Fuzzy Petri Nets for Knowledge Representation, Acquisition and Reasoning

Preface
Contents
Abbreviations
List of Figures
List of Tables
Part I Literature Review and Truth Determination of FPNs
1 FPNs for Knowledge Representation and Reasoning: A Literature Review
	1.1 Introduction
	1.2 FPRs and FPNs
		1.2.1 FPRs
		1.2.2 FPNs
	1.3 Improvements of FPNs
		1.3.1 Reasoning Algorithms
		1.3.2 New FPN Models
	1.4 Applications of FPNs
		1.4.1 Operational Management
		1.4.2 Fault Diagnosis and Risk Assessment
		1.4.3 Wireless Sensor Networks
		1.4.4 Transportation Systems
		1.4.5 Biological and Healthcare Systems
		1.4.6 Other Applications
	1.5 Observations and Findings
	1.6 Chapter Summary
	References
2 FPNs for Knowledge Representation and Reasoning: A Bibliometric Analysis
	2.1 Introduction
	2.2 Research Methodology
	2.3 Results and Discussions
		2.3.1 Publication Trend in the FPN Field
		2.3.2 Cooperation Network Analysis in the FPN Field
		2.3.3 Co-Citation Analysis in the FPN Field
		2.3.4 Keyword Analysis in the FPN Field
		2.3.5 Application Field Analysis
	2.4 Suggestions for Future Research
	2.5 Chapter Summary
	References
3 Determining Truth Degrees of Input Places in FPNs
	3.1 Introduction
	3.2 Preliminaries
		3.2.1 Hesitant 2-Tuple Linguistic Term Sets
		3.2.2 Interval 2-Tuple Linguistic Model
	3.3 The Proposed Model
		3.3.1 Assess the Truth Degrees of Input Places
		3.3.2 Determine the Weight Vector of Experts
		3.3.3 Compute the Truth Values of Input Places
	3.4 Illustrative Example
	3.5 Chapter Summary
	References
Part II Improved FPNs for Knowledge Representation and Acquisition
4 Dynamic Adaptive Fuzzy Petri Nets for Knowledge Representation and Acquisition
	4.1 Introduction
	4.2 Fuzzy Evidential Reasoning Approach
		4.2.1 Acquisition of Rule-Based Knowledge Using Belief Structures
		4.2.2 Group Belief Structures
		4.2.3 Defuzzification
	4.3 Dynamic Adaptive Fuzzy Petri Nets
		4.3.1 Definition of DAFPNs
		4.3.2 DAFPN Representations for WFPRs
		4.3.3 Execution Rules of DAFPNs
		4.3.4 Concurrent Reasoning Algorithm of DAFPNs
	4.4 An Illustrative Example
	4.5 Chapter Summary
	References
5 Interval-Valued Intuitionistic FPNs for Knowledge Representation and Acquisition
	5.1 Introduction
	5.2 Interval 2-Tuple Linguistic Variables
	5.3 Interval-Valued Intuitionistic Fuzzy Petri Nets
		5.3.1 Definition of IVIFPNs
		5.3.2 Representations of IVIFPRs
		5.3.3 Inference Algorithm of IVIFPNs
	5.4 The Proposed KRA Model
	5.5 Empirical Case Study
		5.5.1 Background
		5.5.2 Knowledge Acquisition
		5.5.3 Knowledge Representation and Reasoning
	5.6 Chapter Summary
	References
6 Picture Fuzzy Petri Nets for Knowledge Representation and Acquisition
	6.1 Introduction
	6.2 Preliminaries
		6.2.1 Picture Fuzzy Sets
		6.2.2 Defuzzification of PFNs
	6.3 Picture Fuzzy Petri Nets
		6.3.1 Definition of PFPNs
		6.3.2 PFPN Representations of WPFPRs
		6.3.3 Knowledge Acquisition
		6.3.4 Execution Rules of PFPNs
		6.3.5 Reasoning Algorithm Based on PFPNs
	6.4 Illustrative Example
		6.4.1 Implementation
		6.4.2 Comparisons and Discussions
	6.5 Chapter Summary
	References
7 R-Numbers Petri Nets for Knowledge Representation and Acquisition
	7.1 Introduction
	7.2 Preliminaries
	7.3 R-Numbers Petri Nets
		7.3.1 Definition of RPNs
		7.3.2 Weighted R-numbers Production Rules
		7.3.3 Inference Algorithm of RPNs
		7.3.4 Knowledge Acquisition
		7.3.5 Reasoning Algorithm of RPNs
	7.4 Illustrative Example
