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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.

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.

Due to the increasing size and complexity of construction projects, construction engineering and management involves the coordination of many complex and dynamic processes and relies on the analysis of uncertain, imprecise and incomplete information, including subjective and linguistically expressed information. Various modelling and computing techniques have been used by construction researchers and applied to practical construction problems in order to overcome these challenges, including fuzzy hybrid techniques. Fuzzy hybrid techniques combine the human-like reasoning capabilities of fuzzy logic with the capabilities of other techniques, such as optimization, machine learning, multi-criteria decision-making (MCDM) and simulation, to capitalise on their strengths and overcome their limitations. Based on a review of construction literature, this chapter identifies the most common types of fuzzy hybrid techniques applied to construction problems and reviews selected papers in each category of fuzzy hybrid technique to illustrate their capabilities for addressing construction challenges. Finally, this chapter discusses areas for future development of fuzzy hybrid techniques that will increase their capabilities for solving construction-related problems. The contributions of this chapter are threefold: (1) the limitations of some standard techniques for solving construction problems are discussed, as are the ways that fuzzy methods have been hybridized with these techniques in order to address their limitations; (2) a review of existing applications of fuzzy hybrid techniques in construction is provided in order to illustrate the capabilities of these techniques for solving a variety of construction problems and (3) potential improvements in each category of fuzzy hybrid technique in construction are provided, as areas for future research.

In previous work, the algebraical properties of this rule and its relationship with other generalized operator was studied. In this paper, the aim is to focus on one of the previous steps, which consists in certainty qualification, and it is investigated how this factor influences the behavior of the induced combination rule.

Dubois and Prade have proposed an adaptive combination rule that moves gradually from a conjunctive mode to a disjunctive mode as soon as the conflict between the sources increases. The proposal can be viewed as a result of some rational steps. This includes: conjunctive combination; re‐normalization of a subnormal result that may results from conjunctive operation where the lack of normalization is interpreted as a conflict; certainty qualification; restriction of the conflict influence; generalization to more than two sources.

Algebraical properties of the proposals have been investigated and illustrations of some special cases are highlighted and evaluated. Further studies continue in Part II.

New functional adaptive rules are put forward based on Residual implicators and t‐conorm operators.

Triangular norms have been around since the early 1940s and have been used in the context of statistical metric space. A number of examples of existing t‐norms are given which are known to provide good models of fuzzy set‐theoretic intersections. Pictorial representations of t‐norms that have been made with the aid of a computer are presented and the relationship between t‐norms and parametrised t‐norms is discussed in this context. Several new examples of t‐norms are proposed using triangular functions.

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.

This paper deals with the theoretical analysis of the notion of interval valued fuzzy sets (IVFS) applied to possibility measures. This permits to provide interval valued possibility measure (IVPM) and interval valued necessity measure (IVNM) as well as interval valued possibility distribution (IVPD). Particularly, two kinds of IVPM will be provided. The first one assumes a conjunctive normal form and a disjunctive normal form pertaining to a logical assertion. While the second one considers a logical AND and a logical OR as an essence to construct the underlying interval. The properties of both representations are investigated. Also, some basic mode operations involving conjunction and disjunction combinations are examined. Conditioning in the setting of IVPM is introduced considering either a canonical extension of well established rules, or more interestingly by solving the underlying Cox's axiomatic equation. Finally, some further extensions using general class of t‐norms operators are discussed.

The development of social networks enhances the interaction between people, which brings new challenges to the research of group decision-making (GDM). This study aims at the problem that the synergy and redundancy due to interaction among decision-makers are ignored in the previous GDM, a trust-enhanced consensus reaching model based on interaction among decision-makers with incomplete preferences is proposed.

Firstly, confidence level is introduced to improve the hesitation phenomenon that should be considered when calculating trust degree; Secondly, a new trust propagation operator is developed to deal with indirect trust relationships; Thirdly, trust degree is transformed into interaction index to quantify the synergy and redundancy in decision-making. Fuzzy capacities of decision-makers are used to replace traditional weights, and the final scores of alternatives are obtained through Choquet integral.

The proposed model using fuzzy capacity can reflect the synergy or redundancy among decision-makers and improve the accuracy of final ranking result and reduce the loss of information.

This study proposes a trust-enhanced consensus reaching model, which develops a new trust propagation operator to ensure the continuous attenuation of trust in propagation process. And the proposed model uses fuzzy capacity to improve the enhancement or attenuation on the scores of alternatives.