Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

Solving Linear Programming Problems with Fuzzy Data

Download PDF (517.8 KB) PP. 127 - 138 Pub. Date: October 1, 2018

DOI: 10.22606/jaam.2018.34003

Author(s)

  • Michael Gr. Voskoglou*
    Department of Mathematical Sciences, School of Technological Applications Graduate Technological Educational Institute of Western Greece

Abstract

A Fuzzy Linear Programming problem differs from an ordinary one to the fact that the coefficients of its objective function and / or the technological coefficients and constants of its constraints are fuzzy instead of real numbers. In this work a new method is developed for solving such kind of problems by ranking the fuzzy numbers involved and by solving the obtained in this way ordinary Linear Programming problem with the standard theory. The values of the decision variables may then be converted to fuzzy numbers in order to facilitate a fuzzy expression of the problem’s optimal solution, but this must be strictly checked to avoid non-creditable expressions. Examples involving triangular and trapezoidal fuzzy numbers are also presented in the paper illustrating the applicability of our method to real-life applications.

Keywords

linear programming (LP), SIMPLEX method, duality, fuzzy numbers (FNs), triangular FNs (TFNs), trapezoidal FNs (TpFNs), centre of gravity (COG) defuzzification technique, ranking of FNs, degree of fuzziness (DoF), fuzzy LP

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