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This research attempts to present a solid transportation problem (STP) mechanism in uncertain and indeterminate contexts, allowing decision makers to select their acceptance, indeterminacy and untruth levels.

Due to the lack of reliable information, changeable economic circumstances, uncontrolled factors and especially variable conditions of available resources to adapt to the real situations, the authors are faced with a kind of uncertainty and indeterminacy in constraints and the nature of the parameters of STP. Therefore, an approach based on neutrosophic logic is offered to make it more applicable to real-world circumstances. In this study, the triangular neutrosophic numbers (TNNs) have been utilized to represent demand, transportation capacity, accessibility and cost. Then, the neutrosophic STP was converted into an interval programming problem with the help of the variation degree concept. Then, two simple linear programming models were extracted to obtain the lower and upper bounds of the optimal solution.

The results reveal that the new model is not complicated but more flexible and more relevant to real-world issues. In addition, it is evident that the suggested algorithm is effective and allows decision makers to specify their acceptance, indeterminacy and falsehood thresholds.

Under the transportation literature, there are several solutions for TP and STP in crisp, fuzzy set (FS) and intuitionistic fuzzy set (IFS) conditions. However, the STP has never been explored in connection with neutrosophic sets to the best of the authors’ knowledge. So, this work tries to fill this gap by coming up with a new way to solve this model using NSs.

The Chinese believe that “man will conquer the sky” and “fighting with the sky brings endless joy”. Considering that disaster assessment can be regarded as a two-person, zero-sum game problem between nature and human beings, this paper proposes a multi-attribute decision-making method based on game theory and grey theory in a single-value neutrosophic set environment. Due to the complexity and uncertainty of the decision-making environment, the method builds a decision matrix based on single-valued neutrosophic numbers.

First, the authors use the single-value neutrosophic information entropy to calculate the attribute weights and the weighted decision matrix. Second, the optimal mixed strategy method based on linear programming solves the optimal mixed strategy for both sides of the game so that the expected payoff matrix can be obtained. Finally, grey correlation analysis is used to obtain the closeness coefficient of each alternative based on the expectation payoff matrix to identify the ranking result of the alternative.

An example is used to verify the effectiveness of the proposed method, and its rationality is verified through a comprehensive comparison and analysis of the various aspects.

The proposed decision-making method can be applied to typhoon disaster assessment. Such assessment results can provide intelligent decision support to the relevant disaster management departments, thereby reducing the negative impact of typhoon disasters on society, stabilizing society and improving people's happiness. Further, the method can be used for decision-making, recommendation and evaluation in other fields.

The proposed method uses single-value neutrosophic numbers to solve the information representation problem of decision-making in a complex environment. Under a new perspective, game theory is used to handle the decision matrix, while grey relational analysis converts inexact numbers to exact numbers for comparison and sorting. Thus, the proposed method can be used to make reasonable decisions while preserving information to the extent possible.

Single-valued neutrosophic sets (SVNSs) are efficient models to address the complexity issues potentially with three components, namely indeterminacy, truthness and falsity. Taking advantage of SVNSs, this paper introduces some new aggregation operators (AOs) for information fusion of single-valued neutrosophic numbers (SVNNs) to meet multi-criteria group decision-making (MCGDM) challenges.

Einstein operators are well-known AOs for smooth approximation, and prioritized operators are suitable to take advantage of prioritized relationships among multiple criteria. Motivated by the features of these operators, new hybrid aggregation operators are proposed named as “single-valued neutrosophic Einstein prioritized weighted average (SVNEPWA) operator” and “single-valued neutrosophic Einstein prioritized weighted geometric (SVNEPWG) operators.” These hybrid aggregation operators are more efficient and reliable for information aggregation.

A robust approach for MCGDM problems is developed to take advantage of newly developed hybrid operators. The effectiveness of the proposed MCGDM method is demonstrated by numerical examples. Moreover, a comparative analysis and authenticity analysis of the suggested MCGDM approach with existing approaches are offered to examine the practicality, validity and superiority of the proposed operators.

The study reveals that by choosing a suitable AO as per the choice of the expert, it will provide a wide range of compromise solutions for the decision-maker.

In this paper, a combined TODIM-BSC method with the neutrosophical approach for evaluating the performance of a private insurance company has been proposed. In other words, first, using the BSC technique, and identify the performance evaluation indicators, then evaluate the performance of the insurance company's agencies and rank them with the TODIM decision-making method.

The insurance industry has a special prestige and importance in domestic and foreign trade. The evaluation of insurance companies, in addition to informing the stakeholders, increases competition, industry dynamism, sustainable and balanced development of society. The purpose of this paper is to establish a model for evaluating the performance of private insurance companies by adopting multiple-attribute decision-making and Balanced Scorecard (BSC) with single-values neutrosophic numbers (SVNNs) which will be applied by considering a set of indicators and alternatives deliberated with different viewpoints.

A case study of the private insurance agencies in one of the provinces of Iran based on 26 criteria of agencies is used to confirm the practicality and effectiveness of the proposed model. Finally, there was a discussion about why the results are logical, which shows the strength and robustness of the proposed framework.

To the best of our knowledge, no study has been performed to evaluate the performance of a real-world problem with the integrated TODIM-BSC method in a neutrophilic environment. Therefore, this paper can be effective in bridging the existing research gap and expanding our knowledge of the discussion of evaluating the performance of organizations or companies. Besides, by using these results, the authors can help the planners of these companies as well as similar organizations in attracting satisfaction and retaining target customers.