This book mainly introduces some recent applications of the theory of semi-tensor product of matrices. In particular， we put emphasis on the applications in the fields of fuzzy logical systems， finite state machines and graphs. In the area of the fuzzy logical systems， we limit our discussions to the method of solving the fuzzy logical equation， which is a key technology in the analysis and synthesis of the logical dynamical systems. On the side of the applications in the finite state machines，

Preface
Chapter 1Introduction of the Semi-tensor Product of Matrices
1．1 Definition of STP
1．2 Basic Properties of STP
1．3 Special Properties of STP
1．4 Conclusion
References

Chapter 2 Solving General Type-2 Fuzzy Relation Equations
2．1 Introduction
2．2 Problem Formulation
2．2．1 Type-2 FRs and Their Compositions
2．2．2 STP Method of Solving Type-1 FREs
2．2．3 Problem Formulation
2．3 Type-2 Fuzzy Relation Equations
2．3．1 Properties ofT2 FREs
2．3．2 Solving Type-2 Fuzzy Relation Equations
2．4 Illustrative Examples
2．5 Conclusion
References

Chapter 3 Solving Symmetrical-Valued Type-2 Fuzzy Relation Equations
3．1 Introduction
3．2 Symmetrical-Valued T2 FRs
3．2．1 Symmetrical-Valued T2 FRs and Their Properties
3．2．2 Solving Symmetrical-Valued Type-2 FREs
3．3 Illustrative Examples
3．4 Conclusion
References
……

Chapter 4 Algebraic Approach to Construct Compatible State Set of Finite State Machines
Chapter 5 Algebraic Simplification of Finite State Machines
Chapter 6 Algebraic Criteria for Finite State Machine Understanding of Regular Language
Chapter 7 Reduction Conditions of State Space for Finite State Machines
Chapter 8 Searching Control Sets of Graphs
Chapter 9 Solutions of MTAP