Robust Optimization by Fuzzy Linear Programming

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A method for representation of the decision maker's preference on robust constraints by a necessity measure is proposed and it is shown that fuzzy linear programming problems with general necessity measures are solved without great loss of linearity. Robust optimization in two level linear programming problems and robust efficient solutions in multiple objective problems are investigated. Moreover, it is shown that approximate calculations of graded ill-known sets are rather easy. Then the linear programming problems with graded ill-known sets can be treated in a similar way to fuzzy linear programming problems. Finally, we proposed interval ordinal regression method when a part of pairwise preference information is given. We investigated the generalizations of the interval ordinal regression method.