Abstract:
Many modern technological objects in practice are characterized by the uncertainty of
the initial information necessary for their management. Recently, one of the pressing scientific and
practical problems is the development of new optimization methods for controlling the operating
modes of such objects in a fuzzy environment. In this regard, the objective of this study is to develop
methods of multi-criteria optimization in a fuzzy environment by modifying the simplex method
and various optimality principles based on fuzzy mathematics methods. The methodology of the
proposed study is based on a hybrid approach, which consists of the integrated use and modification
of simplex methods and optimization methods with various optimality principles for working in a
fuzzy environment. The main results are as follows: a simplex method of multi-criteria optimization
of immeasurable criteria (here, we are talking about the impossibility of physical measurements
of criteria, the values of which are estimated by decision maker); a theorem on the convergence of
the solution sequence obtained using the proposed method to the minimum value of the criteria;
a heuristic method based on a modification for fuzziness and a combination of the maximin and
Pareto optimality principles, which allows effectively solving multi-criteria optimization problems
in a fuzzy environment. The heuristic method proposed will be used to solve a real production
problem—optimization of the technological process of benzene production.
