About This Course

In this course we will introduce you to the basics of fuzzy mathematics. We will introduce the definitions of fuzzy sets and notations for them. We will introduce the relations between and operations on them, and we will discuss the properties of operations on them. Then we will talk about the partial ordered sets and lattices, we will discuss some special lattices, such as Boolean algebras, soft algebras and optimal soft algebras.  We will discuss the algebraic structure in the fuzzy power set on the basis of the discussion of lattices. We will talk about the definitions and properties of fuzzy operators. We will talk about the definitions and properties of generalized unions and generalized intersections. Then we will introduce the definitions of cuts and strong cuts, the scalar multiplication, and discuss the properties of them. Finally, we will look through the resolution principles, the representation theorem, and the extension principles.

Requirements

Learners are expected to have some prior knowledge of sets and relations. Of course, here it refers to crisp sets and crisp relations. There are no derivatives or integrals in this course. Although not essential, some prior knowledge of discrete mathematics is desirable. Nevertheless, anyone who wants to learn the basics about fuzzy mathematics is welcome to join.

Course Staff

Bokan Zhang

Department of Mathematics and Statistics, Beijing Institute of Technology