Fuzzy Arithmetic Operations: Theory and Applications in Construction Engineering and Management

Nima Gerami Seresht, Aminah Robinson Fayek

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

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.
Original languageEnglish
Title of host publicationFuzzy Hybrid Computing in Construction Engineering and Management
Subtitle of host publicationTheory and Applications
EditorsAminah Robinson Fayek
Place of PublicationBingley
PublisherEmerald
Pages111-147
Number of pages36
ISBN (Electronic)9781787438682
ISBN (Print)9781787438699
DOIs
Publication statusPublished - 5 Oct 2018
Externally publishedYes

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