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Solving bilevel programming problem with interval coefficients at the lower level : a fuzzy approach
M. Saraj,M. Mousavi 장전수학회 2012 Proceedings of the Jangjeon mathematical society Vol.15 No.1
Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure.This paper presents a procedure for solving bilevel programming problem (BLPP) with interval coefficients at the lower level. In the proposed procedure, this problem is transformed into a classical BLPP with two objective functions at the lower level by considering order relations on the class of all closed intervals. Then, the obtained problem is converted into an ordinary BLPP with a single objective function at each level by use of fuzzy programming technique. Finally, a numerical example is given to illustrate this approach.
A multi objective transportation problem (MOTP) with transshipment under fuzziness
M. Saraj,F. Mashkoorzadeh 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.1
The present paper determines the optimal compromise solution for a multi objective transportation problem(MOTP) with transshipment by fuzzy programming approach. we suppose that the coeffcients of the objective functions, the sources and destination parameters are symmetric triangular fuzzy numbers; and by fuzzy programming approach we will obtain the compromise solution of MOTP with transshipment. Numerical examples are provided to illustrate the aproache.
Fuzzy optimization problem with an interval coefficients approach
M. Saraj,M. Goodarzi 장전수학회 2011 Advanced Studies in Contemporary Mathematics Vol.21 No.3
In this paper we consider a fuzzy programming problem, in which the coefficients of objective function are fuzzy numbers. Since α-cuts of this numbers are crisp intervals,therefore the above problem is converted into a problem whose objective functions’coefficients are interval coefficients. By using the order relations between intervals in the form of right limit, left limit, center and half width, the problem is converted into a multi objective problem and then it is solved by usual techniques. Finally a numerical example is given to illustrate this method.
V. Lokesha,Naveen Kumar B.,K. M. Nagaraja,M. Saraj,Abdelmejid Bayad 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.2
The object of this paper is to introduce three new means on the basis of proportions and its dual forms, study certain properties, monotonicities and new inequalities involving them. Further, we dened weighted three new means and its dual form, its properties are stated and deduced the ten Neo-Pythagorean means, weighted rth Oscillatory mean, weighted rth Oscillatory mean, also some familiar means and various other means.