A Fuzzy Best-Worst Method Based on the Fuzzy Interval Scale

The best worst method (BWM) has been regarded as an ideal alternative to the analytic hierarchy process (AHP) between multi-criteria decision making (MCDM) methods since it reduces the number of pairwise comparisons and maintains the consistency between judgments. In real decision-making problems, decision-makers are not always sure about their decisions and mainly express their preferences with degrees of uncertainty. Moreover, they often face problems that must distinguish a prominent alternative among a shortlist with similar traits, which raises the severity of decision making in an uncertain environment. To deal with these situations, we propose a new linear fuzzy BWM based on a fuzzy interval scale, which is called fuzzy additive BWM. The proposed method maintains the features of the original BWM and also decreases the complexity of fuzzy calculations by eliminating the fuzzy multiplication operation. In addition, a fuzzy consistency index is proposed to check the validity of the input data. Also, fuzzy consistency ratio and total deviation are introduced for evaluating the obtained results by the fuzzy additive BWM. An example is applied and solved by the fuzzy additive BWM to indicate the method's efficiency. Finally, comparative analyses are conducted to show the advantages and suitability of the new BWM method.