On Duality of Multiobjective Rough Convex Programming Problems

Duality assertions are very important in optimization from the theoretical as well as from the numerical point of view. So this paperpresents duality of multiobjective rough convex programming problems in roughenvironment when the multiobjective function is deterministic and roughness is in feasible region. 

Also it discussed the duality when roughness in multiobjective function and the feasible region is deterministic. The conceptsand some theorems of duality in the rough environment are discussed. Also, the procedure of solution of these kind of problems described.

The mathematical programming in rough environment was introduced. The multiobjective rough convex programming problem (MRCPP) can be classified according to existence of roughness is in multiobjective function or constraints. The mathematical problems can be classified into three classes. First class: MRCPP with rough feasible set and deterministic multiobjective function. Second class: problems with deterministic feasible set and rough multiobjective function.