New Challenges in Neutrosophic Theory and Applications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of indeterminacy/neutrality (I) as an independent component in the neutrosophic set. Thus, neutrosophic theory involves the degree of membership-truth (T), the degree of indeterminacy (I), and the degree of non-membership-falsehood (F). In recent years, the field of neutrosophic set, logic, measure, probability and statistics, precalculus and calculus, etc., and their applications in multiple fields have been extended and applied in various fields, such as communication, management, and information technology. We believe that this book serves as useful guidance for learning about the current progress in neutrosophic theories. In total, 22 studies have been presented and reflect the call of the thematic vision. The contents of each study included in the volume are briefly described as follows. The first contribution, authored by Wadei Al-Omeri and Saeid Jafari, addresses the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets in neutrosophic topological spaces. In the article “Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution”, the authors Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, and Abdur Razzaque Mughal discuss the use of probability distribution function of Birnbaum–Saunders distribution as a proportion of defective items and the acceptance probability in a fuzzy environment. Further, the authors Derya Bakbak, Vakkas Uluc¸ay, and Memet S¸ahin present the “Neutrosophic Soft Expert Multiset and Their Application to Multiple Criteria Decision Making” together with several operations defined for them and their important algebraic properties. In “Neutrosophic Multigroups and Applications”, Vakkas Uluc¸ay and Memet S¸ahin propose an algebraic structure on neutrosophic multisets called neutrosophic multigroups, deriving their basic properties and giving some applications to group theory. Changxing Fan, Jun Ye, Sheng Feng, En Fan, and Keli Hu introduce the “Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment” and test the effectiveness of their new methods. Another decision-making study upon an everyday life issue which empowered us to organize the key objective of the industry developing is given in “Neutrosophic Cubic Einstein Hybrid Geometric Aggregation Operators with Application in Prioritization Using Multiple Attribute Decision-Making Method” written by Khaleed Alhazaymeh, Muhammad Gulistan, Majid Khan, and Seifedine Kadry

Multivariate Control Chart based on Neutrosophic Hotelling T2 Statistics and Its Application

Under classical statistics Hotelling 〖 T〗^2 control chart is applied when the observations of quality characteristics are precise, exact, or crips data. However, in reality, under uncertain conditions, the observations are not necessarily precise, exact, or indeterminacy. As a consequence, the classical Hotelling〖 T〗^2control chart is not appropriate to monitor the process for this condition. To tackle this situation, we proposed new Hotelling 〖 T〗^2 monitoring scheme based on a fuzzy neutrosophic concept. Neutrosophic is the generalization of fuzzy. It is used to handle uncertainty using indeterminacy. The combination of statistics based on neutrosophic Hotelling 〖 T〗^2 and classical Hotelling 〖 T〗^2 control chart will be proposed to tackle indeterminacy observations. The proposed Hotelling 〖 T〗^2 statistics, its call neutrosophic Hotelling 〖 T〗^2 (T_N^2 ) control chart. This chart involves the indeterminacy of observations, its call neutrosophic data and will be expressed in the indeterminacy interval. T_N^2 control charts consist T_N^2 lower chart and T_N^2 upper chart. In this paper, the neutrosophic Hotelling T^2will be applied to individual observations of glass production and will be compared by using classical Hotelling T^2 control chart. Based on T_N^2 control charts of glass production, nine points fall outside of 〖UCL〗_N of lower control chart and 24 points outside from 〖UCL〗_N  of upper control chart. Whereas using classical Hotelling T^2 control chart, just one point outside frim UCL. From the comparison, it concluded that the neutrosophic Hotelling T^2 control chart is more suitable for the indeterminacy of observations

The Encyclopedia of Neutrosophic Researchers - vol. 3

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

Design of Sampling Plan Using Regression Estimator under Indeterminacy

The acceptance sampling plans are one of the most important tools for the inspection of a lot of products. Sometimes, it is difficult to study the variable of interest, and some additional or auxiliary information which is correlated to that variable is available

Sampling Plan Using Process Loss Index Using Multiple Dependent State Sampling Under Neutrosophic Statistics

This paper presents the designing of a sampling plan using the process loss consideration for the multiple dependent state sampling under the neutrosophic statistics. The operating characteristics under the neutrosophic statistical interval method (NSIM) are developed to find the neutrosophic plan parameters of the proposed sampling plan. A non-linear optimization under NSIM is used to find the optimal neutrosophic plan parameters under the given conditions. The advantages of the proposed sampling plan are discussed over the existing sampling plans. A real example having some uncertain observations is given for the illustration purpose

A Variable Acceptance Sampling Plan under Neutrosophic Statistical Interval Method

The acceptance sampling plan plays an important role in maintaining the high quality of a product. The variable control chart, using classical statistics, helps in making acceptance or rejection decisions about the submitted lot of the product. Furthermore, the sampling plan, using classical statistics, assumes the complete or determinate information available about a lot of product. However, in some situations, data may be ambiguous, vague, imprecise, and incomplete or indeterminate. In this case, the use of neutrosophic statistics can be applied to guide the experimenters. In this paper, we originally proposed a new variable sampling plan using the neutrosophic interval statistical method. The neutrosophic operating characteristic (NOC) is derived using the neutrosophic normal distribution. The optimization solution is also presented for the proposed plan under the neutrosophic interval method. The effectiveness of the proposed plan is compared with the plan under classical statistics. The tables are presented for practical use and a real example is given to explain the neutrosophic fuzzy variable sampling plan in the industry

La Estadística Neutrosófica es una extensión de la Estadística de Intervalos, mientras que la Estadística Plitogénica es la forma más general de estadística. (Cuarta versión). Neutrosophic Statistics is an extension of Interval Statistics, while Plitogenic Statistics is the most general form of statistics (Fourth version)

In this paper we show that Neutrosophic Statistics is an extension of Interval Statistics, since it deals with all kinds of indeterminacy (with respect to data, inferential procedures, probability distributions, graphical representations, etc.), allows for indeterminacy reduction, and uses neutrosophic probability which is more general than imprecise and classical probabilities, and has more detailed corresponding probability density functions. Whereas Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments of Woodall et al [1]. We show that not all indeterminacies (uncertainties) can be represented by intervals. Moreover, in some applications, we should use hesitant sets (which have less indeterminacy) instead of intervals. We redirect the authors to Plitogenic Probability and Plitogenic Statistics which are the most general forms of Multivariate Probability and Multivariate Statistics respectively (including, of course, Imprecise Probability and Interval Statistics as subclasses)

A new CUSUM control chart under uncertainty with applications in petroleum and meteorology

Please read abstract in the article.http://www.plosone.orgpm2022Statistic

Neutrosophic multivariate EWMA control chart

The MEWMA chart is one of the traditional multivariate charts which are widely employed in inspecting the quality of manufacturing and services. This chart is created through monitoring the small shifts of mean vectors of variable quality characteristics. Often in practice, the measurement of a quality characteristic produces uncertain, incomplete values, so that ambiguous numbers are obtained. In this condition, a neutrosophic-based control chart can overcome the problem resulting from the ambiguous data. The paper’s objective is to construct a new multivariate monitoring scheme based on a neutrosophic chart, namely the neutrosophic Multivariate EWMA (NMEWMA). Furthermore, the performance of the new multivariate monitoring scheme is evaluated in detecting process shifts employing the Average Run Length (ARL) and Standard Deviation Run Length (SDRL). This control chart is an innovation in the quality monitoring of uncertain data. The research result obtained indicates that the NMEWMA chart performs better than the MEWMA in finding the small mean shifts as well as in the real case application