One another important feature of mathematical programming is the existence
of uncertainties. These uncertainties may be due to a lack of information or to the internal
error of measures, and evaluations in a fuzzy environment. All these features will
condition the formulation for a MOO problem. A MOO problem may be a standard
continuous or combinatorial programming problem, a robust optimization problem or a
fuzzy optimization problem. Real-life optimization problems involve more complex
situations including two types of difficulties, namely the existence of nonlinearities and
uncertainties. Bimatrix games with associated quadratic programming problems and
geometric programming illustrate the first type of real-world problems. The second type
of programming models under uncertainties includes robust programming and fuzzy
programming. Robust programming has been developed to increase the quality and
reliability of engineering processes. Fuzzy programming problems refer to situations
where decision-makers face with incorrect or uncertain data. The fuzzy environment
includes uncertain preferences, fuzzy objectives, fuzzy constraints, fuzzy data. In such
problems, decision-makers maximize their degree of satisfaction in a specified decision
set. The extension to multiple objectives uses numerical examples.
Keywords: Bilinear programming, Bimatrix game, Equivalence Theorem, Fuzzy
decision set, Fuzzy goal programming, Fuzzy programming, Geometric
programming, KKT necessary optimality conditions, Matrix game, Maximin
operator, Membership function, Mixed strategies, Multi-objective bimatrix game,
Nash equilibrium, Payoff matrix, Pivot algorithm, Robustness, Robust
optimization, Strategy space, Symmetric method.
