(英文PPT4)模糊控制讲义第二章(2.5 2.6).ppt

CHAPTER 2 Fuzzy Mathematics 2.5 Fuzzy Matrix 2.6 Fuzzy Relation 2.5 Fuzzy Matrix 2.5.1 Basic definitions of fuzzy matrix 2.5.2 Support of fuzzy matrix 2.5.3 Composition of fuzzy matrix 2.5.4 Transpose of fuzzy matrix 2.5.1 Basic definitions of fuzzy matrix If ( , ), there exist , then is a fuzzy matrix. Usually, means all the fuzzy matrixes ( rows, lines). 1 Union: 2 Intersection: 2.5.1 Basic definitions of fuzzy matrix3 Complement: 4 Contain: 5 Equal: 2.5.1 Basic definitions of fuzzy matrixExample 2.5.1: Notes: A fuzzy matrix and its complement are not complementary events similar with fuzzy sets. Example 2.5.2: 2.5.1 Basic definitions of fuzzy matrixExample 2.5.3: 2.5.2 Support of fuzzy matrix Definition: is called the support matrix of . Notes: The support matrix is a Boolean matrix. 2.5.2 Support of fuzzy matrixExample 2.5.4: 2.5.3 Composition of fuzzy matrix Definition: , , , , the composition matrix of these two matrixes is a fuzzy matrix with rows and lines, written as whose element isThe composition of fuzzy matrix is also called as multiplication of fuzzy matrix. 2.5.3 Composition of fuzzy matrixExample 2.5.5: Notes: (popularly) 2.5.4 Transpose of fuzzy matrix Rows change into lines and lines change into rows. 2.6 Fuzzy Relation 2.6.1 Definition of fuzzy relation 2.6.2 Operation of fuzzy relation 2.6.3 Composition of fuzzy relation 2.6.1 Definition of fuzzy relation Relation: A subset of a Cartesian product of and , is called a dualistic relation from to (or relation for short). Fuzzy relation: and are two sets, is a fuzzy subset in , is also called a fuzzy relation from to .The degree of membership of is 2.6.1 Definition of fuzzy relationFuzzy relation can described by fuzzy matrix when and are finite set. When