		7.4.1 Implementation
		7.4.2 Comparison Analysis
	7.5 Chapter Summary
	References
8 Bipolar Fuzzy Petri Nets for Knowledge Representation and Acquisition
	8.1 Introduction
	8.2 Preliminary
	8.3 Bipolar Fuzzy Petri Nets
		8.3.1 Definition of BFPNs
		8.3.2 Weight Bipolar Fuzzy Production Rules
		8.3.3 Execution Rules of BFPNs
		8.3.4 Reasoning Algorithm of BFPNs
	8.4 The Proposed Knowledge Acquisition Method
	8.5 Illustrative Example
		8.5.1 Implementation
		8.5.2 Comparative Analysis
	8.6 Chapter Summary
	References
9 Linguistic Z-Number Petri Nets for Knowledge Representation and Acquisition
	9.1 Introduction
	9.2 Preliminary
		9.2.1 Linguistic Scale Functions
		9.2.2 Linguistic Z-Numbers
	9.3 The Proposed LZPN Model
		9.3.1 Definition of LZPNs
		9.3.2 Linguistic Z-Number Production Rules
		9.3.3 Execution Rules of LZPNs
		9.3.4 Simplification Method of LZPNs
		9.3.5 Reasoning Algorithm of LZPNs
	9.4 The Large Group Knowledge Acquisition Method
	9.5 Illustrative Example
		9.5.1 Background
		9.5.2 Implementation
		9.5.3 Sensitivity Analysis
		9.5.4 Comparison Analysis
	9.6 Chapter Summary
	References
10 Spherical Linguistic Petri Nets for Knowledge Representation and Acquisition
	10.1 Introduction
	10.2 Spherical Linguistic Sets
	10.3 Spherical Fuzzy Petri Nets
		10.3.1 Definition of SLPNs
		10.3.2 Knowledge Representation
		10.3.3 Execution Rules of SLPNs
		10.3.4 Knowledge Acquisition
		10.3.5 Reasoning Algorithm of SLPNs
	10.4 Illustrative Example
		10.4.1 Implementation
		10.4.2 Comparison and Discussions
	10.5 Chapter Summary
	References
11 Grey Reasoning Petri Nets for Knowledge Representation and Acquisition
	11.1 Introduction
	11.2 Preliminaries
		11.2.1 Grey Number
		11.2.2 Grey Aggregation Operators
		11.2.3 Grey Production Rules
	11.3 The Proposed GRPN Model
		11.3.1 Definition of GRPNs
		11.3.2 Execution Rules of GRPNs
		11.3.3 Reasoning Algorithm of GRPNs
	11.4 Knowledge Parameter Determination
		11.4.1 Assess the Knowledge Parameters of GRPNs
		11.4.2 Cluster the Grey Assessments of Experts
		11.4.3 Determine the Values of Knowledge Parameters
	11.5 Illustrative Example
		11.5.1 Implementation
		11.5.2 Comparison and Discussion
	11.6 Chapter Summary
	References
Part III Improved FPNs for Knowledge Representation and Reasoning
12 Intuitionistic Fuzzy Petri Nets for Knowledge Representation and Reasoning
	12.1 Introduction
	12.2 Preliminaries
		12.2.1 The IFSs
		12.2.2 The OWA Operators
	12.3 Intuitionistic Fuzzy Petri Nets
		12.3.1 Definition of IFPNs
		12.3.2 IFPN Representations of WFPRs
		12.3.3 Execution Rules of IFPNs
		12.3.4 Reasoning Algorithm of IFPNs
	12.4 Illustrative Example
		12.4.1 Implementation
		12.4.2 Comparison and Discussions
	12.5 Chapter Summary
	References
13 Linguistic Reasoning Petri Nets for Knowledge Representation and Reasoning
	13.1 Introduction
	13.2 Linguistic 2-Tuple Representation Model
	13.3 Ordered Weighted Linguistic Reasoning Technique
	13.4 Linguistic Reasoning Petri Nets
		13.4.1 Definition of LRPNs
		13.4.2 Execution Rules of LRPNs
		13.4.3 Reasoning Algorithm Based on LRPNs
	13.5 Illustrative Example
		13.5.1 Implementation
		13.5.2 Comparative Analysis
	13.6 Chapter Summary
	References
14 Dynamic Adaptive Fuzzy Petri Nets for Knowledge Representation and Reasoning
	14.1 Introduction
	14.2 DAFPNs
		14.2.1 Definition of DAFPNs
		14.2.2 DAFPN Representations for WFPRs
		14.2.3 Execution Rules of DAFPNs
		14.2.4 Concurrent Reasoning Algorithm of DAFPNs
