Staff Members - Benha University
On Parametric Multi-level Multi-objective Fractional Programming Problems with Fuzziness in the Constraints
British Journal of Mathematics & Computer Science • 2017
Publication Information
Authors
M. S. Osman; O. E. Emam; M. A. El Sayed
Keywords
Multi-level programming; multi-objective programming; fractional programming; fuzzy sets;
parametric programming.
Journal
British Journal of Mathematics & Computer Science
Publisher
SCIENCEDOMAIN international
Volume
18
Issue
5
Pages
1-19
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
In this paper, a new concept of the fuzzy stability set of the first kind for multi-level multi-objective
fractional programming (ML-MOFP) problems having a single-scalar parameter in the objective
functions and fuzziness in the right-hand side of the constraints has been introduced. Firstly, A parametric
ML-MOFP model with crisp set of constraints is established based on the -cut approach. Secondly, a
fuzzy goal programming (FGP) approach is used to find an -Pareto optimal solution of the parametric
ML-MOFP problem. Thus, the FGP approach is used to achieve the highest degree of each membership
goal by minimizing the sum of the negative deviational variables. Finally, the fuzzy stability set of the
first kind corresponding to the obtained -Pareto optimal solution is developed here, by extending the
Karush-Kuhn-Tucker optimality conditions of multi-objective programming problems. An algorithm to
clarify the developed fuzzy stability set of the first for parametric ML-MOFP problem as well as
Illustrative numerical example are presented
fractional programming (ML-MOFP) problems having a single-scalar parameter in the objective
functions and fuzziness in the right-hand side of the constraints has been introduced. Firstly, A parametric
ML-MOFP model with crisp set of constraints is established based on the -cut approach. Secondly, a
fuzzy goal programming (FGP) approach is used to find an -Pareto optimal solution of the parametric
ML-MOFP problem. Thus, the FGP approach is used to achieve the highest degree of each membership
goal by minimizing the sum of the negative deviational variables. Finally, the fuzzy stability set of the
first kind corresponding to the obtained -Pareto optimal solution is developed here, by extending the
Karush-Kuhn-Tucker optimality conditions of multi-objective programming problems. An algorithm to
clarify the developed fuzzy stability set of the first for parametric ML-MOFP problem as well as
Illustrative numerical example are presented