NECESSARY OPTIMALITY CONDITIONS OF APPROXIMATED ROBUST SOLUTIONS OF MULTI-CRITERIA DECISION MAKING PROBLEM WITH UNCERTAINTY DATA

Multi-criteria decision making analysis is an important method in dealing with economic and management problems. This paper is devoted to study multi-criteria decision-making problem with uncertainty data (UMP) in both objective and constraint functions by using robust method. The Fritz-John type necessary optimality conditions of robust epsilon-quasi weak efficient solution of (UMP) are first established by using Mordukhovich sub-differential as well as Clarke sub-differential. We also introduced a new constraint qualification which can be seen as extension of the existing constraint qualifications. By the constraint qualification, we get the Karush-Kuhn-Tucker type necessary optimality conditions of (UMP) concerning robust epsilon-quasi weak efficient solution. Lastly, we also present sufficient conditions for robust approximated critical point to be robust epsilon-quasi (weak) efficient solutions of (UMP) under the (strict) pseudo-quasi generalized convexity assumptions.