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E-raamat: Type-2 Fuzzy Granular Models

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In this book, a series of granular algorithms are proposed. A nature inspired granular algorithm based on Newtonian gravitational forces is proposed. A series of methods for the formation of higher-type information granules represented by Interval Type-2 Fuzzy Sets are also shown, via multiple approaches, such as Coefficient of Variation, principle of justifiable granularity, uncertainty-based information concept, and numerical evidence based. And a fuzzy granular application comparison is given as to demonstrate the differences in how uncertainty affects the performance of fuzzy information granules.

Introduction.- Background and Theory.- Advances in Granular Computing.- Conclusions.
1 Introduction
1(4)
2 Background and Theory
5(14)
2.1 Granular Computing
5(1)
2.2 Information Granule Representations
6(1)
2.3 Principle of Justifiable Granularity
6(2)
2.4 Data Granulation Algorithms
8(2)
2.5 Fuzzy Logic
10(7)
2.5.1 Type-1 Fuzzy Sets
10(2)
2.5.2 Type-2 Fuzzy Sets
12(5)
2.6 Fuzzy Granular Computing
17(2)
References
17(2)
3 Advances in Granular Computing
19(18)
3.1 Fuzzy Granular Gravitational Clustering Algorithm
19(5)
3.2 Higher-Type Information Granule Formation
24(13)
3.2.1 A Hybrid Method for IT2 TSK Formation Based on the Principle of Justifiable Granularity and PSO for Spread Optimization
24(3)
3.2.2 Information Granule Formation via the Concept of Uncertainty-Based Information with IT2 FS Representation with TSK Consequents Optimized with Cuckoo Search
27(2)
3.2.3 Method for Measurement of Uncertainty Applied to the Formation of IT2 FS
29(2)
3.2.4 Formation of GT2 Gaussian Membership Functions Based on the Information Granule Numerical Evidence
31(3)
References
34(3)
4 Experimentation and Results Discussion
37(14)
4.1 Granulation Algorithms
39(1)
4.2 Higher-Type Information Granule Algorithms
40(4)
4.3 Application. General Type-2 Fuzzy Controller
44(7)
References
48(3)
5 Conclusions
51(2)
Appendix A 53(2)
Appendix B 55(18)
Appendix C 73(20)
Index 93