems 114, 89–102 (2000)

    Article  MATH  Google Scholar 

  15. Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1963)

    MATH  Google Scholar 

  16. Das, S.K., Goswami, A., Alam, S.S.: Multiobjective transportation problem with interval cost, source and destination parameters. European Journal of Operational Research 117, 100–112 (1999)

    Article  MATH  Google Scholar 

  17. Dimova, L., Sevastjanov, P., Sevastjanov, D.: MCDM in a Fuzzy Setting: Investment Projects Assessment Application. Int. Journal of Production Economy 100, 10–29 (2006)

    Article  Google Scholar 

  18. Dubois, D., Koenig, J.L.: Social choice axioms for fuzzy set aggregation. Fuzzy Sets and Systems 43, 257–274 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  19. Dyckhoff, H.: Basic concepts for theory of evaluation: hierarchical aggregation via autodistributive connectives in fuzzy set theory. European Journal of Operation Research 20, 221–233 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  20. Ehrgott, M., Verma, R.A.: Note on solving multicriteria transportation-location problems by fuzzy programming. Asia-Pacific Operational Research 18, 149–164 (2001)

    MATH  MathSciNet  Google Scholar 

  21. El-Wahed, W.F.A.: A multi-objective transportation problem under fuzziness. Fuzzy Sets and Systems 117, 27–33 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  22. El-Wahed, W.F.A., Lee, S.M.: Interactive fuzzy goal programming for multi-objective transportation problems. Omega 34, 158–166 (2006)

    Article  Google Scholar 

  23. El-Wahed, W.F.A., Abo-Sinna, M.A.: A hybrid fuzzy-goal programming approach to multiple objective decision making problems. Fuzzy Sets and Systems 119, 71–78 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  24. Galperin, E.A., Ekel, P.Y.: Synthetic Realization Approach to Fuzzy Global optimization via Gamma Algorithm. Mathematical and Computer Modelling 41, 1457–1468 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  25. Ganesan, K., Veeramani, P.: Fuzzy linear programming with trapezoidal fuzzy numbers. Ann. Oper. Res. 143, 305–315 (2006)

    Article  MATH  Google Scholar 

  26. Gottwald, S.: Set theory for fuzzy sets of higher level. Fuzzy Sets and Systems 2, 125–151 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  27. Hauke, W.: Using Yager’s t-norms for aggregation of fuzzy interval. Fuzzy Sets and Systems 101, 59–65 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  28. Isermann, H.: The enumeration of all efficient solution for a linear multiple-objective transportation problem. Naval Research Logistics Quarterly 26, 123–139 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  29. Iskander, M.G.: A computational comparison between two evaluation criteria in fuzzy multiobjective linear programs using possibility programming. Computers and Mathematics with Applications 55, 2506–2511 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  30. Islam, S., Roy, T.K.: A new fuzzy multi-objective programming: Entropy based geometric programming and its application of transportation problems. European Journal of Operational Research 173, 387–404 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  31. Jiménez, M., Arenas, M., Bilbao, A., Rodríguez, M.V.: Linear programming with fuzzy parameters: An interactive method resolution. European Journal of Operational Research 177, 1599–1609 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  32. Kuchta, D.: A generalisation of an algorithm solving the fuzzy multiple choice knapsack problem. Fuzzy Sets and Systems 127, 131–140 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  33. Kuchta, D.: A generalisation of a solution concept for the linear programming problem with interval coefficients. Operations Research and Decisions 4, 115–123 (2003)

    MathSciNet  Google Scholar 

  34. Lai, Y., Hwang, C.: Fuzzy multiple objective decisions making: methods and applications. Springer, Berlin (1996)

    Google Scholar 

  35. Li, G., Guo, R.: Comments on Formulation of fuzzy linear programming problems as four-objective constrained optimization problems. Applied Mathematics and Computation 186, 941–944 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  36. Liu, S.-T.: Fuzzy total transportation cost measures for fuzzy solid transportation problem. Applied Mathematics and Computation 174, 927–941 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  37. Lotfi, F.H., Allahviranloo, T., Jondabeh, M.A., Alizadeh, L.: Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Applied Mathematical Modelling 33, 3151–3156 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  38. Lushu, L., Lai, K.K.: A fuzzy approach to the multiobjective transportation problem. Computers and Operational Research 27, 43–57 (2000)

