Since 2019, COVID disease threats the world. It originated in China, and due to its easy spread characteristics, it spreads quickly among all the countries. As the world faced a new kind of virus, the government could not control its spread, and the fatality rate had also hugely increased. In 2021, the vaccine for the virus was introduced by various countries, which aids in controlling the spread and mortality rate. The mutant form of this virus exhibits high efficiency. So, this study analyzes the effective of COVID vaccines released after 2020 against all COVID variants through the fuzzy superiority and inferiority ranking (SIR) decision-making method. The vaccines and variants are analyzed by the $m\times n$ matrix pattern under the fuzzy SIR-integrated weight method. The disease variants are taken as criteria and that are assigned integrated weight based on subjective, objective weight approaches. The intuitionistic fuzzy set-double parameter (IFS-DP) handles the vagueness by strictly including only membership and non-membership functions with the condition $0\le {\mu }^{\ast }(x)+{\nu }^{\ast }(x)\le 1$. As a result, the vaccines Moderna and Covishield are attained top rank and have a high likelihood to combat all the COVID variants compared to other vaccines. The reached outcomes are corroborated through sensitivity and comparative analysis. The sensitivity and comparative studies are measured by increasing the order of IFS-DP and extant fuzzy MCDM methods, respectively. The comparison of these results with those obtained from the proposed method is similar to the sensitivity study, along with minor variations observed in the comparative study. Therefore, the proposed method generates an efficient outcome. Moreover, the testing hypothesis technique is applied to check the efficiency of proposed method.