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Advances in Algebra and Analysis pp 301–308Cite as

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Direct Solving Method of Fully Fuzzy Linear Programming Problems with Equality Constraints Having Positive Fuzzy Numbers

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Abstract

In the process of solving fully fuzzy linear programming (FLP) problems, many methods have been investigated. To find the fuzzy optimal solution of fully FLP problems, there is a need to convert the fully FLP problems into crisp linear programming (CLP) problems. There is no method which can be used directly to find the fuzzy optimal solution of the fully FLP problems without converting it into CLP problems. In this paper we investigate fully FLP problems with equality constrains in which all the parameters and variables are positive triangular fuzzy numbers. This approach can be used directly to find the fuzzy optimal solution by the simplex method(Big-M).

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References

  1. Zadeh and Bellman: Decision making in a fuzzy environment, Management science. 17, PP.141–164 (1970)

    Google Scholar 

  2. H.J.Zimmerman: Fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems. 1, PP.45–55 (1978)

    Article  MathSciNet  Google Scholar 

  3. Amit Kumar and Jagdeep Kaur: A New method for solving fuzzy linear programs with trapezoidal fuzzy numbers,International scientific publications and consulting services (ISPACS). (2011) doi:10.5899

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. T. Allahviranloo, F. H. Lotfi, M. K. Kiasary, N. A. Kiani and L. Alizadeh: Solving Fully Fuzzy Linear Programming Problem by the Ranking Function, Applied Matematical Sciences. 2, PP.19–32 (2008)

    MathSciNet  MATH  Google Scholar 

  6. F. H. Lotfi, A. Ebrahimnejad, S. H. Nasseri and M. Soltanifar: A Primal Dual Method for Linear Programming Problems with Fuzzy Variables, European Journal of Industrial Engineering. 4, PP.189–209 (2010)

    Article  Google Scholar 

  7. Amit Kumar, Jagdeep Kaur, Pushpinder Singh: Fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints, International Journal of Mathematical and Computer Sciences. 6, PP.37–41 (2010)

    Google Scholar 

  8. S. H. Nasseri et al: Fully fuzzy linear programming with inequality constraints, International Journal of Industrial Mathematics. 5, Article ID IJIM-00280, 8 pages (2013)

    Google Scholar 

  9. M. Dehghan, B. Hashemi and M. Ghatee: Computational methods for solving fully fuzzy linear systems, Applied Mathematics and Computation. 179, PP.328–343 (2006)

    Article  MathSciNet  Google Scholar 

  10. Kumar A, Kaur J and Singh P: A new method for solving fully fuzzy linear programming problems, Appl. Math. Modell. 35, PP.817–823 (2011)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India

    C. Muralidaran & B. Venkateswarlu

Authors
  1. C. Muralidaran
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  2. B. Venkateswarlu
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Corresponding author

Correspondence to B. Venkateswarlu .

Editor information

Editors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    V. Madhu

  2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    A. Manimaran

  3. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    D. Easwaramoorthy

  4. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    D. Kalpanapriya

  5. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    M. Mubashir Unnissa

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Muralidaran, C., Venkateswarlu, B. (2018). Direct Solving Method of Fully Fuzzy Linear Programming Problems with Equality Constraints Having Positive Fuzzy Numbers. In: Madhu, V., Manimaran, A., Easwaramoorthy, D., Kalpanapriya, D., Mubashir Unnissa, M. (eds) Advances in Algebra and Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01120-8_34

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