    Article  MATH  Google Scholar 

  39. Maeda, T.: On characterization of fuzzy vectors and its applications to fuzzy mathematical programming problems. Fuzzy Sets and Systems 159, 3333–3346 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  40. Mahdavi-Amiri, N., Nasseri, S.H.: Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables. Fuzzy Sets and Systems 158, 1961–1978 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  41. Maleki, H.R.: Ranking functions and their applications to fuzzy linear programming. Far East J. Math. Sci (FJMS) 4, 283–301 (2002)

    MATH  MathSciNet  Google Scholar 

  42. Maleki, H.R., Tata, M., Mashinchi, M.: Linear programming with fuzzy variables. Fuzzy Sets and Systems 109, 21–33 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  43. Migdalas, A., Pardalos, P.M.: Editorial: hierarchical and bilevel programming. Journal of Global Optimization 8, 209–215 (1996)

    Article  MathSciNet  Google Scholar 

  44. Mishmast, N.H., Maleki, H.R., Mashinchi, M.: Multiobjective linear programming with fuzzy variables. Far East J. Math. Sci (FJMS) 5, 155–172 (2002)

    MATH  MathSciNet  Google Scholar 

  45. Mitra, G.: Mathematical Models for Decision Support. Springer, Berlin (1988)

    MATH  Google Scholar 

  46. Ramík, J.: Duality in fuzzy linear programming with possibility and necessity relations. Fuzzy Sets and Systems 157, 1283–1302 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  47. Ringuest, J.L., Rinks, D.B.: Interactive solutions for the linear multiobjective transportation problem. European Journal of Operational Research 32, 96–106 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  48. Rommelfanger, H.: A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values. Fuzzy Sets and Systems 158, 1892–1904 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  49. Roubens, M.: Fuzzy sets and decision analysis. Fuzzy Sets and Systems 90, 199–206 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  50. Sevastjanov, P., Figat, P.: Aggregation of aggregating modes in MCDM, Synthesis of Type 2 and Level 2 fuzzy sets. Omega 35, 505–523 (2007)

    Article  Google Scholar 

  51. Steuer, R.E.: Algorithm for linear programming problems with interval objective function co-efficient. Mathematics of Operations Research 6, 333–348 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  52. Tong, S.: Interval number and fuzzy number linear programming. Fuzzy Sets and Systems 66, 301–306 (1994)

    Article  MathSciNet  Google Scholar 

  53. Törn, A., Žilinskas, A.: Global optimization. Springer, Berlin (1989)

    MATH  Google Scholar 

  54. Tre, G., Caluwe, R.: Level-2 fuzzy sets and their usefulness in object-oriented database modeling. Fuzzy Sets and Systems 140, 29–49 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  55. Yager, R.: Multiple objective decision-making using fuzzy sets. International Journal of Man-Machine Studies 9, 375–382 (1979)

    Article  Google Scholar 

  56. Yager, R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems Man and Cybernetics 18, 183–190 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  57. Yang, L., Liu, L.: Fuzzy fixed charge solid transportation problem and algorithm. Applied Soft Computing 7, 879–889 (2007)

    Article  Google Scholar 

  58. Zadeh, L.A.: Quantitative fuzzy semantics. Information Sciences 3, 177–200 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  59. Zadeh, L.A.: Fuzzy logic and its application to approximate reasoning. Information Processing 74, 591–594 (1974)

    MathSciNet  Google Scholar 

  60. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1, 45–55 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  61. Zimmermann, H.J., Zysno, P.: Latest connectives in human decision making. Fuzzy Sets Systems 4, 37–51 (1980)

    Article  MATH  Google Scholar 

  62. Zimmermann, H.J., Zysno, P.: Decision and evaluations by hierarchical aggregation of information. Fuzzy Sets and Systems 104, 243–260 (1983)

    Article  Google Scholar 

Download references

Authors
  1. Ludmila Dymowa
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Dymowa, L. (2011). Interval and Fuzzy Arithmetic in Logistic. In: Soft Computing in Economics and Finance. Intelligent Systems Reference Library, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17719-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17719-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17718-7

  • Online ISBN: 978-3-642-17719-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation