The concepts of fuzziness and parametric analysis are of importance to treat uncertainty in mathematical model and may ofer certain more viewpoints. The basic
notions of the parametric study in nonlinear programming problem are presented
by Osman (Aplikace matematiky 22(5):318–332, 1977; Aplikace matematiky
22(5):333–348, 1977). In general, a parametric programming problem is not easy to
be solved. In addition, sometime, solving a parametric programming problem with
parameters in the objective is easier than solving a parametric problem with parameters in the constraints and vice versa. Therefore, a parametric study in duality space
is important to facilitate solving a parametric programming problem. The fuzzy nonlinear problem is interested area for research as one of the tools for treating uncertainty. The fuzzy nonlinear problem when parameters in the objective function or
constrains or both is called the fuzzy parametric nonlinear problem. Therefore, dealing with fuzziness and duality parametric space is concerned. In this paper, a novelty introduction to the fuzzy basic notions of parametric programming problem are
clarifed, the relations between the concepts concerning duality in parametric spaces
which introduced by Osman et al. (Int J Math Arch 6(12):161–165, 2016) and the
fuzzy concepts are presented. We present and defne the fuzzy parametric notions of
the set of feasible parameters, the solvability set, and the stability sets of the frst and
second kind. These notions are not defned before. The theoretical relations and an
illustration example are introduced. |
