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The Smarandache anti‐geometry is a non‐euclidean geometry that denies all Hilbert’s 20 axioms, each axiom being denied in many ways in the same space. In this paper, one finds an economics model to this geometry by making the following correlations: a point is the balance in a particular checking account, expressed in US currency (points are denoted by capital letters); a line is a person, who can be a human being (lines are denoted by lower case italics); and a plane is a US bank, affiliated to the FDIC (planes are denoted by lower case boldface letters).

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.

This paper proposes a family of estimators of population mean using information on several auxiliary variables and analyzes its properties in the presence of measurement errors.

This article investigates Rugina’s orientation table and gives particular examples for several of its seven models. Leon Walras’s Economics of Stable Equilibrium and Keynes’s Economics of Disequilibrium are combined in Rugina’s orientation table in systems which are s percent stable and 100−s percent unstable, where s may be 100, 95, 65, 50, 35, 5, and 0. Classical logic and modern logic are united in Rugina’s integrated logic, and then generalized in neutrosophic logic.

This paper aims to present a new term weighting approach for text classification as a text mining task. The original method, neutrosophic term frequency – inverse term frequency (NTF-IDF), is an extended version of the popular fuzzy TF-IDF (FTF-IDF) and uses the neutrosophic reasoning to analyze and generate weights for terms in natural languages. The paper also propose a comparative study between the popular FTF-IDF and NTF-IDF and their impacts on different machine learning (ML) classifiers for document categorization goals.

After preprocessing textual data, the original Neutrosophic TF-IDF applies the neutrosophic inference system (NIS) to produce weights for terms representing a document. Using the local frequency TF, global frequency IDF and text N's length as NIS inputs, this study generate two neutrosophic weights for a given term. The first measure provides information on the relevance degree for a word, and the second one represents their ambiguity degree. Next, the Zhang combination function is applied to combine neutrosophic weights outputs and present the final term weight, inserted in the document's representative vector. To analyze the NTF-IDF impact on the classification phase, this study uses a set of ML algorithms.

Practicing the neutrosophic logic (NL) characteristics, the authors have been able to study the ambiguity of the terms and their degree of relevance to represent a document. NL's choice has proven its effectiveness in defining significant text vectorization weights, especially for text classification tasks. The experimentation part demonstrates that the new method positively impacts the categorization. Moreover, the adopted system's recognition rate is higher than 91%, an accuracy score not attained using the FTF-IDF. Also, using benchmarked data sets, in different text mining fields, and many ML classifiers, i.e. SVM and Feed-Forward Network, and applying the proposed term scores NTF-IDF improves the accuracy by 10%.

The novelty of this paper lies in two aspects. First, a new term weighting method, which uses the term frequencies as components to define the relevance and the ambiguity of term; second, the application of NL to infer weights is considered as an original model in this paper, which also aims to correct the shortcomings of the FTF-IDF which uses fuzzy logic and its drawbacks. The introduced technique was combined with different ML models to improve the accuracy and relevance of the obtained feature vectors to fed the classification mechanism.

Each individual investor is different, with different financial goals, levels of risk tolerance and personal preferences. From the point of view of investment management, these characteristics are often defined as objectives and constraints. Objectives can be the type of return being sought, while constraints include factors such as time horizon, how liquid the investor is, any personal tax situation and how risk is handled. It is really a balancing act between risk and return with each investor having unique requirements, as well as a unique financial outlook – essentially a constrained utility maximization objective. To analyze how well a customer fits into a particular investor class, one investment house has even designed a structured questionnaire with about 24 questions that each has to be answered with values from 1 to 5. The questions range from personal background to what the customer expects from an investment. A fuzzy logic system has been designed for the evaluation of the answers to the above questions. The notion of fuzziness with respect to funds allocation is investigated.

This research work has developed an integrated fuzzy Delphi and neutrosophic best–worst framework for selecting the sustailient (sustainable and resilient) supplier for an additive manufacturing (AM)-enabled industry.

An integrated fuzzy Delphi method (FDM) and neutrosophic best–worst method (N-BWM) approach is developed. 34 supplier evaluation criteria falling under 4 groups, that is, traditional, sustainable, resilient, and AM specific, are identified and validated using the FDM. Afterward, the weights of each criterion are measured by N-BWM. Later on, the performance evaluation is carried out to determine the best-suited supplier. Finally, sensitivity analysis is performed to know the stability and robustness of the proposed framework.

The outcome indicates the high performance of the suggested decision-making framework. The analysis reveals that supplier 4 (S4) is selected as the most appropriate for a given firm based on the FDM and N-BWM method.

The applicability of this framework is demonstrated through an industrial case of a 3D-printed trinket manufacturer. The proposed research helps AM decision-makers better understand resiliency, sustainability, and AM-related attributes. With this, the practitioners working in AM business can prioritize the supplier selection criteria.

This is the primitive study to undertake the most critical aspect of supplier selection for AM-enabled firms. Apart from this, an integrated FDM-N-BWM framework is a novel contribution to the literature on supplier selection.

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.