Fuzzy Logic Approach - Computational Intelligence in Time Series Forecasting - page 139

4
Fuzzy Logic Approach
4.1 Introduction
The term “fuzzy” was introduced by Zadeh (1965) in his paper on fuzzy sets,
where a new mathematical discipline, fuzzy logic , based on the theory of fuzzy
sets , was presented. The proposed logic was aimed at supporting of presentation
and consideration of inexact or imprecise concepts by fuzzy sets. The imprecision
is to be understood as grouping of set members into classes, the boundaries of
which are not sharply defined. It was expected that the theory of fuzzy sets should
become a novel methodology suitable enough to help formulate and solve complex
problems in engineering and science that are difficult to handle using “precise”
crisp logic , such as binary logic , where the variables can be either true or false .
The theory of fuzzy sets allows the concept of partial belongingness of an object or
a variable in a fuzzy set and, therefore, allows a gradual transition from a full
membership to a totally non-membership. Thereby, in fuzzy logic an object or a
variable within a domain may partially belong to several fuzzy sets in the same
domain simultaneously and, thus, it provides a framework for a multivalued logic .
This is essential for capturing the vagueness in a natural linguistic description of
any system. Moreover, the underlying fuzzy logic incorporates a variety of rules
with the premises containing fuzzy propositions generally defined using linguistic
terms , such as low and high (temperature, pressure, flow, frequency, voltage, etc .),
old , older , very old (person, engine, sensor, measured value, etc .). The related
linguistic rules are of the IF-THEN art.
The linguistic rules enable the use of both numerical information represented
by numerical values, obtained from the various sensors, or given as set point
values, and linguistic information represented by words such as high, medium,
low, or fast, moderate or slow, etc ., obtained from an experienced plant operator or
a human expert. They replace the traditional approach to modelling of dynamic
systems based on differential equations, and the like, that is unsuccessful in
modelling of nonlinear and complex systems. Moreover, traditionally modeled
engineering systems cannot directly integrate human expert's linguistic knowledge.