A Fuzzy Approach for Solving Fractional Programming Problems

Youness, E.A.; Ibrahim, E. F.

doi:10.21608/djs.2017.139430

A Fuzzy Approach for Solving Fractional Programming Problems

Document Type : Research and Reference

Authors

Department of Mathematics Faculty of Science, Tanta University, Tanta, Egypt.

10.21608/djs.2017.139430

Abstract

In this paper we describe a fuzzy approach for solving nonlinear fractional programming problem with linear
constraints (NLFPP). In the proposed approach, the objective function is transformed into linear function by using
Taylor’s theorem and the considered NLFPP is changed into equivalent linear programming problem (LPP) which it
can be solved as a linear programming problem. The proposed approach is based on choosing three initial points inside
the feasible region which enable us to generate a new point at which the value of objective function is better than the
previous value, and so on to reach the best approximation of optimal solution.

References

[1] Bazaraa, M. S., Sherali, H. D. (2006)
Nonlinear Programming Theory and
Algorithms, 3rd Edition .
[2] Bellman, R. & Zadeh, L.A. (1970). Decision-
Making in a Fuzzy Environment, Management
Science , 17: 141-161.
[3] Frenk, J.B.G. and Schaible, S., (2001).
Fractional Programming: Introduction and
Applications: In: Encyclopedia, Floudas, C.
A. and Pardalos, P.M. (Eds.). Kluwer
Academic Publishers. Dordrecht. Netherlands,
162-172.
[4] Pitam Singh, Shiv Datt Kumar and R. K.
Singh( 2010) . Fuzzy Method for Multi

objecive Linear Plus Linear Fractional
Programming Problem ,International
Mathematical ,60:2971 – 2983.
[5] Schaible, S. and Shi, J. (2004). Recent
Developments in Fractional Programming:
Single Ratio and Max-min Case, Working
Paper Series, 04-02, A. Gary Anderson
Graduate School of Management, University
of California, Riverside, CA 92521, USA.
[6] Stephens,c.(1997).Global optimization theory
versus practice ,PhD thesis , University of
Canterbury ,Christchurch , New Zealand
[7] Youness, E.A., Hassan ,S.Z. and El-Rewaily,
Y.A. (2008). Quadratic Interpolation
Algorithm for Minimizing Tabulated
Function, Journal of Mathematics and
Statistics4 ,4:217-221.
[8] Zimmermann, H. J. (1978). Fuzzy
programming and linear programming with
several objective functions, Fuzzy sets and
systems, 1: 45–55.
[9] Zimmermann, H. J.(1991). Fuzzy Set Theory
and its Application, 2nd Ed., Kluwer Academic
Publishers, Boston.
[10] Zoutendijk, G. (1960). Methods of Feasible
Directions, Elsevier, Amsterdam, and D. Van
Nostrand, Princeton, NJ
[11] Zoutendijk, G. (1976). Mathematical
Programming Methods, North-Holland,
Amsterdam, The Netherlands.