PLCs and Fuzzy Logic (2)

EVOLUTION OF FUZZY LOGIC CONTROL

Fuzzy logic has existed since ancient times, when Aristotle developed the law of the excluded middle. In this law, Aristotle pointed out that the middle ground is lost in the art of logical reasoning— statements are either true or false, never in-between. When PLCs were developed, their discrete logic was based on the ancient reasoning techniques. Thus, inputs and outputs could belong to only one set (i.e., ON or OFF); all other values were excluded. Fuzzy logic breaks the law of the excluded middle in PLCs by allowing elements to belong to more than just one set. In the previous cool air example, the 65°F temperature input belonged to two sets, the cool set and the cold set, with grade levels indicating how well it fit into each set.

The origins of fuzzy logic date back to the early part of the twentieth century when Bertrand Russell discovered an ancient Greek paradox that states:
A Cretan asserts that all Cretans lie. So, is he lying? If he lies, then he is telling the truth and does not lie. If he does not lie, then he tells the truth and, therefore, he lies.
In either case—that all Cretans lie or that all Cretans do not lie—a contradiction exists, because both statements are true and false. Russell found that this same paradox applied to the set theory used in discrete logic. Statements must either be totally true or totally false, leading to areas of contradiction.
Fuzzy logic surmounted this problem in classical logic by allowing statements to be interpreted as both true and false. Therefore, applying fuzzy logic to the Greek paradox yields a statement that is both true and false: Cretans tell the truth 50% of the time and lie 50% of the time. This interpretation is very similar to the idea of a glass of water being half empty or half full. In fuzzy logic, the glass is both—50% full and 50% empty. Even as the amount of water decreases, the glass still retains percentages of both conditions.
Around the 1920s, independent of Bertrand Russell, a Polish logician named Jan Lukasiewicz started working on multivalued logic, which created fractional binary values between logic 1 and logic 0. In a 1937 article in Philosophy of Science, Max Black, a quantum philosopher, applied this
multivalued logic to lists (or sets) and drew the first set of fuzzy curves, calling them vague sets.
Twenty-eight years later, Dr. Lofti Zadeh, the Electrical Engineering Department Chair at the University of California at Berkeley, published a landmark paper entitled “Fuzzy Sets,” which gave the name to the field of fuzzy logic. In this paper, Dr. Zadeh applied Lukasiewicz’s logic to all objects in a set and worked out a complete algebra for fuzzy sets. Due to this groundbreaking work, Dr. Zadeh is considered to be the father of modern fuzzy logic.
Around 1975, Ebrahim Mamdani and S. Assilian of the Queen Mary College of the University of London published a paper entitled “An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller.” This paper proved the feasibility of fuzzy logic control applying fuzzy control to a steam engine. Since then, the term fuzzy logic has come to mean mathematical or computational
reasoning that utilizes fuzzy sets.
to be continued……..