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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.

A flexible and realistic linguistic assessment approach is developed to provide a mathematical tool for synthesis and evaluation analysis of nuclear safeguards indicator information. This symbolic approach, which acts by the direct computation on linguistic terms, is established based on fuzzy set theory. More specifically, a lattice‐valued linguistic algebra model, which is based on a logical algebraic structure of the lattice implication algebra, is applied to represent imprecise information and to deal with both comparable and incomparable linguistic terms (i.e. non‐ordered linguistic values). Within this framework, some weighted aggregation functions introduced by Yager are analyzed and extended to treat these kinds of lattice‐value linguistic information. The application of these linguistic aggregation operators for managing nuclear safeguards indicator information is successfully demonstrated.

Several different simulation techniques, such as discrete event simulation (DES), system dynamics (SD) and agent-based modelling (ABM), have been used to model complex construction systems such as construction processes and project management practices; however, these techniques do not take into account the subjective uncertainties that exist in many construction systems. Integrating fuzzy logic with simulation techniques enhances the capabilities of those simulation techniques, and the resultant fuzzy simulation models are then capable of handling subjective uncertainties in complex construction systems. The objectives of this chapter are to show how to integrate fuzzy logic and simulation techniques in construction modelling and to provide methodologies for the development of fuzzy simulation models in construction. In this chapter, an overview of simulation techniques that are used in construction is presented. Next, the advancements that have been made by integrating fuzzy logic and simulation techniques are introduced. Methodologies for developing fuzzy simulation models are then proposed. Finally, the process of selecting a suitable simulation technique for each particular aspect of construction modelling is discussed.

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.

Focuses on the applications of fuzzy set theory as a tool for the construction of multi‐criteria decision functions from specifications expressed in natural language. Starting with the ability to represent individual criteria satisfactions in terms of membership of fuzzy subsets, shows how different types of linguistic specifications are implemented. Consideration is given to the representation of trade‐offs between criteria, quantifier‐guided aggregations, conditioned criteria and possibilistically qualified criteria.

The first part of this issue investigated the properties of the adaptive rule initially proposed by Dubois and Prade given in the framework of possibility theory, when the certainty qualification is rather expressed in more general t‐norms and t‐conorms connectives. This led to two new family of adaptive rules expressed using residual implication and t‐conorm connective, respectively. The problem of addressing uncertain inputs has also been examined and a waved decomposition has been proposed in PII we study adaptative combinations with incomplete certainty qualification. However, another problem that arises when combining uncertain inputs consists of the relationship between the certainty attached to the inputs and the certainty attached to the output, conceptualized by the resulting distribution when using adaptive combination rule. In other words, how does the combination rule improves or deteriorates the certainty of the overall system? This paper seeks to address this issue.

This paper fully addresses this issue and attempts to evaluate the combination rule from the certainty viewpoint attached to the result in comparison to initial certainty values attached to the inputs.

Especially, it has been proven that under certain hypotheses, the rule allows the user to hide the local certainties attached to the initial inputs, while highlighting only the certainty due to the lack of consistency among the sources.

New functional adaptative rules are put forward based on residual implicators and t‐conorm operators.

Time modeling is a crucial feature in many application domains. However, temporal information often is not crisp, but is subjective and fuzzy. The purpose of this paper is to address the issue related to the modeling and handling of imperfection inherent to both temporal relations and intervals.

On the one hand, fuzzy extensions of Allen temporal relations are investigated and, on the other hand, extended temporal relations to define the positions of two fuzzy time intervals are introduced. Then, a database system, called Fuzzy Temporal Information Management and Exploitation (Fuzz-TIME), is developed for the purpose of processing fuzzy temporal queries.

To evaluate the proposal, the authors have implemented a Fuzz-TIME system and created a fuzzy historical database for the querying purpose. Some demonstrative scenarios from history domain are proposed and discussed.

The authors have conducted some experiments on archaeological data to show the effectiveness of the Fuzz-TIME system. However, thorough experiments on large-scale databases are highly desirable to show the behavior of the tool with respect to the performance and time execution criteria.

The tool developed (Fuzz-TIME) can have many practical applications where time information has to be dealt with. In particular, in several real-world applications like history, medicine, criminal and financial domains, where time is often perceived or expressed in an imprecise/fuzzy manner.

The social implications of this work can be expected, more particularly, in two domains: in the museum to manage, exploit and analysis the piece of information related to archives and historic data; and in the hospitals/medical organizations to deal with time information inherent to data about patients and diseases.

This paper presents the design and characterization of a novel and intelligent database system to process and manage the imperfection inherent to both temporal relations and intervals.

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.