Some Methods for Analyzing the Reliability of Series-Parallel Systems Using Generalized Intuitionistic Fuzzy Number

Abstract

With the growing complexity of an industrial system, it is difficult for the decision makers to get the accurate decision within a reasonable time. In order to maintain the performance of the systems, reliability is one of the importance factor. Reliability is measured as the ability of a system's to perform its intended function, without fail, for a specified period, under predetermined conditions. But uncertainties is an unavoidable phenomenon in most of the system. So it is difficult for the system analyst to get the correct decision without handling these uncertainties.

In the present thesis, some new approaches have been presented for analyzing the reliability of the series-parallel configuration systems in which the uncertainties which are present in the data are handled with the help of the generalized trapezoidal fuzzy numbers. In the approach, preferences of the decision makers, as well as, the highest level of confidence of domain experts are added into the analysis and hence the corresponding data are represented in the form of the generalized trapezoidal intuitionistic fuzzy numbers (GTrIFN). Based on these information, some methods for analyzing the behavior of the system have been analyzed at the different levels of the uncertainties.

The present thesis is organized into five chapters which are briefly summarized as follows:

A brief account of the related work of various authors in the evaluation of reliability analysis of some industrial system under fuzzy and intuitionistic fuzzy environment is presented in the first chapter. In \textbf{Chapter 2}, the basic and preliminaries related to the reliability theory and the fuzzy, as well as, the intuitionistic fuzzy set theory that are used in the subsequent chapters are given.

\textbf{Chapter 3} presents a method for ranking the generalized trapezoidal fuzzy numbers (GTrIFN). In it, the ranking of the two different GTrIFNs has been done by using a new defuzzification method based on the centroid point of the intuitionistic fuzzy numbers (IFNs). Some special cases of the proposed one have also been obtained. The method has been demonstrated through some examples for comparing the two different IFNs.

In \textbf{Chapter 4}, a method for analyzing the reliability of the series, series-parallel system has been presented under the generalized intuitionistic fuzzy number environment. In it, by using the $\alpha-$ cut of the membership and non-membership functions of the GTrIFN, reliability of some system configuration has been computed at different level of the uncertainties. A comparative studies with some of the existing approaches has also been done.

In \textbf{Chapter 5}, a method for analyzing the reliability of the industrial system has been presented by using GTrIFNs. For it, the preference of the decision makers have been taken in the form of the components of the systems and then various reliability parameters which affect the system behavior directly have been computed. The approach has been illustrated with a case study of the washing unit of a paper mill, a complex repairable industrial system.