The intuitionistic fuzzy set, which has a membership and non-membership degree, is a controlling and effective device for dealing with fuzziness and uncertainty. Recently, the square root fuzzy set (SR-FS) which is one of the efficient generalizations of an intuitionistic fuzzy set (IFS) for dealing with uncertainty and haziness in information has been introduced. In this study, a novel method for multiple attribute decision-making (MADM) based on SR-Fuzzy information is investigated. Since aggregation operators are significant in the decision-making process. To achieve this goal, the current paper suggests a variety of novel Bonferroni Mean and Weighted Bonferroni Mean operators to aggregate the SR-Fuzzy values for the various decision-maker preferences. SR-Fuzzy Bonferroni Mean (SRFBM) operator and weighted SR-Fuzzy Bonferroni Mean (WSRFBM) operator are established and describes their properties. Then, we construct a MADM approach using the proposed operators for the SR-Fuzzy information and proved the approach with a mathematical example. In the end, a comparative study of the developed and existing approaches has been discussed to evaluate the pertinency and practicality of the proposed DM technique.