The VIKOR method (from Serbian: VIseKriterijumska Optimizacija I Kompromisno Resenje) is an efficient multi-attribute decision-making (MADM) tool that is highly regarded in the decision-making field for its unique advantage of seeking an overall optimal solution while maintaining a relative balance among various attributes. However, the VIKOR approach exhibits certain drawbacks when used for fuzzy decision-making, especially when dealing with multi-valued neutrosophic set (MVNS) problems. Specifically, this method only considers the distance of the solution to the positive ideal solution (PIS), while neglecting the significance of the negative ideal solution (NIS). This limitation undermines its ability to fully capture decision-makers' attitudes toward risk and profit in practical scenarios. In light of this, this study aims to enhance the traditional VIKOR method within the framework of MVNS. Given that the attribute information is entirely unknown and the decision information is characterized by MVNS, this paper innovatively proposes an attribute weight determination model based on a dual-dimensional approach that considers both alternatives and attributes. Building on this foundation, we introduce an optimistic coefficient k and integrate it into the traditional VIKOR method to simultaneously consider both PIS and NIS. Then, a practical case study on service provider selection is presented to demonstrate the efficacy of the suggested method. Additionally, sensitivity and comparative analyses are conducted to validate the effectiveness and robustness of our proposed methodology. In summary, our research not only enriches the theory of MADM but also provides decision-makers with a novel decision-making tool.

In venture capital, fuzzy information can be effectively represented using single-valued neutrosophic sets, and TOPSIS and TODIM are commonly used methods in multiattribute decision making. Distance measurement plays a crucial role in these methods. This paper introduces a novel parameter distance measure for single-valued neutrosophic sets and an improved method based on TODIM and TOPSIS. First, the proposed distance measure addresses limitations of existing metrics and is rigorously proven to satisfy axiomatic distance definitions. Secondly, to consider the decision-maker’s risk attitude and simplify the calculation process, we propose a new method with the known parameter of risk attitude based on TODIM and TOPSIS. Finally, a case study of venture capital application is provided to showcase the effectiveness and practicality of the proposed distance measure and decision-making method in addressing multi-attribute decision-making problems within SVNS environments. Furthermore, sensitivity analysis of the distance measure parameters demonstrates consistent ranking results across various parameter values, thereby validating the robustness of the proposed approach. Comparative evaluations with other decision-making methods in identical scenarios underscore the rationality and superiority of our proposed methodology. The proposed distance measure and decision-making method offer significant contributions to the theory of single-valued neutrosophic sets and the resolution of venture capital problems.

In 2021, real estate investment and corporate profits declined, residents' consumption was relatively stable but business consumption shrank significantly. Since the upgrading of residents' consumption and the improvement of corporate profits will still be the main driving force for the performance growth of the liquor sector, the liquor industry has made corresponding adjustments and will enter a new development cycle. Financial decisions among enterprises are particularly important. Based on the current situation of liquor enterprises and the characteristics of financial decisions, this paper constructs a composite evaluation model of FCFF and BS for the value of liquor enterprises from the perspective of real options, and uses this model to evaluate the enterprise value of Wuliangye Group. In addition, this paper compares the model's assessment results with the market approach to enhance the rationality of the assessment results and provide a reference for similar studies in the future.

Multiple attribute decision making (MADM) is a vital part of modern decision science and often faces challenges in representing fuzzy information and maintaining dynamic adaptability under complex uncertain conditions. Although existing studies seek to improve heterogeneous information fusion using fuzzy set theory, research gaps persist in dynamic fuzzy decision mechanisms, reduction of subjective factors, and validation in multi-dimensional scenarios. The classic PROBID method, leveraging an ideal-average distance mechanism, has demonstrated considerable effectiveness across various domains. Yet, its strong sensitivity to attribute weight changes and limited adaptability in static contexts restrict broader applicability. To overcome these issues, this research proposes a hybrid model named multivalued neutrosophic contact numbers-based PROBID (MVCN-PROBID). By integrating the ternary semantic representation of multi-valued neutrosophic numbers (MVNNs) with the identity, discrepancy, and contrary theoretical mechanisms of contact numbers (CNs) in set pair analysis (SPA), a dual-dimensional dynamic evaluation system is established. This synergy within the PROBID framework partially alleviates traditional decision-making bottlenecks in dynamic fuzzy environments. Empirical analysis using two cases, agricultural drone procurement and investment firm selection, shows that MVCN-PROBID produces priority rankings closely matching practical needs. Internal robustness was examined via systematic parameter adjustments, and consistency was verified through multi-method comparative ranking, confirming the model's advantages in stability, applicability, and reliability. This work extends the PROBID method’s theoretical boundaries under a fuzzy mathematics framework, offering a structured solution for MADM in complex settings.

