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The purpose of this research is to develop a new approach for analyzing the fuzzy reliability of a series and parallel system. Also to introduce definition of L‐R type interval valued triangular vague set and certain Tω‐based arithmetic operations between two L‐R type interval valued triangular vague sets.

In the proposed approach using a fault tree an interval valued vague fault tree is developed for the system in which the fuzzy reliability of each component of the system is represented by a L‐R type interval valued triangular vague set. Then with the help of a developed interval valued vague fault tree an algorithm is developed to analyze the fuzzy system reliability.

For numerical verification of the proposed approach the fuzzy reliability of the basement flooding has been analyzed using the existing approaches and the proposed approach. Comparing the results of existing approaches and the proposed approach, it has been shown that the uncertainty about the reliability is minimized using the proposed approach and the results are exact. While using the existing approaches the results are approximate due to approximate product of triangular vague sets and interval valued triangular vague sets.

The paper introduces a new approach for analyzing the fuzzy system reliability using Tω‐based arithmetic operations over L‐R type interval valued triangular vague sets.

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.

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 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.

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.

A new method of document retrieval is presented on the basis of fundamental fuzzy set theory operations and the notion of a semantic disjunctive normal form. Concepts of semantic normal forms are defined, i.e. the semantic disjunctive normal form and the semantic conjunctive normal form, and their elementary properties, are presented. The syntax and the semantics of the proposed document retrieval language are given and an algorithm for allocating documents to particular queries is described. The document retrieval strategy based on the concept of a semantic disjunctive normal form is exemplified. A basic advantage of the use of the fuzzy set theory for the document retrieval system description is that it takes, in a simple way, into consideration the differentiation of descriptor importance, document search patterns and the differentiation of formal relevance grades of individual documents to a given query. In an information system the documents of the highest grades of formal relevance to a given query are retrieved by means of the application of simple operations of the fuzzy set theory.

This brief paper considers the various possible mathematical operations on fuzzy sets that are required to implement a set of control rules as a fuzzy logic control element. The influence that these operations have on the characteristics of the final control element is a factor that is used to select those operations most suitable in the control context.

Construction is a highly dynamic environment with numerous interacting factors that affect construction processes and decisions. Uncertainty is inherent in most aspects of construction engineering and management, and traditionally, it has been treated as a random phenomenon. However, there are many types of uncertainty that are not naturally modelled by probability theory, such as subjectivity, ambiguity and vagueness. Fuzzy logic provides an approach for handling such uncertainties. However, fuzzy logic alone has some limitations, including its inability to learn from data and its extensive reliance on expert knowledge. To address these limitations, fuzzy logic has been combined with other techniques to create fuzzy hybrid techniques, which have helped solve complex problems in construction. In this chapter, a background on fuzzy logic in the context of construction engineering and management applications is presented. The chapter provides an introduction to uncertainty in construction and illustrates how fuzzy logic can improve construction modelling and decision-making. The role of fuzzy logic in representing uncertainty is contrasted with that of probability theory. Introductory material is presented on key definitions, properties and methods of fuzzy logic, including the definition and representation of fuzzy sets and membership functions, basic operations on fuzzy sets, fuzzy relations and compositions, defuzzification methods, entropy for fuzzy sets, fuzzy numbers, methods for the specification of membership functions and fuzzy rule-based systems. Finally, a discussion on the need for fuzzy hybrid modelling in construction applications is presented, and future research directions are proposed.

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.

Based on the concept of fuzzy sets of type 2 (or fuzzy‐fuzzy sets) defined by L. A. Zadeh, fuzzy‐fuzzy automata ate newly formulated and some properties of these automata are investigated. It is shown that fuzzy‐fuzzy languages characterized by fuzzy‐fuzzy automata are closed under the operations of union, intersection, concatenation, and Kleene closure in the sense of fuzzy sets of type 2, but are not closed under complement. The power of fuzzy‐fuzzy automata as an acceptor is the same as that of ordinary fuzzy automata and finite automata, though fuzzy‐fuzzy automata include fuzzy automata and finite automata as special cases. Finally, fuzzy‐fuzzy grammars are illustrated and it is shown that fuzzy‐fuzzy grammars with context‐free rules can generate context‐sensitive languages.