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Reliability estimation of a Network Structure using Generalized Trapezoidal Fuzzy Numbers

Kumar Amit, Dhiman Pooja

Journal of KONBiN

2021

Vol. 51, iss. 1

225--241

Classical sets are used commonly to consider reliability. Because of the uncertainty in the data (which considered in the present paper) classical sets fail to describe the reliability accurately. Uncertainty leads to fluctuation in the actual situation of the structure. Fuzzy logic method attempts to test system reliability with the benefit of membership function. Within this context, specific problems of reasoning-based approaches are studied, explored and correlated with standard reliability approaches. In this paper Generalized Trapezoidal Fuzzy numbers (GTrFN) are used to assess the structure's fuzzy reliability. The reliability of each event is assigned with different level of satisfaction and some improved operations on the generalized trapezoidal fuzzy numbers (GTrFN) are used to calculate the fuzzy boundaries for the resultant reliability of the final event along with the degree of satisfaction. Also the results are compared to demonstrate the application of the improved operations on Generalized Trapezoidal Fuzzy Numbers (GTrFN). The obtained results converge to more precise interval values as compare to the vague fuzzy number.

A Boolean encoding of arithmetic operations

Zbrzezny A.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2010

Vol. 15

177--190

In this paper we present algorithms for a Boolean encoding of four basic arithmetic operations on integer numbers: addition, subtraction, multiplication and division. Integer numbers are encoded in two's complement system as vectors of Boolean formulae, and arithmetic operations are faithfully encoded as operations on vectors of Boolean formulae.

Discrete convolution based on polynomial residue representation

Smyk R.

Poznan University of Technology Academic Journals. Electrical Engineering

2010

No. 63

167-173

This paper presents the study of fast discrete convolution calculation with use of the Polynomial Residue Number System (PRNS). Convolution can be based the algorithm similar to polynomial multiplication. The residue arithmetic allows for fast realization of multiplication and addition, which are the most important arithmetic operations in the implementation of convolution. The practical aspects of hardware realization of PRNS convolution in Xilinx FPGA are also presented.