An Adapted Bounded Fuzzy Stepwise Weight Assessment Ratio Analysis (MF SWARA) Method

Abstract

Determining criteria weights represents a significant step in multi-criteria decision-making (MCDM) field, as weights of the criteria directly influence the ranking of alternatives and the robustness of final decisions. Among subjective methods for determining the weights of the criteria, the Stepwise Weight Assessment Ratio Analysis (SWARA) method has been adopted for solving problems in various areas due to its simplicity, applicability and strong interpretability. To address uncertainty and vagueness inherent in human judgments, several fuzzy extensions of the SWARA method have been proposed. Existing SWARA extensions often generate intermediate parameters that exceed the unit interval, which complicates interpretability and reduces numerical transparency. Therefore, this paper proposes a modified fuzzy extension of the SWARA method that ensures all parameters obtained during the calculation procedure of the fuzzy SWARA method to remain within the interval [0, 1]. To validate the proposed approach, several numerical illustrations are presented, including both individual and group decision making scenarios, followed by computational simulation implemented in Python programming language. The conducted numerical examples and simulation results confirm that the proposed extension achieves results identical to those obtained by the improved multiplicative weighting (IMW) SWARA method, with the note that the computational procedure of the proposed extension ensures that all variable values are in the interval [0, 1]. As such, the proposed MF SWARA method represents a bounded, theoretically consistent and a valuable advancement in the ongoing fuzzy MCDM weighting methods.