TOPSIS Approach for Solving Bi-Level Non-Linear Fractional MODM Problems

Authors

  • MAHMOUD A ABO-SINNA PRINCESS NOURAH BINT ABDULRAHMAN UNIVERSITY, RIYADH, SAUDI ARABIA.
  • AZZA H AMER, DR b. Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt.

DOI:

https://doi.org/10.24297/jam.v13i4.6243

Keywords:

Multi-objective decision making, Bi-level programming problems, Fractional programming, TOPSIS, Fuzzy goal programming

Abstract

TOPSIS (technique for order preference similarity to ideal solution) is considered one of the known classical multiple criteria decision making (MCDM) methods to solve bi-level non-linear fractional multi-objective decision making (BL-NFMODM) problems, and in which the objective function at each level is considered nonlinear and maximization type fractional functions. The proposed approach presents the basic terminology of TOPSIS approach and the construction of membership function for the upper level decision variable vectors, the membership functions of the distance functions from the positive ideal solution (PIS) and of the distance functions from the negative ideal solution (NIS). Thereafter a fuzzy goal programming model is adopted to obtain compromise optimal solution of BL-NFMODM problems. The proposed approach avoids the decision deadlock situations in decision making process and possibility of rejecting the solution again and again by lower level decision makers. The presented TOPSIS technique for BL-NFMODM problems is a new fuzzy extension form of TOPSIS approach suggested by Baky and Abo-Sinna (2013) (Applied Mathematical Modelling, 37, 1004-1015, 2013) which dealt with bi -level multi-objective decision making (BL-MODM) problems. Also, an algorithm is presented of the new fuzzy TOPSIS approach for solving BL-NFMODM problems. Finally, an illustrative numerical example is given to demonstrate the approach.

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Author Biographies

MAHMOUD A ABO-SINNA, PRINCESS NOURAH BINT ABDULRAHMAN UNIVERSITY, RIYADH, SAUDI ARABIA.

PROFESSOR OF MATHEMATICS

AZZA H AMER, DR, b. Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt.

  1. Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt.

References

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Published

2018-02-09

How to Cite

ABO-SINNA, M. A., & AMER, A. H. (2018). TOPSIS Approach for Solving Bi-Level Non-Linear Fractional MODM Problems. JOURNAL OF ADVANCES IN MATHEMATICS, 13(4), 7353–7370. https://doi.org/10.24297/jam.v13i4.6243

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