Genetic algorithm based fuzzy weighted average for multi-criteria decision making problems

Ranking of alternatives on the basis of multi-criteria is an important issue in decision making. These criterion may be quantitative as well as qualitative in nature. In this paper, a method is developed using genetic algorithm for the ranking of alternatives on the basis of multi-criteria. Fuzzy numbers are used to evaluate the qualitative criteria. In this method, first, fuzzy weighted average of each alternative is formulated as a pair of non linear programs (in the form of α-cut representation of fuzzy numbers), which represent the left and right bounds of alternative. After that, membership value of fuzzy weighted average of each alternative is constructed by enumerating different values of α. The pair of non linear optimization problems for different values of α are solved using genetic algorithm. Finally, ranking order of alternatives is calculated by Yager's ranking indices. A numerical example is solved successfully to demonstrate the proposed methodology. © 2011 Operational Research Society of India.