Fundamentals of Fuzzy Systems Theory
Plamen Parvanov Angelov · 2012
Fuzzy logic is a very powerful methodology of how to present information and knowledge by rules that have high generalisation and summarisation ability. A fuzzy set is described by its membership function. There are several types of fuzzy rules, but two of them are widely used now: so-called Mamdani or Zadeh-Mamdani type, and so-called Takagi-Sugeno (TS) called sometimes Takagi-Sugeno-Kang type. AnYa (Angelov and Yager, 2010, 2012) includes a nonparametric antecedent part of a new type which also simplifies the linguistic expression removing the need for logical AND, and the ambiguity related to the choice of the t-norm operator. The fuzzy rule-based (FRB) classifiers can be trained/learned using training data or, alternatively, the rules can be provided by expert knowledge. The AnYa-type FRB system and neurofuzzy systems (NFS) can be considered through the prism of state space representation. Controlled Vocabulary Terms fuzzy logic; fuzzy set theory; fuzzy systems; linguistics