Multi objective non linear programming problem in intuitionistic fuzzy environment: Optimistic and pessimistic view point
Multi objective optimization problem under intuitionistic fuzzy environment has been considered.Degree of attainability and non attainability is represented by non linear functions.Optimistic and pessimistic aspect of the problem has been considered.The validity of the problem has been discussed.multiobjective problems arising in the transportation and manufacturing systems have been taken for demonstration. The objective of this manuscript is to present an algorithm for solving multi objective optimization problem under the optimistic and pessimistic view point. The conflicting natures of the different objective have been handled by defining the membership functions corresponding to it in parabolic intuitionistic fuzzy set environment and thus the problem becomes parabolic multi objective non linear optimization programming problem (PMONLOPP) A linear and non linear membership functions corresponding to each objective has been taken in account. An illustrative examples from transportation as well as in manufacturing systems are reported and compared with the typical approaches exist in the literature. As shown, the solutions obtained by the proposed approach are superior to those of existing best solutions reported in the literature. Further more, experimental results indicate that the proposed approach may yield better solutions to these types of problems than those obtained by using current algorithms.
Expert Syst. Appl.