●Preface
Chapter 1 Introduction of the Semi-tensor Product of Matrices
1.1 Definition of STP
1.2 Basic Properties of STP
1.3 Spe Properties of STP
1.4 Conclusion
References
Chapter 2 Solving General Type-2 Fuzzy Relation Equations
2. l 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 of T2 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 i
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
4.1 Introduction
4.2 Related Concepts of Finite State Machines
4.3 Problem Description
4.4 Bilinear Dynamics of FSMs
4.5 Criterion of k-Difference States
4.6 Construction of Incompatibility Graph
4.7 Generation of Compatible States
4.8 Conclusion
References
Chapter 5 Algebraic Simplification of Finite State Machines
5.1 Introduction
5.2 Compatible Cover of State Set (CCSS)
5.3 Representative Set of State Set (RSSS)
5.4 Minimum Representative Set of State Set (MRSSS)
5.5 Illustrative Examples
5.6 Conclusion
References
Chapter 6 Algebraic Criteria for Finite State Machine Understanding of Regular Language
6.1 Introduction
6.2 k-Connectivity Matrix
6.3 Algebraic Criteria of Understanding Regular Language
6.4 Further Results on Nondeterministie Finite State Machines
6.5 Illustrative Examples
6.6 Conclusion
References
Chapter 7 Reduction Conditions of State Space for Finite State Machines
7.1 Introduction
7.2 Related Concepts of Reduction Problem
7.3 Algebraic Conditions of Reduction of State Space
7.4 Mathematical Algorithms
7.5 Illustrative Examples
7.6 Conclusion
References
Chapter 8 Searching Control Sets of Graphs
8.1 Introduction
8.2 Preliminaries and Problem Statement
8.3 Searching Control Sets of Graphs
8.4 Searching k-Degree and k-Balance Control Sets of Graphs
8.5 Testing Examples
8.6 Conclusion
References
Chapter 9 Solutions of MTAP
9.1 Introduction
9.2 Preliminaries on k-Stable Sets of Graphs
9.3 Algebraic Approach to Search k-SSes and k-AMSSs
9.3.1 Searching k-stable sets
9.3.2 Searching k-absolute maximum internally stable set
9.4 Solvability of MATP
9.5 Illustrative Examples
9.6 Conclusion
References
內容簡介
本書主要介紹一種新的矩陣分析工具（矩陣的半張量積）的近期新應用研究進展。特別地，本書重點關注在邏輯動態繫統、有限狀態自動機器以及圖論等領域的應用研究。在邏輯動態繫統領域，本書有且隻有於介紹邏輯動態繫統分析與綜合的一個關鍵技術：模糊邏輯關繫方程的解法，包括對稱值模糊邏輯關繫方程和一般模糊邏輯關繫方程的解法。在有限狀態自動機器方面，本書重點介紹自動機的動態描述、兼容性分析、自動機的化簡以及語言識別等問題的研究。在圖論領域，本書討論了圖的結構分解及其在工業領域中的應用等。本書適合繫統科學、控制理論、控制科學與工程、工業自動化、數學、人工智能等專業的師生及科研人員閱讀參考，也可作為相關學科高年級本科生及研究生的教學參考用書。
