Modeling and optimization of multi-objective programming problems in intuitionistic fuzzy environment:Optimistic, pessimistic and mixed approaches

This paper investigates a new approach for finding efficient solutions of a multi-objective programming problem (MOPP) in intuitionistic fuzzy environment (IFE) based on decision maker's different views, viz., optimistic, pessimistic and mixed. Firstly, the point operator Fα, which transforms intuitionistic fuzzy set (IFS) into the equivalent fuzzy set (FS), is introduced and some desirable properties of Fα are studied. Subsequently, the formulation of MOPP, accuracy function and value function in IFE have been introduced. For resolving the mutual conflicting nature of objectives in MOPP in IFE, we introduce the membership and non-membership functions governed by reference function which do not depend on the upper and lower levels of acceptability. Then a new method is proposed to find the efficient solutions of MOPP in IFE based on different viewpoints. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed method.