This paper proposes an integration of two neutrosophic based multi-criteria decision making methods, namely the neutrosophic data analytical hierarchy process (NDAHP) and the Technique of Order Preference by Similarity to Ideal Solution (TOPSIS) with maximizing deviation method, both based on the single-valued neutrosophic set (SVNS) to evaluate the efficiency of general insurance companies in Malaysia. The level of efficiency of insurance companies is a subjective and vague matter, as the efficiency can be further branched into operational efficiency, investment efficiency, underwriting efficiency, and risk management efficiency. Hence relying on entirely objective decision making methods based on crisp data might not address the problem effectively, and therefore fuzzy based decision making methods are highly appropriate to be used in this situation. Our proposed decision making algorithm uses an integrated weighting mechanism that takes into consideration both the objective and subjective weights of the data attributes. The objective weighting mechanism handles the actual datasets that were used which consists of crisp values, whereas the subjective weighing mechanism handles the opinions of the experts in the general insurance industry who were surveyed in this study. This makes the proposed method a more holistic approach to evaluate the efficiency of general insurance companies in Malaysia as previous researches in this area are generally based on the actual datasets without consideration of the opinions and evaluations of the industry experts, or vice-versa. The proposed decision making algorithm is applied on actual datasets of management expenses, net commission, net earned premium and the net investment income for 19 selected general insurance companies in Malaysia over a two-year period from 2016 to 2017. The results obtained are then discussed and the possible reasons for the results are analyzed. A comprehensive comparative study of the results obtained via our proposed method and two other commonly used methods are then presented, analyzed and discussed.