Dissertation > Excellent graduate degree dissertation topics show

Several studies on the nature of Vague Sets

Author: ZhangLei
Tutor: XinXiaoLong
School: Northwestern University
Course: Basic mathematics
Keywords: Vague sets quasi-Boolean algebra fuzzy entropy decomposition theorem representation theorem
CLC: O159
Type: Master's thesis
Year: 2010
Downloads: 90
Quote: 4
Read: Download Dissertation

Abstract


Vague sets and fuzzy sets are the main targets of fuzzy mathematics. Vague sets are further promotion and development of fuzzy sets. This paper analyzes a number of important definitions and properties of fuzzy sets, and defines some basic concepts of vague sets.Then we obtain a number of important properties and new results of vague sets. Main results are as follows:1. The algebraic properties of the vague sets are studied. We prove that the vague sets with the operations of join intersection and complement form a quasi-Boolean algebra. We obtain the decomposition theorem and the representation theorem of vague sets, by comparing the relationship of vague sets and fuzzy sets.2. The applications of the vague sets are studied. By comparing some of the existing calculating methods of the fuzzy entropy of vague sets, and pointing out that some of their deficiencies, we give a new calculating method of the fuzzy entropy of vague sets. And through some examples, we find that the new method is more reasonable.

Related Dissertations

  1. Fuzzy Multi-atrribute Decision Making Based on Vague Sets,TP18
  2. Research on Segmentation Algorithms of Regions of Interest for Pulmonary Lesions,TP391.41
  3. Vague Set Theory Research and entropy of Vague sets based on Decision,O225
  4. Vague Set Theory in association rules and cluster analysis applied research,TP18
  5. Based on information uncertainty Multiple Attribute Decision Making Method,TP18
  6. Data Reduction Algorithm Based on Information Entropy,TP18
  7. Study on Multiple Determining Weights Optimal Models Based on Entropy Theory and Cases Analysis,O236
  8. The Attribute Reduction Algorithms for Incomplete Information Systems,TP18
  9. Parameters Estimate for a Class of Linear Mixed Models,O212.1
  10. Martingale Method of Queuing Networks with Service Interruptions,O226
  11. On the Diophantine Equation x ~ 2 13 = y ~ n,O156
  12. Interval-valued Level Cut Set on the Interval-valued Fuzzy Set and Its Application,O159
  13. The Loomis-Sikorski Theorems and the Prime Boolean Filter Lattices of IMTL Algebras,O153.1
  14. The Decomposition Theorem of Complete Quasi-Convex Mapping in a Category of Reinhardt Domain,O174.5
  15. On the Diophantine Equation x~2+D=4y~7,O156.2
  16. Further Study for Vector Measures Valued in Locally Convex Space,O189.11
  17. Research on the nature of some semi- ring,O153.3
  18. Vague sets and a number of conclusions based on equal Vague Vague algebraic structure,O159
  19. Research of Logical Foundation on Negative Information and Mathematics in the Field of Information Processing,TP301
  20. K terminal reliability based on decomposition of quantitative network analysis algorithm,TP393.01
  21. L-fuzzy sets and cut set of convex fuzzy subset,O159

CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Fuzzy Mathematics
© 2012 www.DissertationTopic.Net  Mobile