Estimated and analysis of the relationship between the endogenous and exogenous variables using fuzzy semi-paranetric sample selection model

An important progress within the last decade in the development of the selectivity model approach to overcome the inconsistent results if the distributional assumptions of the errors terms are made this problem is through the use of semi-parametric method. However, the uncertainties and ambiguities exist in the models, particularly the relationship between the endogenous and exogenous variables. A new framework of the relationship between the endogenous and exogenous variables of semi-parametric sample selection model using the concept of fuzzy modelling is introduced. Through this approach, a flexible fuzzy concept hybrid with the semi-parametric sample selection models known as Fuzzy Semi-Parametric Sample Selection Model (FSPSSM). The elements of vagueness and uncertainty in the models are represented in the model construction, as a way of increasing the available information to produce a more accurate model. This led to the development of the convergence theorem presented in the form of triangular fuzzy numbers to be used in the model. Besides that, proofs of the theorems are presented. An algorithm using the concept of fuzzy modelling is developed. The effectiveness of the estimators for this model is investigated. Monte Carlo simulation revealed that consistency depends on bandwidth parameter. When bandwidth parameters, c are increased from 0.1, 0.5, 0.75 and 1 as the numbers of N increased (from 100 to 200 and increased to 500), the values of mean approaches (closed to) the real parameter. Through the bandwidth parameter also reveals that the estimated parameter is efficient, i.e., the S.D, MSE and RMSE values become smaller as N increased. In particular, the estimated parameter becomes consistent and efficient as the bandwidth parameters approaches to infinity, c®¥ as the number of observations, n tend to infinity, n®¥. Keywords: Selectivity Model, Semi-Parametric, Fuzzy Concept, Bandwidth, Monte Carl

Statistical correlation coefficients for single-valued neutrosophic sets and their applications in medical diagnosis

The concept of single-valued neutrosophic sets (SVNSs) is considered as an attractive tool for dealing with highly ambiguous and uncertain information. The correlation coefficient of SVNSs acts as an important measure in the single-valued neutrosophic set theory and it has been applied in various fields, such as the pattern recognition, medical diagnosis, decision-making and also clustering analysis. To alleviate the weakness of the existing correlation coefficients, a novel statistical correlation coefficient is put forward to measure the degree of correlation between two SVNSs. This statistical correlation coefficient is developed based on the variance and covariance of SVNSs and its value is between −1 and 1. When solving the multicriteria decision making problems, the criteria show different weight values. To consider the weight information of multiple criteria, the weighted statistical correlation coefficient is developed for SVNSs. Afterwards, two numerical examples are given to show the effectiveness of the proposed statistical correlation coefficient in the pattern recognition, which can accurately classify unknown patterns into known patterns. Finally, the feasibility and practicability of the proposed correlation coefficient formula are illustrated by a practical multiple attribute decision making problem of traditional Chinese medicine diagnosis. The comparative results show that the proposed correlation coefficient formula is rational and effective