Introduction to Neutrosophic Statistics

Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because of some individuals that partially belong to the population or sample, and partially they do not belong, or individuals whose appurtenance is completely unknown. Also, there are population or sample individuals whose data could be indeterminate. In this book, we develop the 1995 notion of neutrosophic statistics. We present various practical examples. It is possible to define the neutrosophic statistics in many ways, because there are various types of indeterminacies, depending on the problem to solve.Comment: 122 pages, many geometrical figures, many table

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

Penerapan Peta Kendali Neutrosophic Exponentially Weighted Moving Average (NEWMA) X dalam Monitoring Rata-Rata Proses Ketebalan Kaca

In the industrial sector, the measurement results of a quality characteristic often involve an uncertainty interval (interval indeterminacy). This causes the classical control chart to be less suitable for monitoring quality. Currently, a control chart with a neutrosophic approach has been developed. The neutrosophic control chart was developed based on the concept of neutrosophic numbers with control charts. One of the control charts that have been developed to monitor the mean process is the Neutrosophic Exponentially Weighted Moving Average (NEWMA) X control chart. This control chart is a combination of neutrosophic with classical EWMA control chart.  The neutrosophic control chart consists of two control charts, namely lower and upper, each of which consists of upper and lower control limits. Therefore, NEWMA X is more sensitive to detect out-of-control observations. In this research, the NEWMA X control chart will be used to monitor the average process of the thickness of the panasap dark grey 5mm glass produced by a glass industry. Through the analysis in this research, it was found that by using weighting λN [0, 10; 0, 10] and constant value kN [2, 565; 2, 675], the average process of the thickness of panasap dark grey 5mm glass has not beet controlled statistically because 21 observations were identified that were outside the control limits (out of control). When compared with the classical EWMA control chart with the same weighting λ, 17 observations were detected out of control. This proves that the NEWMA X control chart is more sensitive in detecting observations that are out of control because the determination of the in-control state is based on two values, lower and upper, both at the lower and upper control limits

Studying Neutrosophic Variables

We present in this paper the neutrosophic randomized variables, which are a generalization of the classical random variables obtained from the application of the neutrosophic logic (a new nonclassical logic which was founded by the American philosopher and mathematical Florentin Smarandache, which he introduced as a generalization of fuzzy logic especially the intuitionistic fuzzy logic ) on classical random variables. The neutrosophic random variable is changed because of the randomization, the indeterminacy and the values it takes, which represent the possible results and the possible indeterminacy. Then we classify the neutrosophic randomized variables into two types of discrete and continuous neutrosophic random variables and we define the expected value and variance of the neutrosophic random variable then offer some illustrative examples

Application of neutrosophic Poisson probability distribution series for certain subclass of analytic univalent function

Necessary and sufficient conditions for neutrosophic Poisson probability distribution series to be in the classes Mnγ (θ) were derived by means of coefficient inequalities. The results obtained further strengthening the relationships between geometric function theory and statistics and by extension, fuzzy logic.Publisher's Versio

Neutrosociology for the Analysis of the Pros and Cons of the LIFE Series in UNIANDES, Ecuador

To teach English in Higher Education is of great importance to have professionals prepared for the challenges imposed by the globalization. Ecuador is a Spanish-speaking country for which the teaching of English is part of the programs of study of the courses taught in the Ecuadorian’s universities. This paper aims to carry out a statistical study of the acceptance of the LIFE program in the teaching of English at the Regional Autonomous University of Los Andes (UNIANDES in Spanish), its pros and cons. This is measured according to a Likert scale, with five options, two positive, two negative and one neutral. We consider that none of these three levels should pass unnoticed, since each of them shows a tendency to consider. This includes the aspect of indeterminacy, which indicates the existence of contradictions, indifference, among other motivations of this type. Therefore, we perform a non-traditional processing of the Likert scale, more in line with the principles of Neutrosociology and Neutrosophic Statistics, where the indeterminate probability is taken into account for the social group which is student body