multi-objective optimization with preemptive priority subject to fuzzy relation equation constraints

this paper studies a new multi-objective fuzzy optimization prob- lem. the objective function of this study has dierent levels. therefore, a suitable optimized solution for this problem would be an optimized solution with preemptive priority. since, the feasible domain is non-convex; the tra- ditional methods cannot be applied. we study this problem and determine some special structures related to the feasible domain, and using them some methods are proposed to reduce the size of the problem. therefore, the prob- lem is being transferred to a similar 0-1 integer programming and it may be solved by a branch and bound algorithm. after this step the problem changes to solve some consecutive optimized problem with linear objective function on discrete region. finally, we give some examples to clarify the subject.