Short answers, pulled from the story.
Mathematician Lotfi Zadeh published a proposal for fuzzy set theory in 1965. This publication reshaped how machines handle uncertainty by applying abstract ideas to real-world problems involving imprecise information.
The Sendai Subway 1000 series became the first notable application of fuzzy logic in Japan during the early development period. This system improved economy, comfort, and precision of the ride by allowing experts to contribute vague rules such as if you are close to the destination station and moving fast increase brake pressure.
Fuzzy logic defines truth values as real numbers between zero and one rather than simply true or false. Each function maps the same temperature value to a truth value between zero and one where systems can handle partial truths without forcing binary decisions onto complex situations.
Bart Kosko claimed that probability theory is a subtheory of fuzzy logic while Lotfi Zadeh argued they differ in character and are not replacement for each other. Academic debates continue regarding how much useful information can be derived from these approaches versus traditional probability methods.
Joseph Goguen later expanded these concepts in the 1970s by examining linguistic variables and lattices within logical frameworks. His work built upon earlier foundations while introducing new ways to model human decision-making processes.