COMPARING PERFORMANCE OF SIMPLE ADDITIVE WEIGHTING AND WEIGHTED PRODUCT METHODS FOR SPHERICAL FUZZY DECISION-MAKING

Abstract

The nature of decision-making is commonly fashioned by uncertainty and vagueness due to lack of information and psychological biases of human beings. Many efforts have been made to cater this issue such the emergence of fuzzy set theory. Recently, the fuzzy set theory has been extended to spherical fuzzy sets (SFS) which generalize other forms of extension of fuzzy sets. The SFS consists of membership, non-membership and hesitancy grades, which are independent of each other, providing larger domains for decision-makers to assign such grades. SFS makes use of the three variables in its calculation as compared to only membership grade in the classical fuzzy set. In this paper, the performance of the SFS using simple additive weighting (SAW) and weighted product method (WPM) for ranking alternatives was compared. The developed models were illustrated using coffee shop selection in Jengka, Pahang based on six criteria: atmosphere, flavor, price, menu variety, service and location. The SAW and WPM models based on spherical fuzzy numbers were applied and compared in ranking three coffee shops. Further, sensitivity analysis was performed to validate the consistency and stability of the models by increasing and decreasing the criteria weights by 50%. As a result, the developed models show unchanged ranking of alternatives (coffee shops) which highlights the stability of the models. Comparing the two models, the WPM model performs better than the SAW model since it produces smaller errors in terms of score functions when compared to the initial values.