Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Inference Systems

Fuzzy set theory (Zadeh (Inf Control 8(3):338–353, 1965)) and fuzzy logic have gained rapid developments in a variety of scientific disciplines, including mathematics, engineering, and computer science. They also have been successfully applied for many real-world problems (Li et al. (Soft Comput 20(8):2939–2949, 2016), Ross (Fuzzy Logic with Engineering Applications. Wiley, Hoboken, 2005), Terano et al. (Applied Fuzzy Systems. Academic, Cambridge, 2014), and Zimmermann (Fuzzy Set Theory–and Its Applications. Springer Science & Business Media, Cham, 2011)), such as systems control, fault diagnosis and computer vision, as an effective tool to address the issues of imprecision and vagueness in modelling and reasoning. This makes systems developed on the basis of fuzzy sets and fuzzy logic a core paradigm in the field of computational intelligence (Bonissone (Soft Comput 1(1):6–18, 1997) and Zadeh (Commun ACM 37(3):77–85, 1994)), forming sharp contrast with the conventional hard computing systems based on Boolean logic and numerical analysis. In particular, fuzzy knowledge-based systems exploit the tolerance for imprecision, partial truth, and approximations to achieve close resemblance with human activity and reasoning intuition. Many of which have been developed using the idea of approximate reasoning (also known as linguistic reasoning or simply, fuzzy reasoning), reflecting the manner of human cogitation and leading to new, more human interpretable, intelligent systems. For academic completeness, this chapter introduces the preliminary concepts and fundamental motivations for the development of approximate knowledge interpolative reasoning systems and outlines the structure of this book.