Multi-attribute decision making using interval-valued pythagorean fuzzy set and differential evolutionary algorithm

This paper presents a multi-attribute decision-making approach based on interval-valued pythagorean fuzzy set and differential evolutionary algorithm. Interval-valued pythagorean fuzzy set has always been effective in representing real world complex problems due to its large scope of bound compared to fuzzy sets. Differential evolutionary algorithm is the most widely and successfully used optimization algorithms for obtaining optimal results. In this paper, initially, we use an accuracy function to transform the input decision matrix represented by interval-valued pythagorean fuzzy values into a transformed decision matrix. Next, for the corresponding attributes, we obtain the optimal weight vector using differential evolutionary algorithm and transformed decision matrix. We apply interval-valued pythagorean fuzzy weighted geometric operator to compute the aggregated interval-valued pythagorean fuzzy values for the various alternatives. Subsequently, we find the final accuracy values of the aggregated interval-valued pythagorean fuzzy values to decide the ranking of the alternatives. Moreover, we perform the said multi-attribute decision-making approach using particle swarm optimization replacing differential evolutionary algorithm. The proposed approaches are explained using numerical examples. Finally, the results of the differential evolutionary based approach have been compared with the existing approaches and particle swarm optimization based approach, where differential evolutionary based decision-making approach is found to perform better in imprecise environments.