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This paper proposed a novel first-order single-valued neutrosophic hesitant fuzzy time series (SVNHFTS) forecasting model. Our aim is to improve the previously proposed neutrosophic time series (NTS) model by incorporating the degree of the hesitancy using single-valued neutrosophic hesitant fuzzy set (SVNHFS) model instead of single-valued neutrosophic set (SVNS). Our paper's novelty is that we incorporate an algorithm that automatically converts the crisp dataset into the neutrosophic set that eliminates the need for experts' input or opinions in determining the membership in each of the partitioned neutrosophic set. We also incorporate Markov Chain algorithm in the de-neutrosophication process to include the weightage of the repeating neutrosophic logical relationships (NLRs). Our paper's significant contribution is to add to the existing body of knowledge related to fuzzy time series (FTS) by developing a new FTS model based on SVNHFS, one of the improved version of fuzzy sets, since this area of research is still relatively underdeveloped. To determine our proposed model's capability, we apply our proposed SVNHFTS model to three real datasets while also comparing the result to the other FTS models based on improved versions of fuzzy sets. Our datasets include benchmark enrollment data of University of Alabama, IDX Composite (Indonesian composite stock index), and MERVAL index (Argentinian composite stock index). The result shows that our proposed SVNHFTS model outperforms most of the other FTS models in terms of AFE and RMSE, especially the previously proposed NTS model.

This paper proposes a multi-criteria decision making method called the neutrosophic data analytic hierarchy process (NDAHP) for the single-valued neutrosophic set (SVNS). This method is an extension of the neutrosophic analytic hierarchy process (NAHP) designed to handle actual datasets which consist of crisp values. The proposed NDAHP method uses an objective weighting mechanism whereas all other existing versions of the AHP, fuzzy AHP, and other fuzzy based AHP method in literature such as the NAHP and picture fuzzy AHP uses a subjective weighting mechanism to arrive at the decision. This makes the proposed NDAHP method effective as the weightage of the criteria which forms the input of the evaluation matrix are determined in an objective manner using actual data collected for the problem, and hence will not change according to the opinions of different decision makers which are subjective. The proposed NDAHP method is applied to a multi-criteria decision making problem related to the ranking of the financial performance of five public listed petrochemical companies trading in the main board of the Kuala Lumpur Stock Exchange (KLSE). Actual dataset of 15 financial indices for the five petrochemical companies for 2017 obtained from Yahoo! Finance was used in this paper. Following this, a brief comparative study is conducted to evaluate the performance of our NDAHP algorithm against the results of other existing SVNS-based decision making methods in the literature. The results are compared against actual results obtained from KLSE. To further verify the rankings obtained through each method, the Spearman and Pearson ranking tests are carried out on each of the decision making methods that are studied. It is proved that NDAHP produces the most accurate results, and this was further verified from the results of the Spearman and Pearson ranking tests.

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.