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The main goal of this paper is to develop novel Tω(weakest t-norm)-based fuzzy arithmetic operations to analyze the intuitionistic fuzzy reliability of Printed Circuit Board Assembly (PCBA) using fault tree.

The paper proposes a fuzzy fault tree analysis (FFTA) method for evaluating the intuitionistic fuzzy reliability of any nonrepairable system with uncertain information about failures of system components. This method uses a fault tree for modeling the failure phenomenon of the system, triangular intuitionistic fuzzy numbers (TIFNs) to determine data uncertainty, while novel arithmetic operations are adopted to determine the intuitionistic fuzzy reliability of a system under consideration. The proposed arithmetic operations employ Tω(weakest t-norm) to minimize the accumulating phenomenon of fuzziness, whereas the weighted arithmetic mean is employed to determine the membership as well as nonmembership degrees of the intuitionistic fuzzy failure possibility of the nonrepairable system. The usefulness of the proposed method has been illustrated by inspecting the intuitionistic fuzzy failure possibility of the PCBA and comparing the results with five other existing FFTA methods.

The results show that the proposed FFTA method effectively reduces the accumulating phenomenon of fuzziness and provides optimized degrees of membership and nonmembership for computed intuitionistic fuzzy reliability of a nonrepairable system.

The paper introduces Tω(weakest t-norm) and weighted arithmetic mean based operations for evaluating the intuitionistic fuzzy failure possibility of any nonrepairable system in an uncertain environment using a fault tree.

Fuzzy numbers are often used to represent non-probabilistic uncertainty in engineering, decision-making and control system applications. In these applications, fuzzy arithmetic operations are frequently used for solving mathematical equations that contain fuzzy numbers. There are two approaches proposed in the literature for implementing fuzzy arithmetic operations: the α-cut approach and the extension principle approach using different t-norms. Computational methods for the implementation of fuzzy arithmetic operations in different applications are also proposed in the literature; these methods are usually developed for specific types of fuzzy numbers. This chapter discusses existing methods for implementing fuzzy arithmetic on triangular fuzzy numbers using both the α-cut approach and the extension principle approach using the min and drastic product t-norms. This chapter also presents novel computational methods for the implementation of fuzzy arithmetic on triangular fuzzy numbers using algebraic product and bounded difference t-norms. The applicability of the α-cut approach is limited because it tends to overestimate uncertainty, and the extension principle approach using the drastic product t-norm produces fuzzy numbers that are highly sensitive to changes in the input fuzzy numbers. The novel computational methods proposed in this chapter for implementing fuzzy arithmetic using algebraic product and bounded difference t-norms contribute to a more effective use of fuzzy arithmetic in construction applications. This chapter also presents an example of the application of fuzzy arithmetic operations to a construction problem. In addition, it discusses the effects of using different approaches for implementing fuzzy arithmetic operations in solving practical construction problems.

The purpose of this paper is to analyze the reliability of the washing system in a paper plant in a more promising way under vague environment by reducing the accumulating phenomenon of fuzziness and accelerating the computation process using the T_ω (weakest t-norm) based fuzzy lambda-tau (TBFLT) technique.

This paper presents a unified approach for analyzing the fuzzy reliability of the washing system under vague environment. This approach applies the TBFLT technique which uses triangular fuzzy numbers for incorporating data uncertainty, fault tree and lambda-tau method for finding system failure rate and repair time mathematical expressions while simplified T_ω-based arithmetic operations are applied for computing various reliability parameters of the system. The effectiveness of the TBFLT technique has been demonstrated by analyzing fuzzy reliability of the system using five different techniques including TBFLT. Moreover, this paper applies extended Tanaka’s (1983) approach to rank the critical components of the system.

The TBFLT technique has the advantage of low computation complexity in comparison to other techniques and effectively reduces the accumulating phenomenon of fuzziness. This main finding verifies the conclusion made by Chen (1994).

The author has suggested a simple and more applicable technique for analyzing the fuzzy reliability of any complex process industrial system under vague environment. The effectiveness of the technique has been demonstrated by computing various reliability parameters of the washing system of a paper plant.