Universities are important talent training bases in China and the main driving force for achieving the strategic layout of “revitalizing the country through science and education” and “strengthening the country through talent". Oil painting is a global art with rich humanistic and artistic value. Most art colleges in China have set up oil painting courses. Analyze the current situation and value of oil painting course teaching in local art (teacher training) majors, and leverage the educational role of oil painting courses by enriching course offerings, emphasizing the integration of humanistic innovation, improving teacher literacy, and striving to further improve the quality and efficiency of oil painting course teaching. The quality evaluation of oil painting teaching in universities is viewed as multiple-attribute decision-making (MADM). The grey relational analysis (GRA) is a useful tool to cope with the MADM issue. The probabilistic simplified Neutrosophic set (PSNSs) is easy to characterize uncertain information during the quality evaluation of oil painting teaching in universities. In this paper, in order to obtain the weight information, an optimization model implemented to obtain a simple and exact formula which can be employed to derive the attribute weights values based on the Lagrange function and the probabilistic simplified neutrosophic number grey relational analysis (PSNN-GRA) technique is implemented for MADM to rank the alternatives. Finally, a numerical example for quality evaluation of oil painting teaching in universities is used to verify the practicability of the PSNN-GRA technique and compares it with other techniques.

single complex neutrosophic sets (SVCNSs) expand upon the concept of neutrosophic sets, offering a framework for handling uncertainty and inconsistency in periodic data. Distance and entropy measures are pivotal tools for managing information characterized by inherent uncertainties. However, research on entropy in the context of single-valued complexes is currently limited. Hence, this paper introduces a range of distance measures and presents an entropy calculation method based on these measures specifically tailored for SVCNS. To start, we provide a definition of single-valued complex neutrosophic sets and expound upon their set-theoretic properties. Following this, we introduce normalized distance formulas and propose an axiomatic definition for SVCNS entropy. Finally, to showcase the practicality and effectiveness of our proposed entropy measure, we include a real-world example involving the selection of green providers. Furthermore, we conduct a comparative analysis with existing methods, highlighting the valuable utility of our approach in addressing uncertainty and inconsistency in data analysis.

The MULTIMOORA (multiple multi-objective optimization by ratio analysis) method is useful for multiple criteria decision-making method. It is based on expected utility theory and assumes that decision makers are completely rational. However, some studies show that human beings are usually bounded rational, and their regret aversion behaviors play an important role in the decision-making process. Interval neutrosophic sets can more flexibly depict uncertain, incomplete and inconsistent information than single-valued neutrosophic sets. Therefore, this paper improves the traditionalMULTIMOORA method by combining the regret theory under interval neutrosophic sets. Firstly, the regret theory is used to calculate the utility value and regret-rejoice value of each alternatives. Secondly, the criteria weights optimization model based on the maximizing deviation is constructed to obtain the weight vector. Then, the MULTIMOORA method is used to determine the order of the alternatives. Finally, an illustrative example about school selection is provided to demonstrate the feasibility of the proposed method. Sensitivity analysis shows the validity of the regret theory in the proposed method, and the ranking order change with different regret avoidance parameter. Comparisons are made with existing approaches to illustrate the advantage of the proposed method in reflecting decision makers' psychological preference.

Single-valued neutrosophic sets (SVNS) are proficient in conveying fuzzy information within the realm of multiple attribute decision making (MADM), and The TOPSIS method effectively ranks alternatives in MADM. Attribute weight and distance measurement are important steps in TOPSIS method. The focus of this paper is to propose a new attribute weight determination method in the SVNS environment, namely Decision Laboratory and Experimentation Method -Analytic Network Process (D-ANP). A new single-valued neutrosophic distance measure is also defined, namely single-valued neutrosophic Kulcynksi distance, and the effectiveness of the generalized single-valued neutrosophic Kulcynksi distance is proved. Finally, the proposed D-ANP method and the defined Kulcynksi distance are applied to the TOPSIS method of MADM, and the feasibility of the D-ANP method and Kulcynksi distance is verified through application examples.

