Optimization and Control Theory Department: 2011-05-17 Seminar

Jakub Bielawski
Embedding theorem for fuzzy sets.

During the seminar we introduce and study new fuzzy algebraic operations: $\oplus$ -sum and scalar $\odot$ -multiplication deﬁned by

$(A \oplus B)(z):=\sup_{x+y=z}A(x)\cdot B(x)$ and $(\lambda \odot A)(z):=(A(z/\lambda))^\lambda$
where $A, B$ are fuzzy subsets and $\lambda \in (0, \infty)$ . This allows us to investigate a new deﬁnition of fuzzy convexity.