In this paper, several new algebraic mathematics for positive fuzzy numbers of type (a,a,a,a) are devised and do not need the computation of α-cut of the fuzzy number. Direct mathematical expressions to evaluate exponential, square root, logarithms, inverse exponential etc. of positive fuzzy numbers of type (a,a,a,a) are obtained using the basic analytical principles of algebraic mathematics an...

The aim of this paper is to analyze Bi-level threshold policy of M/(G1, G2)/1 with single vacation (SV) queue in a fuzzy environment. A mathematical Non linear programming (NLP) method is used to construct the membership function of the system characteristic in which the batch arrival-rate, expected group size, setup time, vacation time, service time for first essential service(FES), service ti...

In reliability optimization problems diverse situation occurs due to which it is not always possible to get relevant precision in system reliability. The imprecision in data can often be represented by triangular fuzzy numbers. In this manuscript, we have considered different fuzzy environment for reliability optimization problem of redundancy. We formulate a redundancy allocation problem for a...

During the last years, the concept of input congestion and technical ineff-ciency in data envelopment analysis (DEA), have been investigated by manyresearchers. The motivation of this paper is to present models which obtain thedecreased output value due to input congestion and technical ineciency. More-over, we extend the models to estimate input congestion, technical ineciencyand output reduct...

The control chart (CC) is an important tool in Statistical Process Control (SPC) to improve the quality of products and processes. An unnatural variation in control maps assumes that an assignable cause affects the process is present, and some actions need to be applied to solve the problem. Thanks to their better recognition capability, NEURO-FUZZY is a powerful tool for process control and ra...

and Applied Analysis 3 2.1. Fuzzy Numbers In this section, we give certain essential concepts of fuzzy numbers and their basic properties. For further information see 2, 3 . A fuzzy set à on a set X is a function à : X → 0, 1 . Generally, the symbol μà is used for the function à and it is said that the fuzzy set à is characterized by itsmembership function μà : X → 0, 1 which associates with ea...

The control chart (CC) is an important tool in Statistical Process Control (SPC) to improve the quality of products and processes. An unnatural variation in control maps assumes that an assignable cause affects the process is present, and some actions need to be applied to solve the problem. Thanks to their better recognition capability, NEURO-FUZZY is a powerful tool for process control and ra...

The control chart (CC) is an important tool in Statistical Process Control (SPC) to improve the quality of products and processes. An unnatural variation in control maps assumes that an assignable cause affects the process is present, and some actions need to be applied to solve the problem. Thanks to their better recognition capability, NEURO-FUZZY is a powerful tool for process control and ra...

c-Chart was frequently used to monitor wafer defects during IC manufacturing. The clustering degree of defect on a wafer will increase along with the area of wafer gradually enlarging. The defect clustering causes the Poisson-based c-chart to exhibit many false alarms. Although several revised control charts have been developed to reduce the number of false alarms, those control charts still ha...