This paper provides a novel target threat assessment model that utilizes TOPSIS and three-way decision-making under a single-valued neutrosophic environment. The presented model provides theoretical support for combat decision-making in complex battlefield environments with uncertain information. The model employs single-valued neutrosophic sets to handle uncertain data, which enhances the descriptive ability of information. The maximum deviation method is used to calculate attribute weight factors, which highlights the importance of each attribute. The final target threat ranking is obtained based on the relative closeness coefficient of each target. Furthermore, the proposed model constructs a multi-attribute aggregation loss function matrix for each target, sets the risk avoidance coefficient under the knowledge of the battlefield condition, and calculates the decision threshold of each target using three-way decision theory. This method produces the classification of the target choice. The numerical examples and comparison analysis demonstrate that the suggested model can handle ambiguous scenario information effectively and reasonably, transform traditional decision-making ranking results into three-way classification findings, and provide a rationale for choosing an attacking target.

The single-valued neutrosophic sets area unit powerful tool to describe uncertain data. TODIM method is usually accustomed solve multi-attributes decision-making issues. supported the cumulative prospect theory, this paper proposes an extended TODIM method that comprehensively reflects the psychological characteristics of decision makers. Firstly, we in short explain the definitions of cumulative prospect theory and single-valued neutrosophic sets. Secondly, we introduce the steps of the classical TODIM method of resolution multiple attributes decision-making issues. On the idea, we propose an extended TODIM method to comprehensively mirror the psychological state of decision makers. Finally, through the case analysis, it's evidenced that extended TODIM method will higher think about the psychological characteristics of decision makers.

应急物流是指为应对突发公共事件的应急物资需求所产生的特殊物流活动.在现有研究的基础上,并结合应急物流自身的特点,给出了应急物流供应商的评价指标体系,采用矩估计组合赋权法确定评价指标的权重.将灰色关联分析与双基点法(也称作TOPSIS法)相结合,构建一种改进TOPSIS法的应急物流供应商评价模型.最后通过实例加以说明,并与其他典型评价方法进行分析比较,发现评价结果基本一致,从而验证了该方法用于应急物流供应商评价是有效且可行的,能够为应急物资采购提供有力参考.

The fairness preference in the principal-agent relationship is a vital factor that can even determine the success or failure of one program. Under normal circumstances, the capital invested by VC is often several times that of EN, which is one of the reasons for the profit gap between EN and VC. Therefore, when establishing a principal-agent model with fairness preferences, it is necessary to project the utility of VC to the level of EN and compare it with the utility of venture entrepreneurs, which will better reflect the profit gap between the two. On the basis of previous studies, this paper considers the amount of contribution of the participants, builds four principal-agent models to find the optimal distribution of income between the Venture Entrepreneur (EN) and the Venture Capital (VC) in a venture capital investment program, two without fairness preference and others with fairness preference. After the simulation we confirm that the fairness preference coefficient exerts a great impact on the distribution of income in both situations where information is symmetric and asymmetric, and a strong fairness preference will lead to a greater net profit gap between the EN and the VC. Thus, the EN should carefully choose the level of his efforts to realize the maximum return for him. In the case of information asymmetry, EN's optimal effort level decreases as the fairness preference coefficient increases.This will affect project revenue. And then affect the VC income.

This paper is concerned with the asymptotic behavior of solution to the damped Euler equation far away from vacuum. First of all, the global existence together with the decay rate of the solution and its derivatives are derived by the standard energy method. The decay rates of the solution operator are further improved by Green function method. Finally, the solution of damped Euler equation is confirmed to converge its best asymptotic profile when the initial data is in a certain weighted function space, which establishes the upper and lower bounds of the decay rate to the solution of the damped Euler equation. Here, we provide a new way to check the optimal decay rate of the solutions to the damped Euler equation when the initial data is set in L-1, which also could be applied to some other diffusive evolution system.

