Welcome

Lotfi A. Zadeh was a versatile scholar, known for his contributions to various fields such as mathematics, computer science, electrical engineering, and artificial intelligence. He held the position of a computer science professor at the University of California, Berkeley. Zadeh's most notable achievement lies in introducing the concept of fuzzy mathematics, which encompasses several related concepts like fuzzy sets, fuzzy logic, fuzzy algorithms, fuzzy semantics, fuzzy languages, fuzzy control, fuzzy systems, fuzzy probabilities, fuzzy events, and fuzzy information. In his theory of fuzzy sets, Zadeh proposed the use of a membership function, operating on a domain of possible values and ranging from 0 to 1. This approach introduced novel operations for logic calculus, demonstrating that fuzzy logic serves as a generalization of classical and Boolean logic. Furthermore, he presented fuzzy numbers as a distinct category within fuzzy sets and established rules for consistent mathematical operations, giving rise to fuzzy arithmetic.

Zadeh's research, particularly in the realm of fuzzy sets and fuzzy logic, has left a lasting impact on artificial intelligence. The foundation of fuzzy mathematics aligns with our understanding of human cognition, acknowledging our comfort with concepts characterized by vague boundaries.

Fuzzy set theory has become a hot topic for researchers across many fields. Fuzzy mathematics, a contemporary extension of applied mathematics, computational mathematics and pure mathematics, emphasizes its connection with other disciplines, including computational intelligence, decision theory, and medical sciences. The fuzzy mathematics group aims to support the shift in scientific approaches involving fuzziness and assist colleagues working in this domain. Group members engage in fundamental research covering areas such as fuzzy algebras, fuzzy graph theory, fuzzy numerical methods, fuzzy fractional calculus, and fuzzy linear programming models, as well as methods for fuzzy multi-criteria decision making. Within the group, members have pioneered developments such as fuzzy K-algebras, m-polar fuzzy graphs, single-valued neutrosophic graphs, rough fuzzy graphs, and fuzzy outranking methods. The research output of the group includes eleven books, nine book chapters, and around 500 journal articles authored by various research members.