Page 126 - DCAP310_INTRODUCTION_TO_ARTIFICIAL_INTELLIGENCE_AND_EXPERT_SYSTEMS

Introduction to Artificial Intelligence & Expert Systems

Notes 6.12 Fuzzy Logic

Fuzzy logic is a form of many-valued logic or probabilistic logic; it deals with reasoning that is
approximate rather than fixed and exact. Compared to traditional binary sets (where variables
may take on true or false values) fuzzy logic variables may have a truth value that ranges in
degree between 0 and 1. Fuzzy logic has been extended to handle the concept of partial truth,
where the truth value may range between completely true and completely false. Furthermore,
when linguistic variables are used, these degrees may be managed by specific functions.
Irrationality can be described in terms of what is known as the fuzzjective. The term “fuzzy
logic” was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Zadeh. Fuzzy logic
has been applied to many fields, from control theory to artificial intelligence. Fuzzy logics
however had been studied since the 1920s as infinite-valued logics notably by Lukasiewicz and
Tarski.
Classical logic only permits propositions having a value of truth or falsity. The notion of
whether 1+1=2 is absolute, immutable, mathematical truth. However, there exist certain
propositions with variable answers, such as asking various people to identify a color. The
notion of truth doesn’t fall by the wayside, but rather a means of representing and reasoning
over partial knowledge is afforded, by aggregating all possible outcomes into a dimensional
spectrum. Both degrees of truth and probabilities range between 0 and 1 and hence may seem
similar at first. For example, let a 100 ml glass contain 30 ml of water. Then we may consider two
concepts: Empty and Full. The meaning of each of them can be represented by a certain fuzzy set.
Then one might define the glass as being 0.7 empty and 0.3 full. Note that the concept of
emptiness would be subjective and thus would depend on the observer or designer. Another
designer might equally well design a set membership function where the glass would be
considered full for all values down to 50 ml. It is essential to realize that fuzzy logic uses truth
degrees as a mathematical model of the vagueness phenomenon while probability is a
mathematical model of ignorance.

6.12.1 Applying Truth Values

A basic application might characterize subranges of a continuous variable.

Example: A temperature measurement for anti-lock brakes might have several separate
membership functions defining particular temperature ranges needed to control the brakes
properly. Each function maps the same temperature value to a truth value in the 0 to 1 range.
These truth values can then be used to determine how the brakes should be controlled.
Figure 6.1: Fuzzy Logic Temperature

In this image, the meanings of the expressions cold, warm, and hot are represented by functions
mapping a temperature scale. A point on that scale has three “truth values”—one for each of the
three functions. The vertical line in the image represents a particular temperature that the three
arrows (truth values) gauge. Since the red arrow points to zero, this temperature may be
interpreted as “not hot”. The orange arrow (pointing at 0.2) may describe it as “slightly warm”
and the blue arrow (pointing at 0.8) “fairly cold”.

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