Covering rough set is a classical generalization of rough set. As covering rough set is a mathematical tool to deal with incomplete and incomplete data, it has been widely used in various fields. The aim of this paper is to extend the covering rough sets to interval neutrosophic sets, which can make multi-attribute decision making problem more tractable. Interval neutrosophic covering rough sets can be viewed as the bridge connecting Interval neutrosophic sets and covering rough sets. Firstly, the paper introduces the definition of interval neutrosophic sets and covering rough sets, where the covering rough set is defined by neighborhood. Secondly, Some basic properties and operation rules of interval neutrosophic sets and covering rough sets are discussed. Thirdly, the definition of interval neutrosophic covering rough sets are proposed. Then, some theorems are put forward and their proofs of interval neutrosophic covering rough sets also be gived. Lastly, this paper gives a numerical example to apply the interval neutrosophic covering rough sets.

Due to the complexity of decision-making problems and the subjectivity of decision-makers in practical application, it is necessary to adopt different forms of information expression according to the actual situation of specific decision-making problems and choose the best method to solve them. Multi-valued neutrosophic set, as an extension of neutrosophic set, can more effectively and accurately describe incomplete, uncertain or inconsistent information. TODIM and TOPSIS methods are two commonly used multi-attribute decision-making methods, each of which has its advantages and disadvantages. This paper proposes a new method based on TODIM and TOPSIS to solve multi-attribute decision-making problems under multi-valued neutrosophic environment. After introducing the related theory of multi-valued neutrosophic set and the traditional TODIM and TOPSIS methods, the new method based on a combination of TODIM and TOPSIS methods is described. And then, two illustrative examples proved the feasibility and validity of the proposed method. Finally, the result has been compared with some existing methods under the same examples and the proposed method's superiority has been proved. This paper studies this kind of decision-making problem from algorithm idea, algorithm steps and decision-making influencing factors.

A single-valued neutrosophic set is a special case of neutrosophic set, which can describe a great deal of imprecise, uncertain and inconsistent information in the real world. Aiming at the problem of multi-attribute decision-making with neutrosophic sets (SVNSs). In this paper, a new method for multi-attribute decsion-making (MADM) under single-valued neutrosophic sets and single-valued neutrosophic sets are introduced, a distance formula based on single-valued neutrosophic sets is given. Secondly, the weighted comprehensive decision matrix is constructed. In addition, TOPSIS method is extended to single-valued neutrosophic environment, the relative closeness coefficient is used to sort the alternatives, the optimal decsion-making shceme is obtained. Finally a numerical example is givent to illustrated the feasibility and effectiveness of the proposed method.

Single-valued neutrosophic sets (SVNSs) can effectively describe the multi-attribute decision-making (MADM) problems which are characterized by incompleteness and uncertainty. Aiming at the MADM problem of SVNSs, a series of methods are proposed to solve the problem, such as the TODIM and PROMETHEE methods. The main idea of the TODIM method is to establish a relative superiority function of scheme relative to other schemes based on the value function of prospect theory, and the ranking of alternatives is determined according to the obtained superiority. In the PROMETHEE method, the decision maker selects the preference function for each attribute according to their preference, and then calculates the priority index, inflow, outflow and net flow according to the difference of the attribute values of scheme, so as to determine the ranking of alternatives. In this paper, a new method based on PROMETHEE and TODIM is proposed to solve the MADM problem under the single-valued neutrosophic environment. Based on the calculation formula of inflow and outflow in PROMETHEE method, and the calculation formula of overall dominance in the TODIM method, a new integrated formula is obtained.

As an extension of neutrosophic set, interval complex neutrosophic set is a new research topic in the field of neutrosophic set theory, which can handle the uncertain, inconsistent and incomplete information in periodic data. Distance measure is an important tool to solve some problems in engineering and science. Hence, this paper presents some interval complex neutrosophic distance measures to deal with multi-criteria group decision-making problems. Firstly, this paper shows the definitions of interval complex neutrosophic set, and especially some novel set theoretic properties. Then, some new distance measures based on Hamming, Euclidean and Hausdorff metrics are proposed. Next, an approach is developed to rank the alternatives in multi-criteria group decision-making problems. Finally, a numerical example is given to demonstrate the practicality and effectiveness of these distance measures.

With the development of the generalized exponential (GE) distribution, the two-parameter generalized exponential (TPGE) distribution has been widely used for the analysis of lifetime data in recent years. In this paper, a new class of TPGE distribution is proposed on the basis of previous work. Then the relevant statistical inferences of the TPGE are also discussed. And, the parameters are estimated by using the moment estimation and the maximum likelihood estimation.