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If the ethos of a DigiPen student is to build it yourself — whether it be a game, graphics engine, or piece of hardware — you could say Mathematics professor Barnabas Bede is leading by example.

Bede is the author of Mathematics of Fuzzy Sets and Fuzzy Logic, published this month by Springer.

Bede describes the book as part textbook, part research monograph, offering a mathematically-based introduction to a subject he teaches at DigiPen. The book, he says, was intended to cover a gap in the literature.

“When I was assigned to teach fuzzy sets and fuzzy logic, I was searching for good mathematics textbooks, and I realized there was no such thing,” Bede says. “So I looked around a little more, and I thought I could try to write one.”

First introduced in 1965, fuzzy logic describes a mathematical framework used to model uncertainty. Unlike probabilistic logic, however, which deals with the mathematical likelihood of certain outcomes, fuzzy logic pertains to things that may be considered subjective, or partially true.

“These are data that are not really statistical, because you cannot say, ‘Well, where is the limit — who is young? Who is not young?’” Bede says. “Fuzzy sets are able to model this uncertainty. A fuzzy set basically is a set with an edge that is not really sharp.”

I enjoy that I have students discover how cool mathematics is — how useful it is also.”

While fuzzy logic has many real and potential applications — from rice cookers that can make real-time temperature adjustments to driverless vehicles — for many of Bede’s students, the most obvious application is within a game’s artificial intelligence systems.

“There have been many projects that students have done in fuzzy logic, and they were really amazing, using fuzzy logic to implement some behavior for agents in a video game that mimics the intelligent behavior of someone or something,” Bede says. “I enjoy that I have students discover how cool mathematics is — how useful it is also.”

Bede earned his Ph.D. in mathematics from Babes-Bolyai University in Cluj-Napoca, Romania. He serves as editorial board member of the journals Fuzzy Sets and Systems and Information Sciences.