Affiliations: Department of Computer Science, Amirkabir University
of Technology, Tehran, Iran | Department of Industrial Engineering, Sharif
University of Technology, Tehran, Iran | Department of Mathematics, Payam Noor University of
Birjand, Birjand, Iran
Abstract: In this paper, we propose a two-phase approach to find the optimal
solutions of a class of fuzzy linear programming problems called fully
fuzzified linear programming (FFLP), where all decision parameters and
variables are fuzzy numbers. Our approach is constructed on the basis of
comparison of mean and standard deviation of fuzzy numbers. In this approach,
the first phase maximizes the possibilistic mean value of fuzzy objective
function and obtains a set of feasible solutions. The second phase minimizes
the standard deviation of the original fuzzy objective function, by considering
all basic feasible solutions obtained at the end of the first phase. The
advantage of the proposed approach is its simplicity in programming and
computation. Moreover, we also generalize the concept of linear programming
duality and extend the duality as well as the weak duality theory to FFLP.
Keywords: Fully fuzzified linear programming, fuzzy numbers, fuzzy linear programming, ranking functions, duality
