Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India.
ISA Trans. 2012 Mar;51(2):288-97. doi: 10.1016/j.isatra.2011.10.002. Epub 2011 Nov 30.
This paper addresses the fuzzy system reliability analysis using different types of intuitionistic fuzzy numbers. Till now, in the literature, to analyze the fuzzy system reliability, it is assumed that the failure rates of all components of a system follow the same type of fuzzy set or intuitionistic fuzzy set. However, in practical problems, such type of situation rarely occurs. Therefore, in the present paper, a new algorithm has been introduced to construct the membership function and non-membership function of fuzzy reliability of a system having components following different types of intuitionistic fuzzy failure rates. Functions of intuitionistic fuzzy numbers are calculated to construct the membership function and non-membership function of fuzzy reliability via non-linear programming techniques. Using the proposed algorithm, membership functions and non-membership functions of fuzzy reliability of a series system and a parallel systems are constructed. Our study generalizes the various works of the literature. Numerical examples are given to illustrate the proposed algorithm.
本文使用不同类型的直觉模糊数来解决模糊系统可靠性分析问题。到目前为止，在文献中，为了分析模糊系统的可靠性，假设系统的所有组件的故障率都遵循相同类型的模糊集或直觉模糊集。然而，在实际问题中，这种情况很少发生。因此，在本文中，引入了一种新的算法来构建具有不同类型的直觉模糊故障率的系统的模糊可靠性的隶属函数和非隶属函数。通过非线性规划技术，计算直觉模糊数的函数来构建模糊可靠性的隶属函数和非隶属函数。使用所提出的算法，构建了串联系统和并联系统的模糊可靠性的隶属函数和非隶属函数。我们的研究推广了文献中的各种工作。给出了数值示例来说明所提出的算法。