In recent years, the application of robots in different industrial sectors such as nuclear power generation, construction, automobile, firefighting and medicine, etc. is increasing day by day. In large industrial plants generally humans and robots work together to accomplish several tasks and lead to the problem of safety and reliability because any malfunction event of robots may cause human injury or even death. To access the reliability of a robot, sufficient amount of failure data is required which is sometimes very difficult to collect due to rare events of any robot failures. Also, different types of their failure pattern increase the difficulty which finally leads to the problem of uncertainty. To overcome these difficulties, this paper presents a case study by assessing fuzzy fault tree analysis (FFTA) to control robot-related accidents to provide safe working environment to human beings in any industrial plant.

Presented FFTA method uses different fuzzy membership functions to quantify different uncertainty factors and applies alpha-cut coupled weakest t-norm (Tω) based approximate fuzzy arithmetic operations to obtain fuzzy failure probability of robot-human interaction fault event which is the main contribution of the paper.

The result obtained from presented FFTA method is compared with other listing approaches. Critical basic events are also ranked using V-index for making suitable action plan to control robot-related accidents. Study indicates that the presented FFTA is a good alternative method to analyze fault in robot-human interaction for providing safe working environment in an industrial plant.

Existing fuzzy reliability assessment techniques designed for robots mainly use triangular fuzzy numbers (TFNs), triangle vague sets (TVS) or triangle intuitionistic fuzzy sets (IFS) to quantify data uncertainty. Present study overcomes this shortcoming and generalizes the idea of fuzzy reliability assessment for robots by adopting different IFS to control robot-related accidents to provide safe working environment to human. This is the main contribution of the paper.

The purpose of this paper is to analyze the fuzzy reliability of the compressor house unit (CHU) system in a coal fired thermal power plant under vague environment by reducing the accumulating phenomenon of fuzziness and accelerating the computation process. This paper uses different fuzzy membership functions to quantify uncertainty and access the system reliability in terms of different fuzzy reliability indices having symmetric shapes.

This study analyses the fuzzy reliability of the CHU system in a coal fired thermal power plant using T_ω-based generalized fuzzy Lambda-Tau (TBGFLT) technique. This approach applies fault tree, Lambda-Tau method, different fuzzy membership functions and α-cut coupled T_ω-based approximate arithmetic operations to compute various reliability parameters (such as failure rate, repair time, mean time between failures, expected number of failures, availability and reliability) of the system. The effectiveness of TBGFLT technique has been demonstrated by comparing the results with results obtained from four different existing techniques. Moreover, this paper applies the extended Tanaka et al. (1983) approach to rank the critical components of the system when different membership functions are used.

The adopted TBGFLT technique in the present study improves the shortcomings of the existing approaches by reducing the accumulating phenomenon of fuzziness, accelerating the computation process and getting symmetric shapes for computed reliability parameters when different membership functions are used to quantify data uncertainty.

In existing fuzzy reliability techniques which are developed for repairable systems either triangular fuzzy numbers, triangle vague sets or triangle intuitionistic fuzzy sets have been used for quantifying uncertainty. These approaches do not examine the systems for components with different membership functions. The present study is an effort in this direction and evaluates the fuzzy reliability of the CHU system in a coal fired thermal power plant for components with different membership functions. This is the main contribution of the paper.

In recent years, online public opinion reversal incidents have been occurring frequently, which has increased the complexity of the evolution of online public opinion, and they have become a difficult issue for public opinion management and control. It is of great significance to explore the regularity of online public opinion reversal.

Combined with the grey characteristics of online public opinion information, a grey graphical evaluation review technique (G-GERT) network model is constructed based on kernel and grey degree, and the frequency, probability and time of online public opinion reversal nodes are calculated using C-marking method and Z-marking method.

Throughout the online public opinion reversal events, there are all repeated outbreak nodes occurring, so the authors regard the repeated occurrence of outbreak nodes as reversal. According to the average frequency, probability and time of repeated outbreak nodes in the G-GERT network model, the authors predict the corresponding key information of reversal. It can simulate the evolution process of public opinion events accurately.

The G-GERT network model based on kernel and grey degree reveals the regulation of public opinion reversal, predicts the frequency, probability and time of reversal nodes, which are the most concerned and difficult issues for decision-makers. The model provides the decision basis and reference for government decision-making departments.