	14.3 Illustrative Example
	14.4 Chapter Summary
	References
15 Two-Dimensional Uncertain Linguistic Petri Net for Knowledge Representation and Reasoning
	15.1 Introduction
	15.2 Preliminaries
		15.2.1 2-Dimensional Uncertain Linguistic Variables
		15.2.2 Choquet Integral
		15.2.3 The 2-Dimensional Uncertain Linguistic Choquet Integral Operators
	15.3 The 2DULPNs
		15.3.1 Definition of 2DULPNs
		15.3.2 2DULPN Representation of LPRs
		15.3.3 Implementation Rules of 2DULPNs
		15.3.4 Reasoning Algorithm of 2DULPNs
	15.4 Illustrative Example
		15.4.1 Implementation
		15.4.2 Comparison Analysis
	15.5 Chapter Summary
	References
16 Cloud Reasoning Petri Nets for Knowledge Representation and Reasoning
	16.1 Introduction
	16.2 Basic Concepts
		16.2.1 Cloud Model Theory
		16.2.2 Conversion Between Linguistic Terms and Clouds
	16.3 The Proposed CRPN Model
		16.3.1 Definition of a CRPN Model
		16.3.2 CRPN Representations of CRPRs
		16.3.3 Implementation Rules of CRPNs
		16.3.4 Reasoning Algorithm Based on CRPNs
	16.4 Illustrative Example
		16.4.1 Implementation
		16.4.2 Comparisons and Discussions
	16.5 Chapter Summary
	References
17 Pythagorean Fuzzy Petri Nets for Knowledge Representation and Reasoning
	17.1 Introduction
	17.2 Pythagorean Fuzzy Sets
	17.3 Pythagorean Fuzzy Petri Nets
		17.3.1 Definition of PFPNs
		17.3.2 PFPN Representations of PFPRs
		17.3.3 Execution Rules of PFPNs
		17.3.4 Reasoning Algorithm of PFPNs
		17.3.5 Determining Truth Degrees of Input Places
	17.4 Illustrative Example
		17.4.1 Application of PFPNs
		17.4.2 Discussions
	17.5 Chapter Summary
	References
Part IV Applications of Improved FPNs
18 Fault Diagnosis and Cause Analysis Using Dynamic Adaptive Fuzzy Petri Nets
	18.1 Introduction
	18.2 Preliminaries
		18.2.1 Fuzzy Evidential Reasoning Approach
		18.2.2 Dynamic Adaptive Fuzzy Petri Nets
	18.3 Reversed DAFPN and FDCA Algorithms
		18.3.1 Definition of Reversed DAFPNs
		18.3.2 FDCA Algorithms
	18.4 An Illustrative Example
		18.4.1 Fault Judgment
		18.4.2 Fault Diagnosis
		18.4.3 Cause Analysis
		18.4.4 Compassions to Other FPN-Based Fault Diagnosis Models
	18.5 Chapter Summary
	References
19 Failure Mode and Effect Analysis Using Fuzzy Petri Nets
	19.1 Introduction
	19.2 Preliminaries
		19.2.1 Fuzzy Petri Nets
		19.2.2 Execution Rules of FPNs
	19.3 The Proposed FMEA Method
	19.4 An Illustrative Example
		19.4.1 Background and Problem Description
		19.4.2 Illustration of the Proposed FMEA
		19.4.3 Comparison and Discussion
	19.5 Chapter Summary
	References
20 Failure Mode and Effect Analysis Using Probabilistic Linguistic Petri Nets
	20.1 Introduction
	20.2 Preliminaries
		20.2.1 Probabilistic Linguistic Term Sets
		20.2.2 Probabilistic Linguistic Fuzzy Petri Nets
		20.2.3 PLPN Representations of WFPRS
		20.2.4 Implementation Rules of PLPNS
	20.3 The Proposed FMEA Model
	20.4 An Illustrative Example
		20.4.1 Implementation
		20.4.2 Sensitivity Analysis
		20.4.3 Comparison and Discussion
	20.5 Chapter Summary
	References
21 Failure Mode and Effect Analysis Using Interval Type-2 Fuzzy Petri Nets
	21.1 Introduction
	21.2 Preliminaries
		21.2.1 Interval Type-2 Fuzzy Sets
		21.2.2 Interval Type-2 Fuzzy Petri Nets
		21.2.3 IT2FPN Representations of WFPRs
		21.2.4 Execution Rules of IT2FPNs
	21.3 The Proposed FMEA Model
	21.4 An Illustrative Example
		21.4.1 Implementation
		21.4.2 Comparison and Discussion
	21.5 Chapter Summary
	References
Appendix