The aim of this paper is to propose a new similarity measure of singlevalued neutrosophic sets (SVNSs). The idea of the construction of the new similarity measure comes from Chi-square distance measure, which is an important measure in the applications of image analysis and statistical inference. Numerical examples are provided to show the superiority of the proposed similarity measure comparing with the existing similarity measures of SVNSs. A weighted similarity is also put forward based on the proposed similarity. Some examples are given to show the effectiveness and practicality of the proposed similarity in pattern recognition, medical diagnosis and multi-attribute decision making problems under single-valued neutrosophic environment.
The aim of this paper is to develop a new hierarchical Bayesian estimation method under symmetric entropy loss function for reliability of the binomial distribution. With the rapid development of manufacturing techniques, some electric products are highly reliable, and thus zero-failure data often occur when putting them in censored lifetime tests. Based on zero-failure data, the reliability analysis is very important for manufacturing. The hierarchical Bayesian estimator is regarded as a robust estimating method, but many existing robust Bayes estimators are complex and difficult to be utilized in practice. The contribution of this article is to present an easy hierarchical Bayesian estimator for reliability of the binomial distribution when reliability has a negative log-gamma prior distribution. Finally, a practical example is provided to show the feasibility and robustness of different estimators.
In this paper the KKT system of a general variational inequality problem (denoted by VIP(X,F)) is reformulated as a constrained optimization problem. A sufficient condition, which ensures a stationary point of the optimization problem being a solution of the KKT system of VIP(X,F), is analyzed. A projection-type method for solving the KKT system of VIP(X,F) with closed convex set X is presented. The new algorithm has nice properties such as retaining feasibility, easy computation if the region X is a box or a ball, and strongly global and local convergence. Numerical examples show that the new algorithm is promising.
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